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GSM 03.48is a secure protocol used in mobile communication devices such as mobile phones to read and update theSIM. It allows the exchange securedpacketsbetween an entity in aGSMPLMNand an entity in theSIM card. Secured packets contain application messages to which certain mechanisms according toGSM03.48 have been applied. Application messages are commands or data exchanged between an application resident in or behind theGSMPLMNand on theWaporMMS.[1][2][3]It is evolved to 3GPP TS 23.048[4]in 3G. From Release 5, TS 23.048 is split into the generic part and the bearers specific application. The generic part on packet structure has been transferred to SCP (ETSI TS 102 225[5]). The bearers specific part is 3GPP TS 31.115.[6]
The sending application prepares an application message and forwards it to the sending entity, with an indication of the security to be applied to the message.
The sending entity prepends a security header (the command header) to the application message. It then applies the requested security to part of the command header and all of the application message, including any paddingoctets. The resulting structure is referred to as the (secured) command packet.
Under normal circumstances the receiving entity receives the command packet and unpacks it according to the security parameters indicated in the command header. The receiving entity subsequently forwards the application message to the receiving application indicating to the receiving application the security that was applied. The interface between the sending application and sending entity and the interface between the receiving entity and receiving application are proprietary.
If so indicated in the command header, the receiving entity shall create a (secured) response packet. The response packet consists of a security header (the response header) and optionally, application specific data supplied by the receiving application. Both the response header and the application specific data are secured using the security mechanisms indicated in the received command packet. The response packet will be returned to the sending entity, subject to constraints in thetransport layer, e.g. timing.
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https://en.wikipedia.org/wiki/GSM_03.48
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TheIntelligent Network(IN) is the standardnetwork architecturespecified in the ITU-T Q.1200 series recommendations.[1]It is intended for fixed as well asmobiletelecomnetworks. It allows operators to differentiate themselves by providingvalue-added servicesin addition to the standard telecom services such asPSTN,ISDNon fixed networks, andGSM servicesonmobile phonesor other mobile devices.
The intelligence is provided by network nodes on theservice layer, distinct from theswitchinglayer of thecore network, as opposed to solutions based on intelligence in the coreswitchesor equipment. The IN nodes are typically owned bytelecommunications service providerssuch as atelephone companyormobile phone operator.
IN is supported by theSignaling System #7 (SS7)protocol between network switching centers and other network nodes owned by network operators.
The IN concepts, architecture and protocols were originally developed as standards by theITU-Twhich is thestandardizationcommittee of theInternational Telecommunication Union; prior to this a number of telecommunications providers had proprietary implementations.[2]The primary aim of the IN was to enhance the core telephony services offered by traditional telecommunications networks, which usually amounted to making and receiving voice calls, sometimes with call divert. This core would then provide a basis upon whichoperatorscould build services in addition to those already present on a standardtelephone exchange.
A complete description of the IN emerged in a set ofITU-Tstandards namedQ.1210toQ.1219, or Capability Set One (CS-1) as they became known. The standards defined a complete architecture including the architectural view, state machines, physical implementation and protocols. They were universally embraced by telecom suppliers and operators, although many variants were derived for use in different parts of the world (seeVariantsbelow).
Following the success of CS-1, further enhancements followed in the form of CS-2. Although the standards were completed, they were not as widely implemented as CS-1, partly because of the increasing power of the variants, but also partly because they addressed issues which pushed traditional telephone exchanges to their limits.
The major driver behind the development of the IN was the need for a more flexible way of adding sophisticated services to the existing network. Before the IN was developed, all new features and/or services had to be implemented directly in the core switch systems. This made for long release cycles as the software testing had to be extensive and thorough to prevent the network from failing. With the advent of the IN, most of these services (such as toll-free numbers and geographical number portability) were moved out of the core switch systems and into self-contained nodes, creating a modular and more secure network that allowed the service providers themselves to develop variations and value-added services to their networks without submitting a request to the core switch manufacturer and waiting for the long development process. The initial use of IN technology was for number translation services, e.g. when translating toll-free numbers to regularPSTNnumbers; much more complex services have since been built on the IN, such asCustom Local Area Signaling Services(CLASS) and prepaid telephone calls.
The main concepts (functional view) surrounding IN services or architecture are connected withSS7architecture:
The core elements described above use standard protocols to communicate with each other. The use of standard protocols allows different manufacturers to concentrate on different parts of the architecture and be confident that they will all work together in any combination.
The interfaces between the SSP and the SCP areSS7based and have similarities withTCP/IPprotocols. The SS7 protocols implement much of theOSI seven-layer model. This means that the IN standards only had to define theapplication layer, which is called the Intelligent Networks Application Part orINAP. The INAP messages are encoded usingASN.1.
The interface between the SCP and the SDP is defined in the standards to be anX.500Directory Access Protocol or DAP. A more lightweight interface calledLDAPhas emerged from theIETFwhich is considerably simpler to implement, so many SCPs have implemented that instead.
The core CS-1 specifications were adopted and extended by other standards bodies. European flavours were developed byETSI, American flavours were developed byANSI, and Japanese variants also exist. The main reasons for producing variants in each region was to ensure interoperability between equipment manufactured and deployed locally (for example different versions of the underlying SS7 protocols exist between the regions).
New functionality was also added which meant that variants diverged from each other and the main ITU-T standard. The biggest variant was calledCustomised Applications for Mobile networks Enhanced Logic, or CAMEL for short. This allowed for extensions to be made for themobile phoneenvironment, and allowedmobile phone operatorsto offer the same IN services to subscribers while they areroamingas they receive in the home network.
CAMEL has become a major standard in its own right and is currently maintained by3GPP. The last major release of the standard was CAMEL phase 4. It is the only IN standard currently being actively worked on.
Bellcore (subsequentlyTelcordia Technologies) developed theAdvanced Intelligent Network(AIN) as the variant of Intelligent Network for North America, and performed the standardization of the AIN on behalf of the major US operators. The original goal of AIN was AIN 1.0, which was specified in the early 1990s (AIN Release 1, Bellcore SR-NWT-002247, 1993).[3]AIN 1.0 proved technically infeasible to implement, which led to the definition of simplified AIN 0.1 and AIN 0.2 specifications. In North America, Telcordia SR-3511 (originally known as TA-1129+)[4]and GR-1129-CORE protocols serve to link switches with the IN systems such asService Control Points(SCPs) or Service Nodes.[5]SR-3511 details a TCP/IP-based protocol which directly connects the SCP and Service Node.[4]GR-1129-CORE provides generic requirements for an ISDN-based protocol which connects the SCP to the Service Node via the SSP.[5]
While activity in development of IN standards has declined in recent years, there are many systems deployed across the world which use this technology. The architecture has proved to be not only stable, but also a continuing source of revenue with new services added all the time. Manufacturers continue to support the equipment and obsolescence is not an issue.
Nevertheless, new technologies and architectures have emerged, especially in the area ofVoIPandSIP. More attention is being paid to the use ofAPIsin preference to protocols like INAP, and new standards have emerged in the form ofJAINandParlay. From a technical viewpoint, the SCE began to move away from its proprietary graphical origins towards aJavaapplication serverenvironment.
The meaning of "intelligent network" is evolving in time, largely driven by breakthroughs in computation and algorithms. From networks enhanced by more flexible algorithms and more advanced protocols, to networks designed using data-driven models[6]to AI enabled networks.[7]
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https://en.wikipedia.org/wiki/Intelligent_Network
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Parlay Xwas a set of standardWeb serviceAPIsfor thetelephonenetwork (fixed and mobile). It is defunct and now replaced byOneAPI, which is the current valid standard from the GSM association for Telecom third party API.
It enables software developers to use the capabilities of an underlying network. The APIs are deliberately high level abstractions and designed to be simple to use. An application developer can, for example, invoke a single Web Service request to get the location of a mobile device or initiate a telephone call.
The Parlay X Web services are defined jointly byETSI, theParlay Group, and theThird Generation Partnership Project (3GPP).OMAhas done the maintenance of the specifications for3GPPrelease 8.
The APIs are defined using Web Service technology: interfaces are defined usingWSDL 1.1and conform withWeb Services Interoperability(WS-I Basic Profile).
The APIs are published as a set of specifications.
In general Parlay X provides an abstraction of functionality exposed by the more complex, but functionally richerParlayAPIs.
ETSI provide a set of (informative not normative) Parlay X to Parlay mapping documents.
Parlay X services have been rolled out by a number of telecom operators, including BT, Korea Telecom, T-Com, Mobilekom and Sprint.
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https://en.wikipedia.org/wiki/Parlay_X
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Radio resource location services (LCS) protocol(RRLP) applies toGSMandUMTSCellular Networks. It is used to exchange messages between a handset and anSMLCin order to provide geolocation information;[1]e.g., in the case of emergency calls. The protocol was developed in order to fulfil theWireless Enhanced 911requirements in the United States. However, since the protocol does not require any authentication, and can be used outside of a voice call or SMS transfer, its use is not restricted to emergency calls and can be used by law enforcement to pinpoint the exact geolocation of the target's mobile phone. RRLP was first specified in3GPPTS 04.31 - Location Services (LCS); Mobile Station (MS) - Serving Mobile Location Centre (SMLC); Radio Resource LCS Protocol (RRLP).[2]
Harald Welteproved atHAR2009[3]that many high-end smart-phones submit their GPS location to the mobile operator when requested. This happened without any sort of authentication.
RRLP supports two positioning methods:
The method type indicates whether MS based or assisted location is to be performed.
In this mode, the network typically needs to send so-called assistance data to the phone.
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https://en.wikipedia.org/wiki/RRLP
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TheUm interfaceis theair interfacefor theGSMmobile telephone standard. It is the interface between themobile station(MS) and theBase transceiver station(BTS). It is called Um because it is the mobile analog to theU interfaceofISDN. Um is defined in the GSM 04.xx and 05.xx series of specifications. Um can also supportGPRSpacket-oriented communication.
The layers of GSM are initially defined in GSM 04.01 Section 7 and roughly follow theOSI model. Um is defined in the lower three layers of the model.
The Umphysical layeris defined in the GSM 05.xx series of specifications, with the introduction and overview in GSM 05.01.
For most channels, Um L1 transmits and receives 184-bit control frames or 260-bit vocoder frames over the radio interface in 148-bit bursts with one burst per timeslot.
There are three sublayers:
Um on the physical channel has 26 TDMA frames each frame consisting of 114 info bits each. The length of 26 TDMA frame also called Multi-frame is 120 ms apart.
GSM usesGMSKor8PSKmodulation with 1 bit per symbol which produces a 13/48 MHz (270.833 kHz or 270.833 K symbols/second) symbol rate and a channel spacing of 200 kHz. Since adjacent channels overlap, the standard does not allow adjacent channels to be used in the same cell. The standard definesseveral bandsranging from 400 MHz to 1990 MHz. Uplink and downlink bands are generally separated by 45 or 50 MHz (at the low-frequency end of the GSM spectrum) and 85 or 90 MHz (at the high-frequency end of the GSM spectrum). Uplink/downlink channel pairs are identified by an index called theARFCN. Within the BTS, these ARFCNs are given arbitrary carrier indexes C0..Cn-1, with C0 designated as aBeacon Channeland always operated at constant power.
GSM has physical and logical channels. The logical channel istime-multiplexedinto 8 timeslots, with each timeslot lasting for 0.577ms and having 156.25 symbol periods. These 8 timeslots form a frame of 1,250 symbol periods. Channels are defined by the number and position of their corresponding burst period. The capacity associated with a single timeslot on a single ARFCN is called a physical channel (PCH) and referred to as "CnTm" where n is a carrier index and m is a timeslot index (0-7).
Each timeslot is occupied by a radio burst with a guard interval, two payload fields, tail bits, and a midamble (ortraining sequence). The lengths of these fields vary with the burst type but the total burst length is 156.25 symbol periods.
The most commonly used burst is the Normal Burst (NB).
The fields of the NB are:
There are several other burst formats, though. Bursts that require higher processing gain for signal acquisition have longer midambles. The random access burst (RACH) has an extended guard period to allow it to be transmitted with incomplete timing acquisition. Burst formats are described in GSM 05.02 Section 5.2.
Each physical channel is time-multiplexed into multiple logical channels according to the rules of GSM 05.02. One logical channel constitute of 8 burst periods (or physical channels) which is called aFrame. Traffic channel multiplexing follows a 26-frame (0.12 second) cycle called a "multiframe". Control channels follow a 51-frame multiframe cycle. The C0T0 physical channel carries the SCH, which encodes the timing state of the BTS to facilitate synchronization to the TDMA pattern.
GSM timing is driven by the serving BTS through the SCH and FCCH. All clocks in the handset, including the symbol clock and local oscillator, are slaved to signals received from the BTS, as described in GSM 05.10.
BTSs in the GSM network can be asynchronous and all timing requirements in the GSM standard can be derived from a stratum-3OCXO.
The coding sublayer providesforward error correction. As a general rule, each GSM channel uses ablock parity code(usually a Fire code), a rate-1/2, 4th-orderconvolutional codeand a 4-burst or 8-burstinterleaver. Notable exceptions are the synchronization channel (SCH) and random access channel (RACH) that use single-burst transmissions and thus have no interleavers. For speech channels, vocoder bits are sorted intoimportance classeswith different degrees of encoding protection applied to each class (GSM 05.03).
Both 260-bit vocoder frames and 184-bit L2 control frames are coded into 456 bit L1 frames. On channels with 4-burst interleaving (BCCH, CCCH, SDCCH, SACCH), these 456 bits are interleaved into 4 radio bursts with 114 payload bits per burst. On channels with 8-burst interleaving (TCH, FACCH), these 456 bits are interleaved over 8 radio bursts so that each radio burst carries 57 bits from the current L1 frame and 57 bits from the previous L1 frame. Interleaving algorithms for the most common traffic and control channels are described in GSM 05.03 Sections 3.1.3, 3.2.3 and 4.1.4.
The Umdata link layer,LAPDm, is defined in GSM 04.05 and 04.06. LAPDm is the mobile analog to ISDN's LAPD.
The Umnetwork layeris defined in GSM 04.07 and 04.08 and has three sublayers. A subscriber terminal must establish a connection in each sublayer before accessing the next higher sublayer.
The access order is RR, MM, CC. The release order is the reverse of that. Note that none of these sublayers terminate in the BTS itself. The standard GSM BTS operates only in layers 1 and 2.
Um logical channel types are outlined in GSM 04.03. Broadly speaking, non-GPRS Um logical channels fall into three categories: traffic channels, dedicated control channels and non-dedicated control channels.
These point-to-point channels correspond to theISDNB channeland are referred to asBm channels.
Traffic channels use 8-burst(Break) diagonal interleaving with a new block starting on every fourth burst and any given burst containing bits from two different traffic frames. This interleaving pattern makes the TCH robust against single-burst fades since the loss of a single burst destroys only 1/8 of the frame's channel bits.
The coding of a traffic channel is dependent on the traffic or vocoder type employed, with most coders capable of overcoming single-burst losses.
All traffic channels use a 26-multiframe TDMA structure.
A GSM full rate channel uses 24 frames out of a 26-multiframe. The channel bit rate of a full-rate GSM channel is 22.7 kbit/s, although the actual payload data rate is 9.6-14 kbit/s, depending on the channel coding. This channel is normally used with the GSM 06.10Full Rate, GSM 06.60Enhanced Full Rateor GSM 06.90Adaptive Multi-Ratespeech codec. It can also be used forfaxandCircuit Switched Data.
A GSM half rate channel uses 12 frames out of a 26-multiframe. The channel bit rate of a half-rate GSM channel is 11.4 kbit/s, although the actual data capacity is 4.8-7 kbit/s, depending on the channel coding. This channel is normally used with the GSM 06.20Half Rateor GSM 06.90 Adaptive Multi-Rate speech codec.
These point-to-point channels correspond to the ISDND channeland are referred to asDm channels.
The SDCCH is used for most short transactions, including initial call setup step, registration andSMStransfer. It has a payload data rate of 0.8 kbit/s. Up to eight SDCCHs can be time-multiplexed onto a single physical channel. The SDCCH uses 4-burst block interleaving in a 51-multiframe.
The FACCH is always paired with a traffic channel. The FACCH is ablank-and-burstchannel that operates by stealing bursts from its associated traffic channel. Bursts that carry FACCH data are distinguished from traffic bursts bystealing bitsat each end of the midamble. The FACCH is used for in-call signaling, including call disconnect,handoverand the later stages of call setup. It has a payload data rate of 9.2 kbit/s when paired with a full-rate channel (FACCH/F) and 4.6 kbit/s when paired with a half-rate channel (FACCH/H). The FACCH uses the same interleaving and multiframe structure as its host TCH.
Every SDCCH or FACCH also has an associated SACCH. Its normal function is to carry system information messages 5 and 6 on the downlink, carry receiver measurement reports on the uplink and to perform closed-loop power and timing control. Closed loop timing and power control are performed with a physical header at the start of each L1 frame. This 16-bit physical header carries actual power and timing advance settings in the uplink and ordered power and timing values in the downlink. The SACCH can also be used for in-call delivery of SMS. It has a payload data rate of 0.2-0.4 kbit/s, depending on the channel with which it is associated. The SACCH uses 4-burst block interleaving and the same multiframe type as its host TCH or SDCCH.
These areunicastandbroadcastchannels that do not have analogs in ISDN. These channels are used almost exclusively for radio resource management. The AGCH and RACH together form the medium access mechanism for Um.
The BCCH carries a repeating pattern of system information messages that describe the identity, configuration and available features of the BTS.
BCCH brings the measurement reports
it bring the information about LAI And CGI
BCCH frequency are fixed in BTS
The SCH transmits aBase station identity codeand the current value of the TDMA clock.
SCH repeats on every 1st, 11th, 21st, 31st and 41st frames of the 51 frame multi frame. So there are 5 SCH frames in a 51 frame multiframe.
TheFCCHgenerates a tone on the radio channel that is used by the mobile station to discipline its local oscillator. FCCH will repeat on every 0th, 10th, 20th, 30th and 40th frames of the 51 frame multiframe. So there are 5 FCCH frames in a 51 frame multiframe.
The PCH carries service notifications (pages) to specific mobiles sent by the network. A mobile station that iscampedto a BTS monitors the PCH for these notifications sent by the network.
The AGCH carries BTS responses to channel requests sent by mobile stations via the Random Access Channel.
The RACH is the uplink counterpart to the AGCH. The RACH is a shared channel on which the mobile stations transmit random access bursts to request channel assignments from the BTS.
The multiplexing rules of GSM 05.02 allow only certain combinations of logical channels to share a physical channel. The allowed combinations for single-slot systems are listed in GSM 05.02 Section 6.4.1.
Additionally, only certain of these combinations are allowed on certain timeslots or carriers and only certain sets of combinations can coexist in a given BTS. These restrictions are intended to exclude non-sensical BTS configurations and are described in GSM 05.02 Section 6.5.
The most common combinations are:
Basic speech service in GSM requires five transactions: radio channel establishment, location update, mobile-originating call establishment, mobile-terminating call establishment and call clearing. All of these transactions are described in GSM 04.08 Sections 3-7.
Unlike ISDN's U channel, Um channels are not hard-wired, so the Um interface requires a mechanism for establishing and assigning a dedicated channel prior to any other transaction.
The Um radio resource establishment procedure is defined in GSM 04.08 Section 3.3 and this is the basic medium access procedure for Um.
This procedure uses the CCCH (PCH and AGCH) as a unicast downlink and the RACH as a shared uplink.
In the simplest form, the steps of the transaction are:
Note that there is a small but non-zero probability that two MSs send identical RACH bursts at the same time in step 2. If these RACH bursts arrive at the BTS with comparable power, the resulting sum of radio signals will not be demodulable and both MSs will move to step 4. However, if there is a sufficient difference in power, the BTS will see and answer the more powerful RACH burst. Both MSs will receive and respond to the resulting channel assignment in step 3. To ensure recovery from this condition, Um uses a "contention resolution procedure" in L2, described in GSM 04.06 5.4.1.4 in which the first L3 message frame from the MS, which always contains some form of mobile ID, is echoed back to the MS for verification.
The location updating procedure is defined in GSM 04.08 Sections 4.4.1 and 7.3.1. This procedure normally is performed when the MS powers up or enters a newLocation areabut may also be performed at other times as described in the specifications.
In its minimal form, the steps of the transaction are:
There are many possible elaborations on this transaction, including:
This is the transaction for an outgoing call from the MS, defined in GSM 04.08 Sections 5.2.1 and 7.3.2 but taken largely from ISDN Q.931.
In its simplest form, the steps of the transaction are:
The TCH+FACCH assignment can occur at any time during the transaction, depending on the configuration of the network. There are three common approaches:
This is the transaction for an incoming call to the MS, defined in GSM 04.08 Sections 5.2.2 and 7.3.3, but taken largely from ISDN Q.931.
As in the MOC, the TCH+FACCH assignment can happen at any time, with the three common techniques being early, late and very early assignment.
The transaction forclearing a callis defined in GSM 04.08 Sections 5.4 and 7.3.4. This transaction is the same whether initiated by the MS or the network, the only difference being a reversal of roles. This transaction is taken from Q.931.
GSM 04.11 and 03.40 define SMS in five layers:
As a general rule, every message transferred in L(n) requires both a transfer and an acknowledgment on L(n-1). Only L1-L4 are visible on Um.
The transaction steps for MO-SMS are defined in GSM 04.11 Sections 5, 6 and Annex B. In the simplest case, error-free delivery outside of an established call, the transaction sequence is:
The transaction steps for MT-SMS are defined in GSM 04.11 Sections 5, 6 and Annex B. In the simplest case, error-free delivery outside of an established call, the transaction sequence is:
GSM 02.09 defines the following security features on Um:
Um also supports frequency hopping (GSM 05.01 Section 6), which is not specifically intended as a security feature but has the practical effect of adding significant complexity to passive interception of the Um link.
Authentication and encryption both rely on a secret key, Ki, that is unique to the subscriber. Copies of Ki are held in the SIM and in theAuthentication Center(AuC), a component of the HLR. Ki is never transmitted across Um.
An important and well-known shortcoming of GSM security is that it does not provide a means for subscribers to authenticate the network. This oversight allows forfalse basestation attacks, such as those implemented in anIMSI catcher.
The Um authentication procedure is detailed in GSM 04.08 Section 4.3.2 and GSM 03.20 Section 3.3.1 and summarized here:
Note that this transaction always occurs in the clear, since the ciphering key is not established until after the transaction is started.
GSM encryption, called "ciphering" in the specifications, is implemented on the channel bits of the radio bursts, at a very low level in L1, after forward error correction coding is applied. This is another significant security shortcoming in GSM because:
A typical GSM transaction also includesLAPDmidle frames and SACCH system information messages at predictable times, affording aKnown plaintext attack.
The GSM ciphering algorithm is called A5. There are four variants of A5 in GSM, only first three of which are widely deployed:
Ciphering is a radio resource function and managed with messages in the radio resource sublayer of L3, but ciphering is tied to authentication because the ciphering key Kc is generated in that process. Ciphering is initiated with the RR Ciphering Mode Command message, which indicates the A5 variant to be used. The MS starts ciphering and responds with the RR Ciphering Mode Complete message in ciphertext.
The network is expected to deny service to any MS that does not support either A5/1 or A5/2 (GSM 02.09 Section 3.3.3). Support of both A5/1 and A5/2 in the MS was mandatory in GSM Phase 2 (GSM 02.07Section 2) until A5/2 was depreciated by the GSMA in 2006.
The TMSI is a 32-bit temporary mobile subscriber identity that can be used to avoid sending the IMSI in the clear on Um. The TMSI is assigned by the BSC and is only meaningful within specific network. The TMSI is assigned by the network with the MM TMSI Reallocation Command, a message that is normally not sent until after ciphering is started, so as to hide the TMSI/IMSI relationship. Once the TMSI is established, it can be used to anonymize future transactions. Note that the subscriber identity must be established before authentication or encryption, so the first transaction in a new network must be initiated by transmitting the IMSI in the clear.
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https://en.wikipedia.org/wiki/Um_interface
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Network switching subsystem(NSS) (orGSM core network) is the component of aGSMsystem that carries outcall outandmobility managementfunctions formobile phonesroamingon thenetwork of base stations. It is owned and deployed bymobile phone operatorsand allows mobile devices to communicate with each other andtelephonesin the widerpublic switched telephone network(PSTN). The architecture contains specific features and functions which are needed because the phones are not fixed in one location.
The NSS originally consisted of the circuit-switchedcore network, used for traditionalGSM servicessuch as voice calls,SMS, andcircuit switched datacalls. It was extended with an overlay architecture to provide packet-switched data services known as theGPRS core network. This allows mobile phones to have access to services such asWAP,MMSand theInternet.
Themobile switching center(MSC) is the primary service delivery node for GSM/CDMA, responsible forroutingvoice calls and SMS as well as other services (such as conference calls, FAX, and circuit-switched data).
The MSC sets up and releases theend-to-end connection, handles mobility and hand-over requirements during the call and takes care of charging and real-time prepaid account monitoring.
In the GSM mobile phone system, in contrast with earlier analogue services, fax and data information is sent digitally encoded directly to the MSC. Only at the MSC is this re-coded into an "analogue" signal (although actually this will almost certainly mean sound is encoded digitally as apulse-code modulation(PCM) signal in a 64-kbit/s timeslot, known as aDS0in America).
There are various different names for MSCs in different contexts which reflects their complex role in the network, all of these terms though could refer to the same MSC, but doing different things at different times.
Thegateway MSC(G-MSC) is the MSC that determines which "visited MSC" (V-MSC) the subscriber who is being called is currently located at. It also interfaces with the PSTN. All mobile to mobile calls and PSTN to mobile calls are routed through a G-MSC. The term is only valid in the context of one call, since any MSC may provide both the gateway function and the visited MSC function. However, some manufacturers design dedicated high capacity MSCs which do not have anybase station subsystems(BSS) connected to them. These MSCs will then be the gateway MSC for many of the calls they handle.
Thevisited MSC(V-MSC) is the MSC where a customer is currently located. Thevisitor location register(VLR) associated with this MSC will have the subscriber's data in it.
Theanchor MSCis the MSC from which ahandoverhas been initiated. Thetarget MSCis the MSC toward which a handover should take place. Amobile switching center serveris a part of the redesigned MSC concept starting from3GPP Release 4.
Themobile switching center serveris a soft-switch variant (therefore it may be referred to as mobile soft switch, MSS) of the mobile switching center, which provides circuit-switched calling mobility management, and GSM services to the mobile phonesroamingwithin the area that it serves. The functionality enables split control between (signaling ) and user plane (bearer in network element called as media gateway/MG), which guarantees better placement of network elements within the network.
MSS andmedia gateway(MGW) makes it possible to cross-connect circuit-switched calls switched by using IP, ATM AAL2 as well asTDM. More information is available in 3GPP TS 23.205.
The termCircuit switching(CS) used here originates from traditional telecommunications systems. However, modern MSS and MGW devices mostly use genericInternettechnologies and formnext-generation telecommunication networks. MSS software may run on generic computers orvirtual machinesincloudenvironment.
The MSC connects to the following elements:
Tasks of the MSC include:
Thehome location register(HLR) is a central database that contains details of each mobile phone subscriber that is authorized to use the GSM core network. There can be several logical, and physical, HLRs perpublic land mobile network(PLMN), though oneinternational mobile subscriber identity(IMSI)/MSISDN pair can be associated with only one logical HLR (which can span several physical nodes) at a time.
The HLRs store details of everySIM cardissued by the mobile phone operator. Each SIM has a unique identifier called an IMSI which is theprimary keyto each HLR record.
Another important item of data associated with the SIM are the MSISDNs, which are thetelephone numbersused by mobile phones to make and receive calls. The primary MSISDN is the number used for making and receiving voice calls and SMS, but it is possible for a SIM to have other secondary MSISDNs associated with it forfaxand data calls. Each MSISDN is also aunique keyto the HLR record. The HLR data is stored for as long as a subscriber remains with the mobile phone operator.
Examples of other data stored in the HLR against an IMSI record is:
The HLR is a system which directly receives and processesMAPtransactions and messages from elements in the GSM network, for example, the location update messages received as mobile phones roam around.
The HLR connects to the following elements:
The main function of the HLR is to manage the fact that SIMs and phones move around a lot. The following procedures are implemented to deal with this:
Theauthentication center(AuC) is a function toauthenticateeachSIM cardthat attempts to connect to thegsmcore network (typically when the phone is powered on). Once the authentication is successful, the HLR is allowed to manage the SIM and services described above. Anencryption keyis also generated that is subsequently used to encrypt all wireless communications (voice, SMS, etc.) between the mobile phone and the GSM core network.
If the authentication fails, then no services are possible from that particular combination of SIM card and mobile phone operator attempted. There is an additional form of identification check performed on the serial number of the mobile phone described in the EIR section below, but this is not relevant to the AuC processing.
Proper implementation of security in and around the AuC is a key part of an operator's strategy to avoidSIM cloning.
The AuC does not engage directly in the authentication process, but instead generates data known astripletsfor the MSC to use during the procedure. The security of the process depends upon ashared secretbetween the AuC and the SIM called theKi. TheKiis securely burned into the SIM during manufacture and is also securely replicated onto the AuC. ThisKiis never transmitted between the AuC and SIM, but is combined with the IMSI to produce achallenge/responsefor identification purposes and an encryption key calledKcfor use in over the air communications.
The AuC connects to the following elements:
The AuC stores the following data for each IMSI:
When the MSC asks the AuC for a new set of triplets for a particular IMSI, the AuC first generates a random number known asRAND. ThisRANDis then combined with theKito produce two numbers as follows:
The numbers (RAND, SRES,Kc) form the triplet sent back to the MSC. When a particular IMSI requests access to the GSM core network, the MSC sends theRANDpart of the triplet to the SIM. The SIM then feeds this number and theKi(which is burned onto the SIM) into the A3 algorithm as appropriate and an SRES is calculated and sent back to the MSC. If this SRES matches with the SRES in the triplet (which it should if it is a valid SIM), then the mobile is allowed to attach and proceed with GSM services.
After successful authentication, the MSC sends the encryption keyKcto thebase station controller(BSC) so that all communications can be encrypted and decrypted. Of course, the mobile phone can generate theKcitself by feeding the same RAND supplied during authentication and theKiinto the A8 algorithm.
The AuC is usually collocated with the HLR, although this is not necessary. Whilst the procedure is secure for most everyday use, it is by no means hack proof. Therefore, a new set of security methods was designed for 3G phones.
In practice, A3 and A8 algorithms are generally implemented together (known as A3/A8, seeCOMP128). An A3/A8 algorithm is implemented in Subscriber Identity Module (SIM) cards and in GSM network Authentication Centers. It is used to authenticate the customer and generate a key for encrypting voice and data traffic, as defined in 3GPP TS 43.020 (03.20 before Rel-4). Development of A3 and A8 algorithms is considered a matter for individual GSM network operators, although example implementations are available. To encrypt Global System for Mobile Communications (GSM) cellular communications A5 algorithm is used.[1]
TheVisitor Location Register (VLR)is a database of the MSs (Mobile stations) that have roamed into the jurisdiction of the Mobile Switching Center (MSC) which it serves. Each mainbase transceiver stationin the network is served by exactly one VLR (oneBTSmay be served by many MSCs in case of MSC in pool), hence a subscriber cannot be present in more than one VLR at a time.
The data stored in the VLR has either been received from theHome Location Register (HLR), or collected from the MS. In practice, for performance reasons, most vendors integrate the VLR directly to the V-MSC and, where this is not done, the VLR is very tightly linked with the MSC via a proprietary interface. Whenever an MSC detects a new MS in its network, in addition to creating a new record in the VLR, it also updates the HLR of the mobile subscriber, apprising it of the new location of that MS. If VLR data is corrupted it can lead to serious issues with text messaging and call services.
Data stored include:
The primary functions of the VLR are:
EIRis a system that handles real-time requests to check theIMEI(checkIMEI) of mobile devices that come from the switching equipment (MSC,SGSN,MME). The answer contains the result of the check:
The switching equipment must use the EIR response to determine whether or not to allow the device to register or re-register on the network. Since the response of switching equipment to ‘greylisted’ and ‘unknown equipment’ responses is not clearly described in the standard, they are most often not used.
Most often, EIR uses the IMEI blacklist feature, which contains the IMEI of the devices that need to be banned from the network. As a rule, these are stolen or lost devices. Mobile operators rarely use EIR capabilities to block devices on their own. Usually blocking begins when there is a law in the country, which obliges all cellular operators of the country to do so. Therefore, in the delivery of the basic components of the network switching subsystem (core network) is often already present EIR with basic functionality, which includes a ‘whitelisted’ response to all CheckIMEI and the ability to fill IMEI blacklist, which will be given a ‘blacklisted’ response.
When the legislative framework for blocking registration of devices in cellular networks appears in the country, the telecommunications regulator usually has a Central EIR (CEIR) system, which is integrated with the EIR of all operators and transmits to them the actual lists of identifiers that must be used when processing CheckIMEI requests. In doing so, there may be many new requirements for EIR systems that are not present in the legacy EIR:
Other functions may be required in individual cases. For example, Kazakhstan has introduced mandatory registration of devices and their binding to subscribers. But when a subscriber appears in the network with a new device, the network operation is not blocked completely, and the subscriber is allowed to register the device. To do this, there are blocked all services, except the following: calls to a specific service number, sending SMS to a specific service number, and all Internet traffic is redirected to a specific landing page. This is achieved by the fact that EIR can send commands to several MNO systems (HLR,PCRF,SMSC, etc.).
The most common suppliers of individual EIR systems (not as part of a complex solution) are the companies BroadForward, Mahindra Comviva, Mavenir, Nokia, Eastwind.
Connected more or less directly to the GSM core network are many other functions.
Thebilling centeris responsible for processing the toll tickets generated by the VLRs and HLRs and generating a bill for each subscriber. It is also responsible for generating billing data of roaming subscriber.
Themultimedia messaging servicecentersupports the sending of multimedia messages (e.g., images,audio,videoand their combinations) to (or from) MMS-bluetooth.
Thevoicemailsystemrecords and stores voicemail.
According to U.S. law, which has also been copied into many other countries, especially in Europe, all telecommunications equipment must provide facilities for monitoring the calls of selected users. There must be some level of support for this built into any of the different elements. The concept oflawful interceptionis also known, following the relevant U.S. law, asCALEA.
Generally, lawful Interception implementation is similar to the implementation of conference call. While A and B are talking with each other, C can join the call and listen silently.
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This is alist of generations of wireless network technologiesinmobile telecommunications.
*latest and optimal iteration of technology**originally not considered 4G, only after a revision of 4G specification
0G systems did not use cellular systems. Referred to aspre-cellular(or sometimeszero generation, that is,0G mobile) systems.
1G or (1-G) refers to the first generation ofcellular networktechnology. These are theanalogtelecommunication standards that were introduced in 1979 and the early to mid-1980s and continued until being replaced by2Gdigital telecommunications. The main difference between these two mobile telephone generations is that in 1G systems the audio was encoded as analog radio signals (though call set-up and other network communications were digital), while 2G networks were entirely digital.
2G (or 2-G) provides three primary benefits over their predecessors: phone conversations are digitally encrypted; 2G systems are significantly more efficient on the spectrum allowing for far greatermobile phonepenetration levels; and 2G introduced data services for mobile, starting withSMS(Short Message Service) plain text-based messages. 2G technologies enable the various mobile phone networks to provide the services such as text messages, picture messages and MMS (Multimedia Message Service). It has 3 main services: Bearer services is one of them which is also known as data services and communication.
Second generation 2G cellular telecom networks were commercially launched on theGSMstandard inFinlandbyRadiolinja(now part ofElisa Oyj) in 1991.[3]
The North American Standards IS-54 and IS-136 were also second-generation (2G) mobile phone systems, known as (Digital AMPS) and used TDMA with three time slots in each 30 kHz channel, supporting 3 digitally compressed calls in the same spectrum as a single analog call in the previous AMPS standard. This was later changed to 6 half rate time slots for more compressed calls. It was once prevalent throughout the Americas, particularly in the United States and Canada since the first commercial network was deployed in 1993 on AT&T and Rogers Wireless Networks.
IS-95was the first ever CDMA-based digital cellular technology. It was developed byQualcommusing Code Division Multiple Access and later adopted as a standard by the Telecommunications Industry Association in TIA/EIA/IS-95 release published in 1995. It was marketed as CDMAOne and deployed globally including China Unicom in 2002 and Verizon in the United States, competing directly with GSM services offered by AT&T andT-Mobile.
2.5Gdenotes 2G-systems that have implemented a packet-switched domain in addition to the circuit-switched domain. It does not necessarily provide faster service because bundling of timeslots is used forcircuit-switcheddata services (HSCSD) as well. Also called General Packet Radio Service or GPRS
GPRS networks evolved toEDGEnetworks with the introduction of8PSKencoding.
3G technology provides an information transfer rate of at least 144kbit/s. Later 3G releases, often denoted3.5Gand3.75G, also providemobile broadbandaccess of severalMbit/stosmartphonesandmobile modemsin laptop computers. This ensures it can be applied to wireless voice telephony, mobile Internet access, fixed wireless Internet access, video calls and mobile TV technologies.
CDMA2000is a family of 3G mobile technology standards for sending voice, data, and signaling data between mobile phones and cell sites. It is a backwards-compatible successor to second-generationcdmaOne(IS-95) set of standards and used especially in North America and South Korea, China, Japan, Australia and New Zealand. It was standardized in the international 3GPP2 standards body,
The name CDMA2000 denotes a family of standards that represent the successive, evolutionary stages of the underlying technology. These are:
A new generation of cellular standards has appeared approximately every tenth year since1Gsystems were introduced in 1981/1982. Each generation is characterized by new frequency bands, higher data rates and non–backward-compatible transmission technology. The first 3G networks were introduced in 1998.
3.5G is a grouping of disparatemobiletelephony and data technologies designed to provide better performance than3Gsystems, as an interim step towards the deployment of full4Gcapability. The technology includes:
Evolved High Speed Packet Access, or HSPA+, or HSPA(Plus), or HSPAP is a technical standard for wireless broadband telecommunication. It is the second phase ofHigh Speed Packet Access(HSPA).
4G provides, in addition to the usual voice and other services of 3G, mobile broadband Internet access, for example to laptops withwireless modems, tosmartphones, and to other mobile devices. Potential and current applications include amendedmobile webaccess,IP telephony, gaming services,high-definitionmobile TV, video conferencing,3D television, andcloud computing.
LTE(Long Term Evolution) is commonly marketed as4G LTE, but it did not initially meet the technical criteria of a4Gwireless service, as specified in the3GPPRelease 8 and 9 document series forLTE Advanced. Given the competitive pressures ofWiMAXand its evolution with Advanced new releases, it has become synonymous with4G. It was first commercially deployed in Norway and Stockholm in 2009 and in the United States by Verizon in 2011 in their newly acquired 700 MHz band.
4.5G provides better performance than4Gsystems, as a process step towards deployment of full5Gcapability.[citation needed]
The technology includes:
4.5G is marketed byAT&Tas 5GE.
5G is a major phase of mobile telecommunications standards beyond the4G/IMT Advancedstandards.
NGMN Alliance or Next Generation Mobile Networks Alliance define 5G network requirements as:
Next Generation Mobile Networks Alliancefeels that 5G needs to be rolled out in 2021-2023 to meet business and consumer demands.[5]In addition to simply providing faster speeds, they predict that 5G networks will also need to meet the needs of new use-cases such as theInternet of things(IoT) as well as broadcast-like services and lifeline communications in times of disaster.
3GPP has set an early revision, non-standalone release of 5G calledNew Radio(5G NR).[6]It will be deployed in two ways, Mobile and Fixed Wireless. The specification is subdivided into two frequency bands, FR1 (<6 GHz) and FR2 (mmWave) respectively.[7]
6G has been in development since 2017, and multiple specifications are being proposed. However, none of them have achieved universal acceptance. Competitors include Xiaomi and Nokia. 6G is expected to offer faster speeds than 5G but with a shorter range. The IEEE recommends the use of frequencies ranging from 100 GHz to 3 THz, as these frequencies are relatively unused and would allow for exploration of new frequency bands.[8]The methods of deployment of cellular networks is undetermined. An option is to install a 6G tower at every building. The second option would involve integrating the functions of a 6G tower into devices like smartphones, allowing these devices to create their own cell for other users. The commercial release date is estimated to be 2028~2030.[9]
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Mobile radio telephonesystems weremobile telephonysystems that preceded moderncellular networktechnology. Since they were the predecessors of the first generation of cellular telephones, these systems are sometimes retroactively referred to aspre-cellular(or sometimeszero generation, that is,0G) systems. Technologies used in pre-cellular systems included thePush-to-talk(PTT or manual),Mobile Telephone Service(MTS),Improved Mobile Telephone Service(IMTS), andAdvanced Mobile Telephone System(AMTS) systems. These early mobile telephone systems can be distinguished from earlier closedradiotelephonesystems in that they were available as a commercial service that was part of thepublic switched telephone network, with their own telephone numbers, rather than part of a closed network such as apolice radioortaxi dispatchingsystem.
These mobile telephones were usually mounted in cars or trucks (thus calledcar phones), although portable briefcase models were also made. Typically, thetransceiver (transmitter-receiver)was mounted in the vehicle trunk and attached to the "head" (dial, display, and handset) mounted near the driver seat. They were sold through WCCs (Wireline Common Carriers, a.k.a. telephone companies), RCCs (Radio Common Carriers), andtwo-way radiodealers.
Early examples of this technology include:
Parallel toImproved Mobile Telephone Service(IMTS) in the US until the rollout of cellular AMPS systems, a competing mobile telephone technology was calledRadio Common Carrier(RCC). The service was provided from the 1960s until the 1980s when cellular AMPS systems made RCC equipment obsolete. These systems operated in a regulated environment in competition with the Bell System's MTS and IMTS. RCCs handled telephone calls and were operated by private companies and individuals. Some systems were designed to allow customers of adjacent RCCs to use their facilities, but the universe of RCCs did not comply with any single interoperable technical standard (a capability known in modern systems asroaming). For example, the phone of an Omaha, Nebraska-based RCC service would not be likely to work in Phoenix, Arizona. At the end of RCC's existence, industry associations were working on a technical standard that would potentially have allowed roaming, and some mobile users had multiple decoders to enable operation with more than one of the common signaling formats (600/1500, 2805, and Reach). Manual operation was often a fallback for RCC roamers.
Roaming was not encouraged, in part because there was no centralized industry billing database for RCCs. Signaling formats were not standardized. For example, some systems usedtwo-tone sequential pagingto alert a mobile or handheld that a wired phone was trying to call them. Other systems usedDTMF. Some used a system calledSecode 2805which transmitted an interrupted 2805 Hz tone (in a manner similar to IMTS signaling) to alert mobiles of an offered call. Some radio equipment used with RCC systems was half-duplex, push-to-talk equipment such as Motorola hand-helds or RCA 700-series conventional two-way radios. Other vehicular equipment had telephone handsets, rotary or push-button dialing, and operated full duplex like a conventional wired telephone. A few users had full-duplex briefcase telephones (which were radically advanced for their day).
RCCs used paired UHF 454/459 MHz and VHF 152/158 MHz frequencies near those used by IMTS.
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Mobile broadbandis the marketing term forwirelessInternet accessviamobile (cell) networks. Access to the network can be made through aportable modem,wireless modem, or atablet/smartphone(possiblytethered) or other mobile device. The first wireless Internet access became available in 1991 as part of the second generation (2G) of mobile phone technology. Higher speeds became available in 2001 and 2006 as part of the third (3G) and fourth (4G) generations. In 2011, 90% of the world's population lived in areas with 2G coverage, while 45% lived in areas with 2G and 3G coverage.[1]Mobile broadband uses the spectrum of 225MHzto 3700MHz.[2]
Mobile broadband is the marketing term for wireless Internet access delivered throughcellulartowers to computers and other digital devices usingportable modems. Althoughbroadbandhas a technical meaning,wireless-carriermarketing uses the phrase "mobile broadband" as a synonym for mobileInternet access. Some mobile services allow more than one device to be connected to the Internet using a single cellular connection using a process calledtethering.[3]
Thebit ratesavailable with Mobile broadband devices support voice and video as well as other data access. Devices that provide mobile broadband tomobile computersinclude:
Internet access subscriptions are usually sold separately from mobile service subscriptions.
Roughly every ten years, new mobile network technology and infrastructure involving a change in the fundamental nature of the service, non-backwards-compatible transmission technology, higher peak data rates, new frequency bands, and/or wider channel frequency bandwidth in Hertz, becomes available. These transitions are referred to as generations. The first mobile data services became available during the second generation (2G).[4][5][6]
[7]
The download (to the user) and upload (to the Internet) data rates given above are peak or maximum rates and end users will typically experience lower data rates.
WiMAXwas originally developed to deliver fixed wireless service with wireless mobility added in 2005. CDPD, CDMA2000 EV-DO, and MBWA are no longer being actively developed.
In 2011, 90% of the world's population lived in areas with 2G coverage, while 45% lived in areas with 2G and 3G coverage,[1]and 5% lived in areas with 4G coverage. By 2017 more than 90% of the world's population is expected to have 2G coverage, 85% is expected to have 3G coverage, and 50% will have 4G coverage.[9]
A barrier to mobile broadband use is the coverage provided by the mobile service networks. This may mean no mobile network or that service is limited to older and slower mobile broadband technologies. Customers will not always be able to achieve the speeds advertised due to mobile data coverage limitations including distance to the cell tower. In addition, there are issues with connectivity, network capacity, application quality, and mobile network operators' overall inexperience with data traffic.[10]Peak speeds experienced
by users are also often limited by the capabilities of their mobile phone or other mobile device.[9]
At the end of 2012 there were estimated to be 6.6 billion mobile network subscriptions worldwide (89% penetration), representing roughly 4.4 billion subscribers (many people have more than one subscription). Growth has been around 9% year-on-year.[16]Mobile phone subscriptions were expected to reach 9.3 billion in 2018.[9]
At the end of 2012 there were roughly 1.5 billion mobile broadband subscriptions, growing at a 50% year-on-year rate.[16]Mobile broadband subscriptions were expected to reach 6.5 billion in 2018.[9]
Mobile data traffic doubled between the end of 2011 (~620 Petabytes in Q4 2011) and the end of 2012 (~1280 Petabytes in Q4 2012).[16]This traffic growth is and will continue to be driven by large increases in the number of mobile subscriptions and by increases in the average data traffic per subscription due to increases in the number of smartphones being sold, the use of more demanding applications and in particular video, and the availability and deployment of newer 3G and 4G technologies capable of higher data rates. Total mobile broadband traffic was expected to increase by a factor of 12 to roughly 13,000 PetaBytes by 2018 .[9]
On average, a mobile laptop generates approximately seven times more traffic than a smartphone (3 GB vs. 450 MB/month). This ratio was forecast to fall to 5 times (10 GB vs. 2 GB/month) by 2018. Traffic from mobile devices that tether (share the data access of one device with multiple devices) can be up to 20 times higher than that from non-tethering users and averages between 7 and 14 times higher.[9]
It has also been shown that there are large differences in subscriber and traffic patterns between different provider networks, regional markets, device and user types.[9]
Demand from emerging markets has fuelled growth in both mobile device and mobile broadband subscriptions and use. Lacking widespread fixed-line infrastructure, many emerging markets use mobile broadband technologies to deliver affordable high-speed internet access to the mass market.[17]
One common use case of mobile broadband is among the construction industry.[18]
In 1995 telecommunication, mobile phone,integrated-circuit, and laptop computer manufacturers formed theGSM Associationto push for built-in support for mobile-broadband technology on notebook computers. The association established aservice markto identify devices that include Internet connectivity.[19]Established in early 1998, the globalThird Generation Partnership Project(3GPP) develops the evolving GSM family of standards, which includes GSM, EDGE, WCDMA/UMTS, HSPA, LTE and 5G NR.[20]In 2011 these standards were the most used method to deliver mobile broadband.[citation needed]With the development of the 4GLTEsignalling standard, download speeds could be increased to 300 Mbit/s per second within the next several years.[21]
The IEEE working groupIEEE 802.16, produces standards adopted in products using theWiMAXtrademark. The original "Fixed WiMAX" standard was released in 2001 and "Mobile WiMAX" was added in 2005.[22]The WiMAX Forum is a non-profit organization formed to promote the adoption of WiMAX compatible products and services.[23]
Established in late 1998, the globalThird Generation Partnership Project 2(3GPP2) develops the evolving CDMA family of standards, which includes cdmaOne, CDMA2000, and CDMA2000 EV-DO. CDMA2000 EV-DO is no longer being developed.[24]
In 2002, theInstitute of Electrical and Electronics Engineers(IEEE) established a Mobile Broadband Wireless Access (MBWA) working group.[25]They developed theIEEE 802.20standard in 2008, with amendments in 2010.[26]
Edholm's lawin 2004 noted that the bandwidths ofwirelesscellular networkshave been increasing at a faster pace compared to wiredtelecommunications networks.[27]This is due to advances inMOSFETwireless technology enabling the development and growth of digital wireless networks.[28]The wide adoption ofRF CMOS(radio frequencyCMOS),power MOSFETandLDMOS(lateral diffused MOS) devices led to the development and proliferation of digital wireless networks in the 1990s, with further advances in MOSFET technology leading to rapidly increasingnetwork bandwidthsince the 2000s.[29][30][31]
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The antennas contained inmobile phones, includingsmartphones, emit radiofrequency (RF) radiation (non-ionizing "radio waves"such asmicrowaves); the parts of the head or body nearest to the antenna can absorb this energy and convert it to heat or to synchronisedmolecular vibrations(the term 'heat', properly applies only to disordered molecular motion). Since at least the 1990s, scientists have researched whether the now-ubiquitous radiation associated with mobile phone antennas or cell phone towers is affecting human health.[1]Mobile phone networks use various bands of RF radiation, some of which overlap with the microwave range. Other digital wireless systems, such as data communication networks, produce similar radiation.
In response to public concern, theWorld Health Organization(WHO) established theInternational EMF (Electric and Magnetic Fields) Projectin 1996 to assess thescientific evidenceof possible health effects of EMF in the frequency range from 0 to 300 GHz. They have stated that although extensive research has been conducted into possible health effects of exposure to many parts of the frequency spectrum, all reviews conducted so far have indicated that, as long as exposures are below the limits recommended in theICNIRP(1998) EMF guidelines, which cover the full frequency range from 0–300 GHz, such exposures do not produce any known adverse health effect.[2]In 2024, theNational Cancer Institutewrote: "The evidence to date suggests that cell phone use does not cause brain or other kinds of cancer in humans."[1]In 2011,International Agency for Research on Cancer(IARC), an agency of the WHO, classified wireless radiation asGroup 2B– possiblycarcinogenic. That means that there "could be some risk" of carcinogenicity, so additional research into the long-term, heavy use of wireless devices needs to be conducted.[3]The WHO states that "A large number of studies have been performed over the last two decades to assess whether mobile phones pose a potential health risk. To date, no adverse health effects have been established as being caused by mobile phone use."[4]
In 2018 the US National Toxicology Program (NTP) published theresultsof its ten year, $30 million study of the effects of radio frequency radiation on laboratory rodents, which found 'clear evidence' of malignant heart tumors (schwannomas) and 'some evidence' of malignant gliomas and adrenal tumors in male rats.[5]In 2019, the NTP scientists published anarticlestating that RF scientists found evidence of 'significant' DNA damage in the frontal cortex and hippocampus of male rat brains and the blood cells of female mice. In 2018 the Ramazzini Cancer Research Institute study of cell phone radiation and cancer published itsresultsand conclusion that 'The RI findings on far field exposure to RFR are consistent with and reinforce the results of the NTP study on near field exposure, as both reported an increase in the incidence of tumors of the brain and heart in RFR-exposed Sprague-Dawley rats. These tumors are of the same histotype of those observed in some epidemiological studies on cell phone users. These experimental studies provide sufficient evidence to call for the re-evaluation of IARC conclusions regarding the carcinogenic potential of RFR in humans.'[6]
International guidelines on exposure levels to microwave frequency EMFs such as ICNIRP limit the power levels of wireless devices and it is uncommon for wireless devices to exceed the guidelines. These guidelines only take into account thermal effects and not the findings of biological effects published in the NTP and Ramazzini Institute studies. The official stance of the BritishHealth Protection Agency(HPA) is that "there is no consistent evidence to date thatWi-Fiand WLANs adversely affect the health of the general population", but also that "it is a sensible precautionary approach ... to keep the situation under ongoing review ...".[7]In a 2018 statement, theFDAsaid that "the current safety limits are set to include a 50-fold safety margin from observed effects of Radio-frequency energy exposure".[8]
A mobile phone connects to thetelephone networkbyradio wavesexchanged with a localantennaand automatedtransceivercalled acellular base station(cell siteorcell tower). The service area served by each provider is divided into small geographical areas calledcells, and all the phones in a cell communicate with that cell's antenna. Both the phone and the tower haveradio transmitterswhich communicate with each other. Since in a cellular network the same radio channels are reused every few cells, cellular networks use low power transmitters to avoid radio waves from one cell spilling over and interfering with a nearby cell using the same frequencies.
Mobile phones are limited to aneffective isotropic radiated power(EIRP) output of 3 watts, and the network continuously adjusts the phone transmitter to the lowest power consistent with good signal quality, reducing it to as low as one milliwatt when near the cell tower. Tower channel transmitters usually have an EIRP power output of around 50 watts. Even when it is not being used, unless it is turned off, a mobile phone
periodically emits radio signals on its control channel, to keep contact with its cell tower and for functions like handing off the phone to another tower if the user crosses into another cell. When the user is making a call, the phone transmits a signal on a second channel which carries the user's voice. Existing2G,3G, and4Gnetworks use frequencies in theUHFor lowmicrowavebands, 600 MHz to 3.5 GHz. Many household wireless devices such asWiFinetworks,garage door openers, andbaby monitorsuse other frequencies in this same frequency range.
Radio waves decrease rapidly in intensity by theinverse squareof distance as they spread out from a transmitting antenna. So the phone transmitter, which is held close to the user's face when talking, is a much greater source of human exposure than the tower transmitter, which is typically at least hundreds of metres away from the user. A user can reduce their exposure by using aheadsetand keeping the phone itself farther away from their body.
Next generation5Gcellular networks, which began deploying in 2019, use higher frequencies in or near themillimetre waveband, 24 to 52 GHz.[9][10]Millimetre waves are absorbed by atmospheric gases so 5G networks will use smaller cells than previous cellular networks, about the size of a city block. Instead of a cell tower, each cell will use an array of multiple small antennas mounted on existing buildings and utility poles. In general, millimetre waves penetrate less deeply into biological tissue than microwaves, and are mainly absorbed within the first centimetres of the body surface.
The HPA also says that due to the mobile phone's adaptive power ability, aDECTcordless phone's radiation could actually exceed the radiation of a mobile phone. The HPA explains that while the DECT cordless phone's radiation has an average output power of 10 mW, it is actually in the form of 100 bursts per second of 250 mW, a strength comparable to some mobile phones.[11]
Mostwireless LANequipment is designed to work within predefined standards. Wireless access points are also often close to people, but the drop off in power over distance is fast, following theinverse-square law.[12]However, wireless laptops are typically used close to people.WiFihad been anecdotally linked toelectromagnetic hypersensitivity[13]but research into electromagnetic hypersensitivity has found no systematic evidence supporting claims made by affected people.[14][15]
Users of wireless networking devices are typically exposed for much longer periods than for mobile phones and the strength of wireless devices is not significantly less. Whereas aUniversal Mobile Telecommunications System (UMTS)phone can range from 21dBm(125 mW) for Power Class 4 to 33 dBm (2W) for Power class 1, awireless routercan range from a typical 15 dBm (30 mW) strength to 27 dBm (500 mW) on the high end.
However, wireless routers are typically located significantly farther away from users' heads than a phone the user is handling, resulting in far less exposure overall. TheHealth Protection Agency(HPA) says that if a person spends one year in a location with a WiFi hot spot, they will receive the same dose of radio waves as if they had made a 20-minute call on a mobile phone.[16]
The HPA's position is that "... radio frequency (RF) exposures from WiFi are likely to be lower than those from mobile phones." It also saw "... no reason why schools and others should not use WiFi equipment."[7]In October 2007, the HPA launched a new "systematic" study into the effects of WiFi networks on behalf of the UK government, in order to calm fears that had appeared in the media in a recent period up to that time.[17]Michael Clark of the HPA says published research on mobile phones andmastsdoes not add up to an indictment of WiFi.[18][19]
Modulation of neurological function is possible using radiation in the range hundreds of GHz up to a few THz at relatively low energies (without significant heating or ionisation) achieving either beneficial or harmful effects.[20][21]The relevant frequencies for neurological interaction are at or beyond the upper end of what is typically employed for consumer wireless devices and are thus expected to have poor penetration into human tissue. Many of the studies referenced in the review[21]examined rodents rather than humans, thus overcoming the screening typically provided by the thicker skulls of larger mammals.
A 2010 review stated that "The balance of experimental evidence does not support an effect of 'non-thermal' radio frequency fields" on the permeability of theblood–brain barrier, but noted that research on low frequency effects and effects in humans was sparse.[22]A 2012 study of low-frequency radiation on humans found "no evidence for acute effects of short-term mobile phone radiation on cerebral blood flow".[1][23]
There have been rumors that mobile phone use can cause cancer, but this has not been conclusively proven.[24]In 2024, theNational Cancer Institutewrote: "The evidence to date suggests that cell phone use does not cause brain or other kinds of cancer in humans."[1][25]
In a 2018 statement, the USFood and Drug Administrationsaid that "the current safety limits are set to include a 50-fold safety margin from observed effects of radiofrequency energy exposure".[8][26]
A 2021 review found "limited" but "sufficient" evidence for radio frequencies in the range of 450 MHz to 6,000 MHz to be related togliomasandacoustic neuromasin humans, however concluding also that "... the evidence is not yet sufficiently strong to establish a direct relationship". Conclusions could not be drawn for higher frequencies due to insufficient adequate studies.[27]
Adecline in male sperm qualityhas been observed over several decades.[28][29][30]Studies on the impact of mobile radiation on male fertility are conflicting, and the effects of theradio frequencyelectromagnetic radiation(RF-EMR) emitted by these devices on the reproductive systems are currently under active debate.[31][32][33][34]A 2012 review concluded that "together, the results of these studies have shown thatRF-EMRdecreases sperm count and motility and increasesoxidative stress".[35][36]A 2017 study of 153 men that attended an academic fertility clinic in Boston, Massachusetts found that self-reported mobile phone use was not related tosemen quality, and that carrying a mobile phone in the pants pocket was not related to semen quality.[37]
A 2021 review concluded5Gradio frequencies in the range of 450 MHz to 6,000 MHz affect male fertility, possibly affect female fertility, and may have adverse effects on the development of embryos, fetuses and newborns. Conclusions could not be drawn for higher frequencies due to insufficient adequate studies. The magnitude of the effect was not quantified.[27]
Some users of mobile phones and similar devices have reported feeling variousnon-specific symptomsduring and after use. Studies have failed to link any of these symptoms to electromagnetic exposure. In addition, EHS is not a recognized medical diagnosis.[38]
According to theNational Cancer Institute, two small studies exploring whether and how mobile phone radiation affects brain glucose metabolism showed inconsistent results.[1]
A report from the Australian Government's Radiation Protection and Nuclear Safety Agency (ARPANSA) in June 2017 noted that:
The 2010 WHO Research Agenda identified a lack of sufficient evidence relating to children and this is still the case. ... Given that no long-term prospective study has looked at this issue to date this research need remains a high priority.
For cancer in particular only one completed case-control study involving four European countries has investigated mobile phone use among children or adolescents and risk of brain tumour; showing no association between the two (Aydin et al. 2011). ... Given this paucity of information regarding children using mobile phones and cancer ... more epidemiological studies are needed.[39]
Low-level EMF does have some effects on other organisms.[40]Vianet al., 2006 finds an effect ofmicrowaveongene expressioninplants.[40]
Experts consulted by France considered it was mandatory that the main antenna axis should not to be directly in front of a living place at a distance shorter than 100 metres.[41]This recommendation was modified in 2003[42]to say that antennas located within a 100-metre radius of primary schools or childcare facilities should be better integrated into the city scape and was not included in a 2005 expert report.[43]TheAgence française de sécurité sanitaire environnementale, as of 2009[update], says that there is no demonstrated short-term effect of electromagnetic fields on health, but that there are open questions for long-term effects, and that it is easy to reduce exposure via technological improvements.[44]A 2020 study inEnvironmental Researchfound that "Although direct causation of negative human health effects from RFR from cellular phone base stations has not been finalized, there is already enough medical and scientific evidence to warrant long-term liability concerns for companies deployingcellular phone towers" and thus recommended voluntary setbacks from schools and hospitals.[45]
To protect the population living around base stations and users of mobile handsets, governments and regulatory bodies adopt safety standards, which translate to limits on exposure levels below a certain value. There are many proposed national and international standards, but that of theInternational Commission on Non-Ionizing Radiation Protection(ICNIRP) is the most respected one, and has been adopted so far by more than 80 countries. For radio stations, ICNIRP proposes two safety levels: one for occupational exposure, another one for the general population. Currently there are efforts underway to harmonize the different standards in existence.[46]
Radio base licensing procedures have been established in the majority of urban spaces regulated either at municipal/county, provincial/state or national level. Mobile telephone service providers are, in many regions, required to obtain construction licenses, provide certification of antenna emission levels and assure compliance to ICNIRP standards and/or to other environmental legislation.
Many governmental bodies also require that competing telecommunication companies try to achieve sharing of towers so as to decrease environmental and cosmetic impact. This issue is an influential factor of rejection of installation of new antennas and towers in communities.
The safety standards inthe USare set by theFederal Communications Commission(FCC). The FCC has based its standards primarily on those standards established by the National Council on Radiation Protection and Measurements (NCRP) a Congressionally chartered scientific organization located in the WDC area and theInstitute of Electrical and Electronics Engineers(IEEE), specifically Subcommittee 4 of the "International Committee on Electromagnetic Safety".
Switzerland has set safety limits lower than the ICNIRP limits for certain "sensitive areas" (classrooms, for example).[47]
In March 2020, for the first time since 1998, ICNIRP updated its guidelines for exposures to frequencies over 6 GHz, including the frequencies used for 5G that are over 6 GHz. The Commission added a restriction on acceptable levels of exposure to the whole body, added a restriction on acceptable levels for brief exposures to small regions of the body, and reduced the maximum amount of exposure permitted over a small region of the body.[48]
Inthe US,personal injurylawsuitshave been filed by individuals against manufacturers (includingMotorola,[49]NEC,Siemens, andNokia) on the basis of allegations of causation ofbrain cancerand death. In US federal courts, expert testimony relating to science must be first evaluated by a judge, in aDaubert hearing, to be relevant and valid before it is admissible as evidence. In a 2002 case againstMotorola, the plaintiffs alleged that the use of wireless handheld telephones couldcause brain cancerand that the use of Motorola phones caused one plaintiff's cancer. The judge ruled that no sufficiently reliable and relevant scientific evidence in support of either general or specific causation was proffered by the plaintiffs, accepted a motion to exclude the testimony of the plaintiffs' experts, and denied a motion to exclude the testimony of the defendants' experts.[50]
Two separate cases inItaly, in 2009[51][52]and 2017,[53][54]resulted in pensions being awarded to plaintiffs who had claimed theirbenignbrain tumorswere the result of prolonged mobile phone use in professional tasks, for 5–6 hours a day, which they ruled different from non-professional use.
In the UK Legal Action Against 5G sought a Judicial Review of the government's plan to deploy 5G. If successful, the group was to be represented byMichael Mansfield QC, a prominent British barrister. This application was denied on the basis that the government had demonstrated that 5G was as safe as 4G, and that the applicants had brought their action too late.[55]
In 2000, theWorld Health Organization(WHO) recommended that theprecautionary principlecould be voluntarily adopted in this case.[56]It follows the recommendations of theEuropean Communityfor environmental risks.
According to the WHO, the "precautionary principle" is "a risk management policy applied in circumstances with a high degree of scientific uncertainty, reflecting the need to take action for a potentially serious risk without awaiting the results of scientific research." Other less stringent recommended approaches areprudent avoidance principleandas low as reasonably practicable. Although all of these are problematic in application, due to the widespread use and economic importance of wireless telecommunication systems in modern civilization, there is an increased popularity of such measures in the general public, though also evidence that such approaches may increase concern.[57]They involve recommendations such as the minimization of usage, the limitation of use by at-risk population (e.g., children), the adoption of phones and microcells with as low as reasonably practicable levels of radiation, the wider use of hands-free andearphonetechnologies such asBluetoothheadsets, the adoption of maximal standards of exposure, RF field intensity and distance of base stations antennas from human habitations, and so forth.[citation needed]Overall, public information remains a challenge as various health consequences are evoked in the literature and by the media, putting populations under chronic exposure to potentially worrying information.[58]
In May 2011, theWorld Health Organization'sInternational Agency for Research on Cancerclassified electromagnetic fields from mobile phones and other sources as "possibly carcinogenic to humans" and advised the public to adopt safety measures to reduce exposure, like use of hands-free devices or texting.[3]
Some national radiation advisory authorities, including those of Austria,[59]France,[60]Germany,[61]and Sweden,[62]have recommended measures to minimize exposure to their citizens. Examples of the recommendations are:
The use of "hands-free" was not recommended by the BritishConsumers' Associationin a statement in November 2000, as they believed that exposure was increased.[63]However, measurements for the (then)UK Department of Trade and Industry[64]and others for the FrenchAgence française de sécurité sanitaire environnementale[fr][65]showed substantial reductions. In 2005, Professor Lawrie Challis and others said clipping aferrite beadonto hands-free kits stops the radio waves travelling up the wire and into the head.[66]
Several nations have advised moderate use of mobile phones for children.[67]An article by Gandhi et al. in 2006 states that children receive higher levels ofSpecific Absorption Rate(SAR). When 5- and 10-year-olds are compared to adults, they receive about 153% higher SAR levels. Also, with thepermittivityof the brain decreasing as one gets older and the higher relative volume of the exposed growing brain in children, radiation penetrates far beyond themid-brain.[68]
The FDA is quoted as saying that it "...continues to believe that the current safety limits for cellphone radiofrequency energy exposure remain acceptable for protecting the public health."[69]
During theCOVID-19 pandemic, misinformation circulated claiming that 5G networks contribute to the spread of COVID-19.[70]
Products have been advertised that claim to shield people from EM radiation from mobile phones; in the US theFederal Trade Commissionpublished a warning that "Scam artists follow the headlines to promote products that play off the news – and prey on concerned people."[71]
According to the FTC, "there is no scientific proof that so-called shields significantly reduce exposure from electromagnetic emissions. Products that block only the earpiece – or another small portion of the phone – are totally ineffective because the entire phone emits electromagnetic waves." Such shields "may interfere with the phone's signal, cause it to draw even more power to communicate with the base station, and possibly emit more radiation."[71]The FTC has enforced false advertising claims against companies that sell such products.[72]
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1Grefers to the first generation ofmobile telecommunicationsstandards, introduced in the 1980s. This generation was characterized by the use ofanalogaudio transmissions, a major distinction from the subsequent2Gnetworks, which were fullydigital. The term "1G" itself was not used at the time, but has since been retroactively applied to describe the early era ofcellular networks.
During the 1G era, various regional standards were developed and deployed in different countries, rather than a single global system. Among the most prominent were theNordic Mobile Telephone(NMT) system and theAdvanced Mobile Phone System(AMPS), which were widely adopted in their respective regions.[1]The lack of a unified global standard resulted in a fragmented landscape, with different countries and regions utilizing different technologies for mobile communication.
As digital technology advanced, the inherent advantages of digital systems over analog led to the eventual replacement of 1G by 2G networks. While many 1G networks were phased out by the early 2000s, some continued to operate into the 2010s, particularly in less developed regions.
The antecedent to 1G technology is themobile radio telephone(i.e. "0G"), where portable phones would connect to a centralised operator. 1G refers to the very first generation of cellular networks.[2]Cellular technology employ a network of cells throughout a geographical area using low-power radio transmitters.[1]
The first commercialcellular networkwas launched in Japan byNippon Telegraph and Telephone(NTT) in 1979, initially in the metropolitan area of Tokyo. The first phone that used this network was called TZ-801 built byPanasonic.[3]Within five years, the NTT network had been expanded to cover the whole population of Japan and became the first nationwide 1G/cellular network. Before the network in Japan,Bell Laboratoriesbuilt the first cellular network aroundChicagoin 1977 and trialled it in 1978.[4]
As in the pre-cellular era, theNordic countrieswere among the pioneers in wireless technologies. These countries together designed theNMTstandard which first launched in Sweden in 1981.[5]NMT was the first mobile phone network to feature internationalroaming. In 1983, the first 1G cellular network launched in the United States, which was Chicago-basedAmeritechusing theMotorola DynaTACmobile phone.
In the early to mid 1990s, 1G was superseded by newer 2G (second generation) cellular technologies such asGSMandcdmaOne. Although 1G also used digital signaling to connect the radio towers (which listen to the handsets) to the rest of the telephone system, the voice itself during a call is encoded to digital signals in 2G whereas 1G uses analog FM modulation for the voice transmission, much like a 2-wayland mobile radio. Most 1G networks had been discontinued by the early 2000s. Some regions especially Eastern Europe continued running these networks for much longer. The last operating 1G network was closed down in Russia in 2017.
After Japan, the earliest commercial cellular networks launched in 1981 in Sweden, Norway and Saudi Arabia, followed by Denmark, Finland and Spain in 1982, the U.S. in 1983 and Hong Kong, South Korea, Austria and Canada in 1984. By 1986 networks had also launched in Tunisia, Malaysia, Oman, Ireland, Italy, Luxembourg, Netherlands, United Kingdom, West Germany, France, South Africa, Israel, Thailand, Indonesia, Iceland, Turkey, the Virgin Islands and Australia.[6]Generally, African countries were slower to take up 1G networks, while Eastern European were among the last due to the political situation.[7]
In Europe, the United Kingdom had the largest number of cellular subscribers as of 1990 numbering 1.1 million, while the second largest market was Sweden with 482 thousand.[7]Although Japan was the first country with a nationwide cellular network, the number of users was significantly lower than other developed economies with a penetration rate of only 0.15 percent in 1989.[5]As of January 1991, the highest penetration rates were in Sweden and Finland with both countries above 50 percent closely followed by Norway and Iceland. The United States had a rate of 21.2 percent. In most other European countries it was below 10 percent.[8]
Analog cellular technologies that were used were:[6]
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2Grefers to the second-generation ofcellular networktechnology, which were rolled out globally starting in the early 1990s. The main differentiator to previous mobile telephone systems, retrospectively dubbed1G, is that the radio signals of 2G networks aredigitalrather thananalog, for communication betweenmobile devicesandbase stations. In addition tovoice telephony, 2G also made possible the use ofdataservices.
The most common 2G technology has been theGSMstandard, which became the first globally adopted framework formobile communications. Other 2G technologies includecdmaOneand the now-discontinuedDigital AMPS(D-AMPS/TDMA),[1]as well thePersonal Digital Cellular(PDC) andPersonal Handy-phone System(PHS) in Japan.
The transition to digital technology enabled the implementation ofencryptionfor voice calls and data transmission, significantly improving the security of mobile communications while also increasing capacity and efficiency compared to earlier analog systems. 2G networks were primarily designed to support voice calls and Short Message Service (SMS), with later advancements such as General Packet Radio Service (GPRS) enabling always-on packet data services, includingemailand limitedinternet access. 2G was succeeded by3Gtechnology, which provided higher data transfer rates and expanded mobile internet capabilities.
In 1990,AT&T Bell LabsengineersJesse Russell, Farhad Barzegar and Can A. Eryaman filed a patent for a digital mobile phone that supports the transmission of digital data. Their patent was cited several years later byNokiaandMotorolawhen they were developing 2G digital mobile phones.[2]
2G was first commercially launched in 1991 byRadiolinja(now part ofElisa Oyj) in Finland in the form ofGSM, which was defined by theEuropean Telecommunications Standards Institute(ETSI).[3]TheTelecommunications Industry Association(TIA) defined thecdmaOne(IS-95) 2G standard, with an eight to ten fold increase in voice call capacity compared to analogAMPS.[4]The first deployment of cdmaOne was in 1995.[5]In North America,Digital AMPS(IS-54 and IS-136) andcdmaOne(IS-95) were dominant, but GSM was also used.
Later 2G releases in the GSM space, often referred to as 2.5G and 2.75G, include General Packet Radio Service (GPRS) and Enhanced Data Rates for GSM Evolution (EDGE). GPRS allows 2G networks to achieve a theoretical maximumtransfer speedof 40 kbit/s (5 kB/s). EDGE increases this capacity, providing a theoretical maximum transfer speed of 384 kbit/s (48 kB/s).
Three primary benefits of 2G networks over their 1G predecessors were:
2.5G ("second-and-a-half generation") refers to 2G systems that incorporate apacket-switcheddomain alongside the existingcircuit-switcheddomain, most commonly implemented through General Packet Radio Service (GPRS).[6]GPRS enables packet-based data transmission by dynamically allocating multiple timeslots to users, improving network efficiency. However, this does not inherently provide faster speeds, as similar techniques, such as timeslot bundling, are also employed in circuit-switched data services like High-Speed Circuit-Switched Data (HSCSD). Within GPRS-enabled 2G systems, the theoretical maximumtransfer rateis 40 kbit/s (5 kB/s).[7]
2.75G refers to the evolution of GPRS networks intoEDGE(Enhanced Data Rates for GSM Evolution) networks, achieved through the introduction of 8PSK (8 Phase Shift Keying) encoding. While the symbol rate remained constant at 270.833 samples per second, the use of 8PSK allowed each symbol to carry three bits instead of one, significantly increasing data transmission efficiency. Enhanced Data Rates for GSM Evolution (EDGE), also known as Enhanced GPRS (EGPRS) or IMT Single Carrier (IMT-SC), is a backward-compatible digital mobile phone technology built as an extension to standard GSM. First deployed in 2003 by AT&T in the United States, EDGE offers a theoretical maximum transfer speed of 384 kbit/s (48 kB/s).[7]
Evolved EDGE(also known as EDGE Evolution or 2.875G) is an enhancement of the EDGE mobile technology that was introduced as a late-stage upgrade to 2G networks. While EDGE was first deployed in the early 2000s as part of GSM networks, Evolved EDGE was launched much later, coinciding with the widespread adoption of 3G technologies such asHSPAand just before the emergence of4Gnetworks. This timing limited its practical application.
Evolved EDGE increased data throughput and reduced latencies (down to 80 ms) by utilizing improved modulation techniques, dual carrier support, dual antennas, andturbo codes. It achieved peak data rates of up to 1 Mbit/s, significantly enhancing network efficiency for operators that had not yet transitioned to 3G or 4G infrastructures. However, despite its technical improvements, Evolved EDGE was never widely deployed. By the time it became available, most network operators were focused on implementing more advanced technologies likeUMTSandLTE. As of 2016, no commercial networks were reported to support Evolved EDGE.
2G, understood asGSMandCdmaOne, has been superseded by newer technologies such as3G(UMTS/CDMA2000),4G(LTE/WiMAX) and5G(5G NR). However, 2G networks were still available as of 2023[update]in most parts of the world, while notably excluding the majority of carriers inNorth America,East Asia, andAustralasia.[8][9][10]
Many modern LTE-enabled devices have the ability to fall back to 2G for phone calls, necessary especially in rural areas where later generations have not yet been implemented.[11]In some places, its successor 3G is being shut down rather than 2G –Vodafonepreviously announced that it had switched off 3G across Europe in 2020 but still retains 2G as a fallback service.[12]In the UST-Mobileshut down their 3G services while retaining their 2G GSM network.[13][14]
Various carriers have made announcements that 2G technology in the United States, Japan, Australia, and other countries are in the process of being shut down, or have already shut down 2G services so that carriers can re-use the frequencies for newer technologies (e.g. 4G, 5G).[15][16]
As a legacy protocol, 2G connectivity is considered insecure.[17]Specifically, there exist well known methods to attack weaknesses in GSM since 2009[18]with practical use in crime.[19]Attack routes on 2G CdmaOne were found later and remain less publicized.[20]
Android12and later provide a network setting to disable 2G connectivity for the device.[21]iOS16and later can disable 2G connectivity by enablingLockdown Mode.[22]
In some parts of the world, including the United Kingdom, 2G remains widely used for olderfeature phonesand forinternet of things(IoT) devices such as smart meters,eCallsystems andvehicle trackersto avoid the high patent licensing cost of newer technologies.[23]Terminating 2G services could leave vulnerable people who rely on 2G infrastructure unable to communicate even with emergency contacts, causing harm and possibly deaths.[24]
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4Grefers to the fourth-generation ofcellular networktechnology, first introduced in the late 2000s and early 2010s. Compared to preceding third-generation (3G) technologies, 4G has been designed to supportall-IPcommunications andbroadbandservices, and eliminatescircuit switchingin voice telephony.[1]It also has considerably higher data bandwidth compared to 3G, enabling a variety of data-intensive applications[2]such ashigh-definitionmedia streamingand the expansion ofInternet of Things(IoT) applications.[1]
The earliest deployed technologies marketed as "4G" wereLong Term Evolution(LTE), developed by the3GPPgroup, andMobile Worldwide Interoperability for Microwave Access(Mobile WiMAX), based onIEEEspecifications.[3][4]These provided significant enhancements over previous 3G and2G.
In November 2008, theInternational Telecommunication Union-Radio communications sector(ITU-R) specified a set of requirements for 4G standards, named the International Mobile Telecommunications Advanced (IMT-Advanced) specification, setting peak speed requirements for 4G service at 100megabits per second(Mbit/s)(=12.5 megabytes per second) for high mobility communication (such as from trains and cars) and 1gigabit per second(Gbit/s) for low mobility communication (such as pedestrians and stationary users).[5]
Since the first-release versions ofMobile WiMAXandLTEsupport much less than 1 Gbit/s peak bit rate, they are not fully IMT-Advanced compliant, but are often branded 4G by service providers. According to operators, a generation of the network refers to the deployment of a new non-backward-compatible technology. On December 6, 2010, ITU-R recognized that these two technologies, as well as other beyond-3G technologies that do not fulfill the IMT-Advanced requirements, could nevertheless be considered "4G", provided they represent forerunners to IMT-Advanced compliant versions and "a substantial level of improvement in performance and capabilities with respect to the initial third generation systems now deployed". Both the original LTE and WiMAX standards had previously sometimes been referred to as 3.9G/3.95G.[6][7]The ITU's new definition for 4G also includedEvolved High Speed Packet Access(HSPA+).[8]
Mobile WiMAX Release 2(also known asWirelessMAN-AdvancedorIEEE 802.16m) andLTE Advanced(LTE-A) are IMT-Advanced compliant backwards compatible versions of the above two systems, standardized during the spring 2011,[citation needed]and promising speeds in the order of 1 Gbit/s. In January 2012, the ITU backtracked on its previous definition for 4G, claiming that Mobile WiMAX 2 and LTE Advanced are "true 4G" while their predecessors are "transitional" 3G-4G.[1]
As opposed to earlier generations, a 4G system does not support traditionalcircuit-switchedtelephony service, but instead relies on all-Internet Protocol(IP) based communication such asIP telephony. As seen below, thespread spectrumradio technology used in 3G systems is abandoned in all 4G candidate systems and replaced byOFDMAmulti-carriertransmission and otherfrequency-domain equalization(FDE) schemes, making it possible to transfer very high bit rates despite extensivemulti-path radio propagation(echoes). The peak bit rate is further improved bysmart antennaarrays formultiple-input multiple-output(MIMO) communications.
In the field of mobile communications, a "generation" generally refers to a change in the fundamental nature of the service, non-backwards-compatible transmission technology, higher peak bit rates, new frequency bands, wider channel frequency bandwidth in Hertz, and higher capacity for many simultaneous data transfers (highersystem spectral efficiencyinbit/second/Hertz/site).
New mobile generations have appeared about every ten years since the first move from 1981 analog (1G) to digital (2G) transmission in 1992. This was followed, in 2001, by 3G multi-media support,spread spectrumtransmission and a minimum peak bit rate of 200kbit/s, in 2011/2012 to be followed by "real" 4G, which refers to all-IPpacket-switchednetworks giving mobile ultra-broadband (gigabit speed) access.
While the ITU has adopted recommendations for technologies that would be used for future global communications, they do not actually perform the standardization or development work themselves, instead relying on the work of other standard bodies such as IEEE, WiMAX Forum, and 3GPP.
In the mid-1990s, theITU-Rstandardization organization released theIMT-2000requirements as a framework for what standards should be considered3Gsystems, requiring 2000 kbit/s peak bit rate.[9]The fastest 3G-based standard in theUMTSfamily is theHSPA+standard, which has been commercially available since 2009 and offers 21 Mbit/s downstream (11 Mbit/s upstream) withoutMIMO, i.e. with only one antenna, and in 2011 accelerated up to 42 Mbit/s peak bit rate downstream using eitherDC-HSPA+(simultaneous use of two 5 MHz UMTS carriers)[10]or
2x2 MIMO. In theory speeds up to 672 Mbit/s are possible, but have not been deployed yet. The fastest 3G-based standard in theCDMA2000family is theEV-DO Rev. B, which is available since 2010 and offers 15.67 Mbit/s downstream.
In 2008, ITU-R specified theIMT Advanced(International Mobile Telecommunications Advanced) requirements for 4G systems.
This article refers to 4G using IMT-Advanced (International Mobile Telecommunications Advanced), as defined byITU-R. An IMT-Advancedcellular systemmust fulfill the following requirements:[11]
In September 2009, the technology proposals were submitted to the International Telecommunication Union (ITU) as 4G candidates.[13]Basically all proposals are based on two technologies:
Implementations of Mobile WiMAX and first-release LTE were largely considered a stopgap solution that would offer a considerable boost until WiMAX 2 (based on the 802.16m specification) and LTE Advanced was deployed. The latter's standard versions were ratified in spring 2011.
The first set of 3GPP requirements on LTE Advanced was approved in June 2008.[14]LTE Advanced was standardized in 2010 as part of Release 10 of the 3GPP specification.
Some sources consider first-release LTE and Mobile WiMAX implementations as pre-4G or near-4G, as they do not fully comply with the planned requirements of 1Gbit/s for stationary reception and 100Mbit/s for mobile.
Confusion has been caused by some mobile carriers who have launched products advertised as 4G but which according to some sources are pre-4G versions, commonly referred to as 3.9G, which do not follow the ITU-R defined principles for 4G standards, but today can be called 4G according to ITU-R.Vodafone Netherlandsfor example, advertised LTE as 4G, while advertising LTE Advanced as their '4G+' service. A common argument for branding 3.9G systems as new-generation is that they use different frequency bands from 3G technologies; that they are based on a new radio-interface paradigm; and that the standards are not backwards compatible with 3G, whilst some of the standards are forwards compatible with IMT-2000 compliant versions of the same standards.
As of October 2010, ITU-R Working Party 5D approved two industry-developed technologies (LTE Advanced and WirelessMAN-Advanced)[15]for inclusion in the ITU's International Mobile Telecommunications Advanced program (IMT-Advancedprogram), which is focused on global communication systems that will be available several years from now.
LTE Advanced(Long Term Evolution Advanced) is a candidate forIMT-Advancedstandard, formally submitted by the3GPPorganization to ITU-T in the fall 2009, and as of 2013 has been released to the public.[16][needs update]The target of 3GPP LTE Advanced is to reach and surpass the ITU requirements.[17]LTE Advanced is essentially an enhancement to LTE. It is not a new technology, but rather an improvement on the existing LTE network. This upgrade path makes it more cost effective for vendors to offer LTE and then upgrade to LTE Advanced which is similar to the upgrade from WCDMA to HSPA. LTE and LTE Advanced will also make use of additional spectrums and multiplexing to allow it to achieve higher data speeds. Coordinated Multi-point Transmission will also allow more system capacity to help handle the enhanced data speeds.
TheIEEE 802.16morWirelessMAN-Advanced(WiMAX 2) evolution of 802.16e is under development, with the objective to fulfill the IMT-Advanced criteria of 1 Gbit/s for stationary reception and 100 Mbit/s for mobile reception.[18]
The pre-4G3GPP Long Term Evolution(LTE) technology is often branded "4G – LTE", but the first LTE release does not fully comply with the IMT-Advanced requirements. LTE has a theoreticalnet bit ratecapacity of up to 100 Mbit/s in the downlink and 50 Mbit/s in the uplink if a 20 MHz channel is used — and more ifmultiple-input multiple-output(MIMO), i.e. antenna arrays, are used.
The physical radio interface was at an early stage namedHigh SpeedOFDMPacket Access(HSOPA), now namedEvolved UMTS Terrestrial Radio Access(E-UTRA).
The firstLTEUSB dongles do not support any other radio interface.
The world's first publicly available LTE service was opened in the two Scandinavian capitals,Stockholm(EricssonandNokia Siemens Networkssystems) andOslo(aHuaweisystem) on December 14, 2009, and branded 4G. The user terminals were manufactured by Samsung.[19]As of November 2012, the five publicly available LTE services in the United States are provided byMetroPCS,[20]Verizon Wireless,[21]AT&T Mobility,U.S. Cellular,[22]Sprint,[23]andT-Mobile US.[24]
T-Mobile Hungary launched a public beta test (calledfriendly user test) on 7 October 2011, and has offered commercial 4G LTE services since 1 January 2012.[citation needed]
In South Korea, SK Telecom and LG U+ have enabled access to LTE service since 1 July 2011 for data devices, slated to go nationwide by 2012.[25]KT Telecom closed its 2G service by March 2012 and completed nationwide LTE service in the same frequency around 1.8 GHz by June 2012.
In the United Kingdom, LTE services were launched byEEin October 2012,[26]byO2andVodafonein August 2013,[27]and byThreein December 2013.[28]
TheMobile WiMAX(IEEE 802.16e-2005) mobile wireless broadband access (MWBA) standard (also known asWiBroin South Korea) is sometimes branded 4G, and offers peak data rates of 128 Mbit/s downlink and 56 Mbit/s uplink over 20 MHz wide channels.[citation needed]
In June 2006, the world's first commercial mobile WiMAX service was opened byKTinSeoul,South Korea.[30]
Sprinthas begun using Mobile WiMAX, as of 29 September 2008, branding it as a "4G" network even though the current version does not fulfill the IMT Advanced requirements on 4G systems.[31]
In Russia, Belarus and Nicaragua WiMax broadband internet access were offered by a Russian companyScartel, and was also branded 4G,Yota.[32]
In the latest version of the standard, WiMax 2.1, the standard has been updated to be not compatible with earlier WiMax standard, and is instead interchangeable with LTE-TDD system, effectively merging WiMax standard with LTE.
Just asLong-Term Evolution(LTE) and WiMAX are being vigorously promoted in the global telecommunications industry, the former (LTE) is also the most powerful 4G mobile communications leading technology and has quickly occupied the Chinese market.TD-LTE, one of the two variants of the LTE air interface technologies, is not yet mature, but many domestic and international wireless carriers are, one after the other turning to TD-LTE.
IBM's data shows that 67% of the operators are considering LTE because this is the main source of their future market. The above news also confirms IBM's statement that while only 8% of the operators are considering the use of WiMAX, WiMAX can provide the fastest network transmission to its customers on the market and could challenge LTE.
TD-LTE is not the first 4G wireless mobile broadband network data standard, but it is China's 4G standard that was amended and published by China's largest telecom operator –China Mobile. After a series of field trials, is expected to be released into the commercial phase in the next two years. Ulf Ewaldsson, Ericsson's vice president said: "the Chinese Ministry of Industry and China Mobile in the fourth quarter of this year will hold a large-scale field test, by then, Ericsson will help the hand." But viewing from the current development trend, whether this standard advocated by China Mobile will be widely recognized by the international market is still debatable.
UMB (Ultra Mobile Broadband) was the brand name for a discontinued 4G project within the3GPP2standardization group to improve theCDMA2000mobile phone standard for next generation applications and requirements. In November 2008,Qualcomm, UMB's lead sponsor, announced it was ending development of the technology, favoring LTE instead.[33]The objective was to achieve data speeds over 275 Mbit/s downstream and over 75 Mbit/s upstream.
At an early stage theFlash-OFDMsystem was expected to be further developed into a 4G standard.
TheiBurstsystem (or HC-SDMA, High Capacity Spatial Division Multiple Access) was at an early stage considered to be a 4G predecessor. It was later further developed into theMobile Broadband Wireless Access(MBWA) system, also known as IEEE 802.20.
The following key features can be observed in all suggested 4G technologies:
As opposed to earlier generations, 4G systems do not support circuit switched telephony. IEEE 802.20, UMB and OFDM standards[36]lacksoft-handoversupport, also known ascooperative relaying.
Recently, new access schemes likeOrthogonal FDMA(OFDMA),Single Carrier FDMA(SC-FDMA), Interleaved FDMA, andMulti-carrier CDMA(MC-CDMA) are gaining more importance for the next generation systems. These are based on efficientFFTalgorithms and frequency domain equalization, resulting in a lower number of multiplications per second. They also make it possible to control the bandwidth and form the spectrum in a flexible way. However, they require advanced dynamic channel allocation and adaptive traffic scheduling.
WiMaxis using OFDMA in the downlink and in the uplink. For theLTE (telecommunication), OFDMA is used for the downlink; by contrast,Single-carrier FDMAis used for the uplink since OFDMA contributes more to thePAPRrelated issues and results in nonlinear operation of amplifiers. IFDMA provides less power fluctuation and thus requires energy-inefficient linear amplifiers. Similarly, MC-CDMA is in the proposal for theIEEE 802.20standard. These access schemes offer the same efficiencies as older technologies like CDMA. Apart from this, scalability and higher data rates can be achieved.
The other important advantage of the above-mentioned access techniques is that they require less complexity for equalization at the receiver. This is an added advantage especially in theMIMOenvironments since thespatial multiplexingtransmission of MIMO systems inherently require high complexity equalization at the receiver.
In addition to improvements in these multiplexing systems, improvedmodulationtechniques are being used. Whereas earlier standards largely usedPhase-shift keying, more efficient systems such as 64QAMare being proposed for use with the3GPP Long Term Evolutionstandards.
Unlike 3G, which is based on two parallel infrastructures consisting ofcircuit switchedandpacket switchednetwork nodes, 4G is based on packet switchingonly. This requireslow-latencydata transmission.
As IPv4 addresses are (nearly)exhausted,[Note 1]IPv6is essential to support the large number of wireless-enabled devices that communicate using IP. By increasing the number ofIP addressesavailable, IPv6 removes the need fornetwork address translation(NAT), a method of sharing a limited number of addresses among a larger group of devices, which hasa number of problems and limitations. When using IPv6, some kind of NAT is still required for communication with legacy IPv4 devices that are not also IPv6-connected.
As of June 2009[update],Verizonhas posted specifications that require any 4G devices on its network to support IPv6.[37][38]
The performance of radio communications depends on an antenna system, termedsmartorintelligent antenna. Recently,multiple antenna technologiesare emerging to achieve the goal of 4G systems such as high rate, high reliability, and long range communications. In the early 1990s, to cater for the growing data rate needs of data communication, many transmission schemes were proposed. One technology,spatial multiplexing, gained importance for its bandwidth conservation and power efficiency. Spatial multiplexing involves deploying multiple antennas at the transmitter and at the receiver. Independent streams can then be transmitted simultaneously from all the antennas. This technology, calledMIMO(as a branch ofintelligent antenna), multiplies the base data rate by (the smaller of) the number of transmit antennas or the number of receive antennas. Apart from this, the reliability in transmitting high speed data in the fading channel can be improved by using more antennas at the transmitter or at the receiver. This is calledtransmitorreceive diversity. Both transmit/receive diversity and transmit spatial multiplexing are categorized into the space-time coding techniques, which does not necessarily require the channel knowledge at the transmitter. The other category is closed-loop multiple antenna technologies, which require channel knowledge at the transmitter.
One of the key technologies for 4G and beyond is called Open Wireless Architecture (OWA), supporting multiple wireless air interfaces in anopen architectureplatform.
SDRis one form of open wireless architecture (OWA). Since 4G is a collection of wireless standards, the final form of a 4G device will constitute various standards. This can be efficiently realized using SDR technology, which is categorized to the area of the radio convergence.
In 1991,WiLANfounders Hatim Zaghloul and Michel Fattouche inventedwidebandorthogonal frequency-division multiplexing(WOFDM), the basis for widebandwireless communicationapplications,[39]including 4G mobile communications.[40]
The 4G system was originally envisioned by theDARPA, the US Defense Advanced Research Projects Agency.[citation needed]DARPA selected the distributed architecture and end-to-end Internet protocol (IP), and believed at an early stage in peer-to-peer networking in which every mobile device would be both a transceiver and a router for other devices in the network, eliminating the spoke-and-hub weakness of 2G and 3G cellular systems.[41][page needed]Since the 2.5G GPRS system, cellular systems have provided dual infrastructures: packet switched nodes for data services, and circuit switched nodes for voice calls. In 4G systems, the circuit-switched infrastructure is abandoned and only apacket-switched networkis provided, while 2.5G and 3G systems require both packet-switched and circuit-switchednetwork nodes, i.e. two infrastructures in parallel. This means that in 4G traditional voice calls are replaced by IP telephony.
Since 2009, the LTE-Standard has strongly evolved over the years, resulting in many deployments by various operators across the globe. For an overview of commercial LTE networks and their respective historic development see:List of LTE networks. Among the vast range of deployments, many operators are considering the deployment and operation of LTE networks. A compilation of planned LTE deployments can be found at: List of planned LTE networks.
4G introduces a potential inconvenience for those who travel internationally or wish to switch carriers. In order to make and receive 4G voice calls (VoLTE), the subscriber handset must not only have a matchingfrequency band(and in some cases requireunlocking), it must also have the matching enablement settings for the local carrier and/or country. While a phone purchased from a given carrier can be expected to work with that carrier, making 4G voice calls on another carrier's network (including international roaming) may be impossible without a software update specific to the local carrier and the phone model in question, which may or may not be available (although fallback to 2G/3G for voice calling may still be possible if a 2G/3G network is available with a matching frequency band).[69]
A major issue in 4G systems is to make the high bit rates available in a larger portion of the cell, especially to users in an exposed position in between several base stations. In current research, this issue is addressed bymacro-diversitytechniques, also known asgroup cooperative relay, and also by Beam-Division Multiple Access (BDMA).[70]
Pervasive networksare an amorphous and at present entirely hypothetical concept where the user can be simultaneously connected to several wireless access technologies and can seamlessly move between them (Seevertical handoff,IEEE 802.21). These access technologies can beWi-Fi,UMTS,EDGE, or any other future access technology. Included in this concept is also smart-radio (also known ascognitive radio) technology to efficiently manage spectrum use and transmission power as well as the use ofmesh routingprotocols to create a pervasive network.
As of 2023, many countries and regions have started the transition from 4G to 5G, the next generation of cellular technology. 5G promises even faster speeds, lower latency, and the ability to connect a vast number of devices simultaneously.
4G networks are expected to coexist with 5G networks for several years, providing coverage in areas where 5G is not available.
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https://en.wikipedia.org/wiki/4G
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Intelecommunications,5Gis the "fifth generation" ofcellular networktechnology, as the successor to the fourth generation (4G), and has been deployed bymobile operatorsworldwide since 2019.
Compared to 4G, 5G networks offer not only higherdownload speeds, with a peak speed of 10gigabits per second(Gbit/s),[a]but also substantially lowerlatency, enabling near-instantaneous communication through cellularbase stationsand antennae.[1]There is one global unified 5G standard:5G New Radio(5G NR),[2]which has been developed by the 3rd Generation Partnership Project (3GPP) based on specifications defined by the International Telecommunication Union (ITU) under theIMT-2020requirements.[3]
The increasedbandwidthof 5G over 4G allows them to connect more devices simultaneously and improving the quality of cellulardataservices in crowded areas.[4]These features make 5G particularly suited for applications requiring real-time data exchange, such asextended reality(XR),autonomous vehicles,remote surgery, and industrial automation. Additionally, the increased bandwidth is expected to drive the adoption of 5G as a generalInternet service provider(ISP), particularly throughfixed wireless access(FWA), competing with existing technologies such ascable Internet, while also facilitating new applications in themachine-to-machinecommunication and theInternet of Things(IoT), the latter of which may include diverse applications such assmart cities, connected infrastructure, industrial IoT, and automated manufacturing processes. Unlike 4G, which was primarily designed for mobile broadband, 5G can handle millions of IoT devices with stringent performance requirements, such as real-time sensor data processing andedge computing. 5G networks also extend beyond terrestrial infrastructure, incorporating non-terrestrial networks (NTN) such as satellites and high-altitude platforms, to provide global coverage, including remote and underserved areas.
5G deployment faces challenges such as significant infrastructure investment, spectrum allocation, security risks, and concerns about energy efficiency and environmental impact associated with the use of higher frequency bands. However, it is expected to drive advancements in sectors like healthcare, transportation, and entertainment.
5G networks arecellular networks,[5]in which the service area is divided into small geographical areas calledcells. All 5G wireless devices in a cell communicate by radio waves with acellular base stationvia fixedantennas, over frequencies assigned by the base station. The base stations, termednodes, are connected to switching centers in thetelephone networkand routers forInternet accessby high-bandwidthoptical fiberor wirelessbackhaul connections. As in othercellular networks, a mobile device moving from one cell to another is automaticallyhanded offseamlessly.
The industry consortium setting standards for 5G, the3rd Generation Partnership Project(3GPP), defines "5G" as any system using5G NR(5G New Radio) software—a definition that came into general use by late 2018. 5G continues to useOFDMencoding.
Several network operators usemillimeter wavesormmWavecalledFR2in 5G terminology, for additional capacity and higher throughputs. Millimeter waves have a shorter range than the lower frequencymicrowaves, therefore the cells are of a smaller size. Millimeter waves also have more trouble passing through building walls and humans. Millimeter-wave antennas are smaller than the large antennas used in previous cellular networks. The increased data rate is achieved partly by using additional higher-frequency radio waves in addition to the low- and medium-band frequencies used in previouscellular networks. For providing a wide range of services, 5G networks can operate in three frequency bands—low, medium or high.
5G can be implemented in low-band, mid-band or high-band millimeter-wave. Low-band 5G uses a similar frequency range to 4G smartphones, 600–900MHz, which can potentially offer higher download speeds than 4G: 5–250megabits per second(Mbit/s).[6][7]Low-bandcell towershave a range and coverage area similar to 4G towers. Mid-band 5G usesmicrowavesof 1.7–4.7GHz, allowing speeds of 100–900 Mbit/s, with each cell tower providing service up to several kilometers in radius. This level of service is the most widely deployed, and was deployed in many metropolitan areas in 2020. Some regions are not implementing the low band, making Mid-band the minimum service level. High-band 5G uses frequencies of 24–47 GHz, near the bottom of the millimeter wave band, although higher frequencies may be used in the future. It often achieves download speeds in thegigabit-per-second(Gbit/s) range, comparable to co-axial cable Internet service. However,millimeter waves(mmWave or mmW) have a more limited range, requiring many small cells.[8]They can be impeded or blocked by materials in walls or windows or pedestrians.[9][10]Due to their higher cost, plans are to deploy these cells only in dense urban environments and areas where crowds of people congregate such as sports stadiums and convention centers. The above speeds are those achieved in actual tests in 2020, and speeds are expected to increase during rollout.[6]The spectrum ranging from 24.25 to 29.5 GHz has been the most licensed and deployed 5G mmWave spectrum range in the world.[11]
Rollout of 5G technology has led to debate over its security andrelationship with Chinese vendors. It has also been the subject ofhealth concernsand misinformation, includingdiscredited conspiracy theorieslinking it to theCOVID-19 pandemic.
TheITU-Rhas defined three main application areas for the enhanced capabilities of 5G. They are Enhanced Mobile Broadband (eMBB), Ultra Reliable Low Latency Communications (URLLC), and Massive Machine Type Communications (mMTC).[12]Only eMBB is deployed in 2020; URLLC and mMTC are several years away in most locations.[13]
Enhanced Mobile Broadband (eMBB) uses 5G as a progression from 4G LTEmobile broadbandservices, with faster connections, higher throughput, and more capacity. This will benefit areas of higher traffic such as stadiums, cities, and concert venues.[14]'Ultra-Reliable Low-Latency Communications' (URLLC) refers to using the network for mission-critical applications that require uninterrupted and robust data exchange. Short-packet data transmission is used to meet both reliability and latency requirements of the wireless communication networks.
Massive Machine-Type Communications (mMTC) would be used to connect to a large number ofdevices. 5G technology will connect some of the 50 billion connected IoT devices.[15]Most will use the less expensive Wi-Fi. Drones, transmitting via 4G or 5G, will aid in disaster recovery efforts, providing real-time data for emergency responders.[15]Most cars will have a 4G or 5G cellular connection for many services. Autonomous cars do not require 5G, as they have to be able to operate where they do not have a network connection.[16]However, most autonomous vehicles also feature tele-operations for mission accomplishment, and these greatly benefit from 5G technology.[17][18]
The5G Automotive Associationhas been promoting theC-V2Xcommunication technology that will first be deployed in 4G. It provides for communication between vehicles and infrastructures.[19]
A real timedigital twinof the real object such as aturbine engine, aircraft, wind turbines,offshore platformand pipelines. 5G networks helps in building it due to the latency and throughput to capture near real-time IoT data and supportdigital twins.
Mission-critical push-to-talk (MCPTT) and mission-critical video and data are expected to be furthered in 5G.[20]
Fixed wireless connections will offer an alternative to fixed-line broadband (ADSL,VDSL,fiber optic, andDOCSISconnections) in some locations. Utilizing 5G technology,fixed wireless access(FWA) can deliver high-speed internet to homes and businesses without the need for extensive physical infrastructure. This approach is particularly beneficial in rural or underserved areas where traditional broadband deployment is too expensive or logistically challenging. 5G FWA can outperform older fixed-line technologies such as ADSL and VDSL in terms of speed and latency, making it suitable for bandwidth-intensive applications like streaming, gaming, and remote work.[21][22][23]
Sony has tested the possibility of using local 5G networks to replace theSDIcables currently used in broadcast camcorders.[24]The5G Broadcasttests started around 2020 (Orkney,Bavaria,Austria,Central Bohemia) based on FeMBMS (Further evolved multimedia broadcast multicast service).[25]The aim is to serve unlimited number of mobile or fixed devices with video (TV) and audio (radio) streams without these consuming any data flow or even being authenticated in a network.
5G networks, like 4G networks, do not natively support voice calls traditionally carried overcircuit-switchedtechnology. Instead, voice communication is transmitted over theIP network, similar toIPTVservices. To address this,Voice over NR(VoNR) is implemented, allowing voice calls to be carried over the 5G network using the samepacket-switchedinfrastructure as other IP-based services, such as video streaming and messaging. Similarly to howVoice over LTE(VoLTE) enables voice calls on 4G networks, VoNR (Vo5G) serves as the 5G equivalent for voice communication, but it requires a5G standalone(SA) network to function.[26]
5G is capable of delivering significantly faster data rates than 4G (5G is approximately 10 times faster than 4G),[27][28]with peak data rates of up to 20 gigabits per second (Gbps).[29]Furthermore, average 5G download speeds have been recorded at 186.3 Mbit/s in theU.S.byT-Mobile,[30]whileSouth Korea, as of May 2022[update], leads globally with average speeds of 432 megabits per second (Mbps).[31][32]5G networks are also designed to provide significantly more capacity than 4G networks, with a projected 100-fold increase in network capacity and efficiency.[33]
The most widely used form of 5G, sub-6 GHz 5G (mid-band), is capable of delivering data rates ranging from 10 to 1,000 megabits per second (Mbps), with a much greater reach than mm Wave bands. C-Band (n77/n78) was deployed by various U.S. operators in 2022 in the sub-6 bands, although its deployment byVerizonandAT&Twas delayed until early January 2022 due to safety concerns raised by theFederal Aviation Administration. The record for 5G speed in a deployed network is 5.9 Gbit/s as of 2023, but this was tested before the network was launched.[34]Low-band frequencies (such as n5) offer a greater coverage area for a given cell, but their data rates are lower than those of mid and high bands in the range of 5–250 megabits per second (Mbps).[7]
In 5G, the ideal "air latency" is of the order of 8 to 12 milliseconds i.e., excluding delays due toHARQretransmissions, handovers, etc. Retransmission latency and backhaul latency to the server must be added to the "air latency" for correct comparisons. Verizon reported the latency on its 5G early deployment is 30 ms.[35]Edge Servers close to the towers have the possibility to reduceround-trip time(RTT) latency to 14 milliseconds and the minimumjitterto 1.84 milliseconds.[36]
Latency is much higher during handovers; ranging from 50 to 500 milliseconds depending on the type of handover[citation needed]. Reducing handover interruption time is an ongoing area of research and development; options include modifying the handover margin (offset) and the time-to-trigger (TTT).
5G uses an adaptive modulation and coding scheme (MCS) to keep the block error rate (BLER) extremely low. Whenever the error rate crosses a (very low) threshold the transmitter will switch to a lower MCS, which will be less error-prone. This way speed is sacrificed to ensure an almost zero error rate.
The range of 5G depends on many factors: transmit power, frequency, andinterference. For example, mmWave (e.g.: band n258) will have a lower range than mid-band (e.g.: band n78) which will have a lower range than low-band (e.g.: band n5)
Given the marketing hype on what 5G can offer,simulatorsanddrive testsare used by cellular service providers for the precise measurement of 5G performance.
Initially, the term was associated with theInternational Telecommunication Union'sIMT-2020standard, which required a theoretical peak download speed of 20 gigabits per second and 10 gigabits per second upload speed, along with other requirements.[29]Then, the industry standards group 3GPP chose the5G NR(New Radio) standard together with LTE as their proposal for submission to the IMT-2020 standard.[37][38]
5G NR can include lower frequencies (FR1), below 6 GHz, and higher frequencies (FR2), above 24 GHz.[39]However, the speed and latency in early FR1 deployments, using 5G NR software on 4G hardware (non-standalone), are only slightly better than new 4G systems, estimated at 15 to 50% better.[40][41]The standard documents are organized by 3rd Generation Partnership Project (3GPP),[42][43]with its system architecture defined in TS 23.501.[44]The packet protocol for mobility management (establishing connection and moving between base stations) and session management (connecting to networks and network slices) is described in TS 24.501.[45]Specifications of key data structures are found in TS 23.003.[46]DECT NR+ is a related, non-cellular standard of 5G based onDECT-2020specifications based on a mesh network.[47][48]
IEEEcovers several areas of 5G with a core focus on wireline sections between the Remote Radio Head (RRH) and Base Band Unit (BBU). The 1914.1 standards focus on network architecture and dividing the connection between the RRU and BBU into two key sections. Radio Unit (RU) to the Distributor Unit (DU) being the NGFI-I (Next Generation Fronthaul Interface) and the DU to the Central Unit (CU) being the NGFI-II interface allowing a more diverse and cost-effective network. NGFI-I and NGFI-II have defined performance values which should be compiled to ensure different traffic types defined by the ITU are capable of being carried.[page needed]The IEEE 1914.3 standard is creating a new Ethernet frame format capable of carryingIQ datain a much more efficient way depending on the functional split utilized. This is based on the3GPPdefinition of functional splits.[page needed]
5G NR(5G New Radio) is the de factoair interfacedeveloped for 5G networks.[49]It is the global standard for 3GPP 5G networks.[50]
The study of 5G NR within 3GPP started in 2015, and the first specification was made available by the end of 2017. While the 3GPP standardization process was ongoing, the industry had already begun efforts to implement infrastructure compliant with the draft standard, with the first large-scale commercial launch of 5G NR having occurred at the end of 2018. Since 2019, many operators have deployed 5G NR networks and handset manufacturers have developed 5G NR enabled handsets.[51]
5Gi is an alternative 5G variant developed in India. It was developed in a joint collaboration between IIT Madras, IIT Hyderabad, TSDSI, and the Centre of Excellence in Wireless Technology (CEWiT)[citation needed]. 5Gi is designed to improve 5G coverage in rural and remote areas over varying geographical terrains. 5Gi uses Low Mobility Large Cell (LMLC) to extend 5G connectivity and the range of a base station.[52]
In April 2022, 5Gi was merged with the global 5G NR standard in the3GPPRelease 17 specifications.[53]
In theInternet of things(IoT), 3GPP is going to submit the evolution ofNB-IoTandeMTC(LTE-M) as 5G technologies for theLPWA(Low Power Wide Area) use case.[56]
Standards are being developed by 3GPP to provide access to end devices via non-terrestrial networks (NTN), i.e. satellite or airborne telecommunication equipment to allow for better coverage outside of populated or otherwise hard to reach locations.[57][58]The enhanced communication quality relies on the unique properties ofAir to Ground channel.
Several manufacturers have announced and released hardware that integrates 5G with satellite networks:
5G-Advanced (also known as 5.5G or 5G-A) is an evolutionary upgrade to 5G technology, defined under the 3GPP Release 18 standard. It serves as a transitional phase between 5G and future6Gnetworks, focusing on performance optimization, enhanced spectral efficiency, energy efficiency, and expanded functionality. This technology supports advanced applications such asextended reality(XR), massive machine-type communication (mMTC), and ultra-low latency for critical services, such asautonomous vehicles.[66][67][68]5G-Advanced would offer a theoretical 10 Gbps downlink, 1 Gbps uplink, 100 billion device connections and lower latency.[69]
Additionally, 5G-Advanced integratesartificial intelligence(AI) andmachine learning(ML) to optimize network operations, enabling smarter resource allocation and predictive maintenance. It also enhances network slicing, allowing highly customized virtual networks for specific use cases such as industrial automation,smart cities, and critical communication systems. 5G-Advanced aims to minimize service interruption times duringhandoversto nearly zero, ensuring robust connectivity for devices in motion, such as high-speed trains and autonomous vehicles. To further support emerging IoT applications, 5G-Advanced expands the capabilities of RedCap (Reduced Capability) devices, enabling their efficient use in scenarios that require low complexity and power consumption.[70][71]Furthermore, 5G-Advanced introduces advanced time synchronization methods independent ofGNSS, providing more precise timing for critical applications. For the first time in the development of mobile network standards defined by 3GPP, it offers fully independent geolocation capabilities, allowing position determination without relying on satellite systems such as GPS.
The standard includes extended support for non-terrestrial networks (NTN), enabling communication via satellites and unmanned aerial vehicles, which facilitates connectivity in remote or hard-to-reach areas.[72]
In December 2023, Finnish operatorDNAdemonstrated 10 Gbps speeds on its network using 5G-Advanced technology.[73][74]The Release 18 specifications were finalized by mid-2024.[75][76]On February 27, 2025,Elisaannounced its deployment of the first 5G-Advanced network in Finland.[77]In March 2025,China Mobilestarted deployment of 5G-Advanced network inHangzhou.[78]
Beyond mobile operator networks, 5G is also expected to be used for private networks with applications in industrial IoT, enterprise networking, and critical communications, in what being described asNR-U(5G NR in Unlicensed Spectrum)[79]and Non-Public Networks (NPNs) operating in licensed spectrum. By the mid-to-late 2020s, standalone private 5G networks are expected to become the predominant wireless communications medium to support the ongoing Industry 4.0 revolution for the digitization and automation of manufacturing and process industries.[80]5G was expected to increase phone sales.[81]
Initial 5G NR launches depended on pairing with existing LTE (4G) infrastructure innon-standalone (NSA) mode(5G NR radio with 4G core), before maturation of thestandalone (SA) modewith the 5G core network.[82]
As of April 2019, theGlobal Mobile Suppliers Associationhad identified 224 operators in 88 countries that have demonstrated, are testing or trialing, or have been licensed to conduct field trials of 5G technologies, are deploying 5G networks or have announced service launches.[83]The equivalent numbers in November 2018 were 192 operators in 81 countries.[84]The first country to adopt 5G on a large scale was South Korea, in April 2019. Swedish telecoms giant Ericsson predicted that 5G Internet will cover up to 65% of the world's population by the end of 2025.[85]Also, it plans to invest 1 billion reals ($238.30 million) in Brazil to add a new assembly line dedicated to fifth-generation technology (5G) for its Latin American operations.[86]
When South Korea launched its 5G network, all carriers used Samsung, Ericsson, and Nokiabase stationsand equipment, except forLG U Plus, who also used Huawei equipment.[87][88]Samsung was the largest supplier for 5G base stations in South Korea at launch, having shipped 53,000 base stations at the time, out of 86,000 base stations installed across the country at the time.[89]
The first fairly substantial deployments were in April 2019. In South Korea,SK Telecomclaimed 38,000 base stations,KT Corporation30,000 andLG U Plus18,000; of which 85% are in six major cities.[90]They are using 3.5 GHz (sub-6) spectrum innon-standalone (NSA) modeand tested speeds were from 193 to 430Mbit/sdown.[91]260,000 signed up in the first month and 4.7 million by the end of 2019.[92]T-Mobile USwas the first company in the world to launch a commercially available 5G NR Standalone network.[93]
Nine companies sell 5G radio hardware and 5G systems for carriers:Altiostar,Cisco Systems,Datang Telecom/Fiberhome,Ericsson,Huawei,Nokia,Qualcomm,Samsung, andZTE.[94][95][96][97][98][99][100]As of 2023, Huawei is the leading 5G equipment manufacturer and has the greatest market share of 5G equipment and has built approximately 70% of worldwide 5G base stations.[101]: 182
Large quantities of newradio spectrum(5G NR frequency bands) have been allocated to 5G.[102]For example, in July 2016, the U.S.Federal Communications Commission(FCC) freed up vast amounts of bandwidth in underused high-band spectrum for 5G. The Spectrum Frontiers Proposal (SFP) doubled the amount of millimeter-wave unlicensed spectrum to 14 GHz and created four times the amount of flexible, mobile-use spectrum the FCC had licensed to date.[103]In March 2018,European Unionlawmakers agreed to open up the 3.6 and 26 GHz bands by 2020.[104]
As of March 2019[update], there are reportedly 52 countries, territories, special administrative regions, disputed territories and dependencies that are formally considering introducing certain spectrum bands for terrestrial 5G services, are holding consultations regarding suitable spectrum allocations for 5G, have reserved spectrum for 5G, have announced plans toauction frequenciesor have already allocated spectrum for 5G use.[105]
In March 2019, theGlobal Mobile Suppliers Associationreleased the industry's first database tracking worldwide 5G device launches.[106]In it, the GSA identified 23 vendors who have confirmed the availability of forthcoming 5G devices with 33 different devices including regional variants. There were seven announced 5G device form factors: (telephones (×12 devices), hotspots (×4), indoor and outdoorcustomer-premises equipment(×8), modules (×5), Snap-on dongles and adapters (×2), and USB terminals (×1)).[107]By October 2019, the number of announced 5G devices had risen to 129, across 15 form factors, from 56 vendors.[108]
In the 5G IoT chipset arena, as of April 2019 there were four commercial 5G modem chipsets (Intel, MediaTek, Qualcomm, Samsung) and one commercial processor/platform, with more launches expected in the near future.[109]
On March 4, 2019, the first-ever all-5G smartphoneSamsung Galaxy S10 5Gwas released. According toBusiness Insider, the 5G feature was showcased as more expensive in comparison with the 4GSamsung Galaxy S10e.[110]On March 19, 2020,HMD Global, the current maker of Nokia-branded phones, announced theNokia 8.3 5G, which it claimed as having a wider range of 5G compatibility than any other phone released to that time. The mid-range model is claimed to support all 5G bands from 600 MHz to 3.8 GHz.[111]Google Pixelsmartphones support 5G starting with the4a 5GandPixel 5,[112]whileApplesmartphones support 5G starting with theiPhone 12.[113][114]
The air interface defined by 3GPP for 5G is known as 5G New Radio (5G NR), and the specification is subdivided into two frequency bands, FR1 (below 6 GHz) and FR2 (24–54 GHz).
Otherwise known as sub-6, the maximum channel bandwidth defined for FR1 is 100 MHz, due to the scarcity of continuous spectrum in this crowded frequency range. The band most widely being used for 5G in this range is 3.3–4.2 GHz. The Korean carriers use the n78 band at 3.5 GHz.
Some parties used the term "mid-band" frequency to refer to higher part of this frequency range that was not used in previous generations of mobile communication.
The minimum channel bandwidth defined for FR2 is 50 MHz and the maximum is 400 MHz, with two-channel aggregation supported in 3GPP Release 15. Signals in this frequency range with wavelengths between 4 and 12 mm are called millimeter waves. The higher the carrier frequency, the greater the ability to support high data-transfer speeds. This is because a given channel bandwidth takes up a lower fraction of the carrier frequency, so high-bandwidth channels are easier to realize at higher carrier frequencies.
5G in the 24 GHz range or above use higher frequencies than 4G, and as a result, some 5G signals are not capable of traveling large distances (over a few hundred meters), unlike 4G or lower frequency 5G signals (sub 6 GHz). This requires placing 5G base stations every few hundred meters in order to use higher frequency bands. Also, these higher frequency 5G signals cannot penetrate solid objects easily, such as cars, trees, walls, and even humans, because of the nature of these higher frequency electromagnetic waves. 5G cells can be deliberately designed to be as inconspicuous as possible, which finds applications in places like restaurants and shopping malls.[115]
MIMO (multiple-input and multiple-output) systems use multiple antennas at the transmitter and receiver ends of a wireless communication system. Multiple antennas use the spatial dimension for multiplexing in addition to the time and frequency ones, without changing the bandwidth requirements of the system. Spatial multiplexing gains allow for an increase in the number of transmission layers, thereby boosting system capacity.
Massive MIMOantennasincreases sector throughput and capacity density using large numbers of antennas. This includes Single User MIMO andMulti-user MIMO(MU-MIMO). Theantenna arraycan schedule users separately to satisfy their needs andbeamformtowards the intended users, minimizing interference.[116]
Edge computingis delivered by computing servers closer to the ultimate user. It reduces latency, data traffic congestion[117][118]and can improve service availability.[119]
Small cells are low-powered cellular radio access nodes that operate in licensed and unlicensed spectrum that have a range of 10 meters to a few kilometers. Small cells are critical to 5G networks, as 5G's radio waves can't travel long distances, because of 5G's higher frequencies.[120][121][122][123]
There are two kinds of beamforming (BF): digital and analog. Digital beamforming involves sending the data across multiple streams (layers), while analog beamforming shaping the radio waves to point in a specific direction. The analog BF technique combines the power from elements of the antenna array in such a way that signals at particular angles experience constructive interference, while other signals pointing to other angles experience destructive interference. This improves signal quality in the specific direction, as well as data transfer speeds. 5G uses both digital and analog beamforming to improve the system capacity.[124][125]
One expected benefit of the transition to 5G is the convergence of multiple networking functions to achieve cost, power, and complexity reductions. LTE has targeted convergence withWi-Fiband/technology via various efforts, such asLicense Assisted Access(LAA; 5G signal in unlicensed frequency bands that are also used by Wi-Fi) andLTE-WLAN Aggregation(LWA; convergence with Wi-Fi Radio), but the differing capabilities of cellular and Wi-Fi have limited the scope of convergence. However, significant improvement in cellular performance specifications in 5G, combined with migration from DistributedRadio Access Network(D-RAN) to Cloud- or Centralized-RAN (C-RAN) and rollout of cellularsmall cellscan potentially narrow the gap between Wi-Fi and cellular networks in dense and indoor deployments. Radio convergence could result in sharing ranging from the aggregation of cellular and Wi-Fi channels to the use of a single silicon device for multiple radio access technologies.[126]
NOMA (non-orthogonal multiple access) is a proposed multiple-access technique for future cellular systems via allocation of power.[127]
Initially, cellular mobile communications technologies were designed in the context of providing voice services and Internet access. Today a new era of innovative tools and technologies is inclined towards developing a new pool of applications. This pool of applications consists of different domains such as the Internet of Things (IoT), web of connected autonomous vehicles, remotely controlled robots, and heterogeneous sensors connected to serve versatile applications.[128]In this context,network slicinghas emerged as a key technology to efficiently embrace this new market model.[129]
The 5G Service-Based architecture replaces the referenced-based architecture of theEvolved Packet Corethat is used in 4G. The SBA breaks up the core functionality of the network into interconnected network functions (NFs), which are typically implemented asCloud-Native Network Functions. These NFs register with the Network Repository Function (NRF) which maintains their state, and communicate with each other using the Service Communication Proxy (SCP). The interfaces between the elements all utilizeRESTfulAPIs.[130]By breaking functionality down this way, mobile operators are able to utilize different infrastructure vendors for different functions, and the flexibility to scale each function independently as needed.[130]
In addition, the standard describes network entities for roaming and inter-network connectivity, including the Security Edge Protection Proxy (SEPP), the Non-3GPP InterWorking Function (N3IWF), the Trusted Non-3GPP Gateway Function (TNGF), the Wireline Access Gateway Function (W-AGF), and the Trusted WLAN Interworking Function (TWIF). These can be deployed by operators as needed depending on their deployment.
Thechannel codingtechniques for 5G NR have changed fromTurbo codesin 4G topolar codesfor the control channels andLDPC(low-density parity check codes) for the data channels.[132][133]
In December 2018,3GPPbegan working onunlicensed spectrumspecifications known as 5G NR-U, targeting 3GPP Release 16.[134]Qualcomm has made a similar proposal forLTE in unlicensed spectrum.
5G wireless power is a technology based on 5G standards thattransfers wireless power.[135][136]It adheres totechnical standardsset by the3rd Generation Partnership Project, theInternational Telecommunication Union, and theInstitute of Electrical and Electronics Engineers. It utilizesextremely high frequencyradio waves withwavelengthsfrom one to ten millimeters, also known asmmWaves.[137][138]Up to 6μW of power has been demonstrated being captured from 5G signals at a distance of 180m by researchers atGeorgia Tech.[135]
Internet of thingsdevices could benefit from 5G wireless power technology, given their low power requirements that are within the range of what has been achieved using 5G power capture.[139]
A report published by theEuropean CommissionandEuropean Agency for Cybersecuritydetails the security issues surrounding 5G. The report warns against using a single supplier for a carrier's 5G infrastructure, especially those based outside the European Union;NokiaandEricssonare the only European manufacturers of 5G equipment.[140]
On October 18, 2018, a team of researchers fromETH Zurich, theUniversity of Lorraineand theUniversity of Dundeereleased a paper entitled, "A Formal Analysis of 5G Authentication".[141][142]It alerted that 5G technology could open ground for a new era of security threats. The paper described the technology as "immature and insufficiently tested," and one that "enables the movement and access of vastly higher quantities of data, and thus broadens attack surfaces". Simultaneously, network security companies such asFortinet,[143]Arbor Networks,[144]A10 Networks,[145]and Voxility[146]advised on personalized and mixed security deployments against massiveDDoS attacksforeseen after 5G deployment.
IoT Analytics estimated an increase in the number ofIoTdevices, enabled by 5G technology, from 7 billion in 2018 to 21.5 billion by 2025.[147]This can raise the attack surface for these devices to a substantial scale, and the capacity for DDoS attacks,cryptojacking, and othercyberattackscould boost proportionally.[142]In addition, the EPS solution for 5G networks has identified a design vulnerability. The vulnerability affects the operation of the device during cellular network switching.[148]
Due to fears of potential espionage of users of Chinese equipment vendors, several countries (including the United States, Australia and the United Kingdom as of early 2019)[149]have taken actions to restrict or eliminate the use of Chinese equipment in their respective 5G networks. A 2012 U.S. House Permanent Select Committee on Intelligence report concluded that using equipment made by Huawei and ZTE, another Chinese telecommunications company, could "undermine core U.S. national security interests".[150]In 2018, six U.S. intelligence chiefs, including the directors of the CIA and FBI, cautioned Americans against using Huawei products, warning that the company could conduct "undetected espionage".[151]Further, a 2017 investigation by the FBI determined that Chinese-made Huawei equipment could disrupt U.S. nuclear arsenal communications.[152]Chinese vendors and the Chinese government have denied claims of espionage, but experts have pointed out that Huawei would have no choice but to hand over network data to the Chinese government if Beijing asked for it because of Chinese National Security Law.[153]
In August 2020, the U.S. State Department launched "The Clean Network" as a U.S. government-led, bi-partisan effort to address what it described as "the long-term threat to data privacy, security, human rights and principled collaboration posed to the free world from authoritarian malign actors". Promoters of the initiative have stated that it has resulted in an "alliance of democracies and companies", "based on democratic values". On October 7, 2020, theUK Parliament's Defence Committeereleased a report claiming that there was clear evidence of collusion between Huawei and Chinese state and theChinese Communist Party. The UK Parliament's Defence Committee said that the government should consider removal of all Huawei equipment from its 5G networks earlier than planned.[154]In December 2020, the United States announced that more than 60 nations, representing more than two thirds of the world's gross domestic product, and 200 telecom companies, had publicly committed to the principles of The Clean Network. This alliance of democracies included 27 of the 30NATOmembers; 26 of the 27EUmembers, 31 of the 37OECDnations, 11 of the 12Three Seasnations as well as Japan, Israel, Australia, Singapore, Taiwan, Canada, Vietnam, and India.
Thespectrumused by various 5G proposals, especially the n258 band centered at 26 GHz, will be near that of passiveremote sensingsuch as byweatherandEarth observation satellites, particularly forwater vapormonitoring at 23.8 GHz.[155]Interferenceis expected to occur due to such proximity and its effect could be significant without effective controls. An increase in interference already occurred with some other prior proximatebandusages.[156][157]Interference to satellite operations impairsnumerical weather predictionperformance with substantially deleterious economic and public safety impacts in areas such ascommercial aviation.[158][159]
The concerns promptedU.S. Secretary of CommerceWilbur Rossand NASA AdministratorJim Bridenstinein February 2019 to urge the FCC to delay some spectrum auction proposals, which was rejected.[160]The chairs of theHouse Appropriations CommitteeandHouse Science Committeewrote separate letters to FCC chairmanAjit Paiasking for further review and consultation withNOAA,NASA, andDoD, and warning of harmful impacts to national security.[161]Acting NOAA director Neil Jacobs testified before the House Committee in May 2019 that 5G out-of-band emissions could produce a 30% reduction inweather forecastaccuracy and that the resulting degradation inECMWF modelperformance would have resulted in failure to predict the track and thus the impact ofSuperstorm Sandyin 2012. TheUnited States Navyin March 2019 wrote a memorandum warning of deterioration and made technical suggestions to control band bleed-over limits, for testing and fielding, and for coordination of the wireless industry and regulators with weather forecasting organizations.[162]
At the 2019 quadrennialWorld Radiocommunication Conference(WRC), atmospheric scientists advocated for a strong buffer of −55dBW, European regulators agreed on a recommendation of −42 dBW, and US regulators (the FCC) recommended a restriction of −20 dBW, which would permit signals 150 times stronger than the European proposal. The ITU decided on an intermediate −33 dBW until September 1, 2027, and after that a standard of −39 dBW.[163]This is closer to the European recommendation but even the delayed higher standard is much weaker than that requested by atmospheric scientists, triggering warnings from theWorld Meteorological Organization(WMO) that the ITU standard, at 10 times less stringent than its recommendation, brings the "potential to significantly degrade the accuracy of data collected".[164]A representative of theAmerican Meteorological Society(AMS) also warned of interference,[165]and theEuropean Centre for Medium-Range Weather Forecasts(ECMWF), sternly warned, saying that society risks "history repeat[ing] itself" by ignoring atmospheric scientists' warnings (referencingglobal warming, monitoring of which could be imperiled).[166]In December 2019, a bipartisan request was sent from the US House Science Committee to theGovernment Accountability Office(GAO) to investigate why there is such a discrepancy between recommendations of US civilian and military science agencies and the regulator, the FCC.[167]
The United StatesFAAhas warned thatradar altimeterson aircraft, which operate between 4.2 and 4.4 GHz, might be affected by 5G operations between 3.7 and 3.98 GHz. This is particularly an issue with older altimeters usingRF filters[168]which lack protection from neighboring bands.[169]This is not as much of an issue in Europe, where 5G uses lower frequencies between 3.4 and 3.8 GHz.[170]Nonetheless, theDGACin France has also expressed similar worries and recommended 5G phones be turned off or be put inairplane modeduring flights.[171]
On December 31, 2021, U.S. Transportation SecretaryPete Buttigiegand Steve Dickinson, administrator of theFederal Aviation Administrationasked the chief executives of AT&T and Verizon to delay 5G implementation over aviation concerns. The government officials asked for a two-week delay starting on January 5, 2022, while investigations are conducted on the effects on radar altimeters. The government transportation officials also asked the cellular providers to hold off their new 5G service near 50 priority airports, to minimize disruption to air traffic that would be caused by some planes being disallowed from landing in poor visibility.[172]After coming to an agreement with government officials the day before,[173]Verizon and AT&T activated their 5G networks on January 19, 2022, except for certain towers near 50 airports.[174]AT&T scaled back its deployment even further than its agreement with the FAA required.[175]
The FAA rushed to test and certify radar altimeters for interference so that planes could be allowed to perform instrument landings (e.g. at night and in low visibility) at affected airports. By January 16, it had certified equipment on 45% of the U.S. fleet, and 78% by January 20.[176]Airlines complained about the avoidable impact on their operations, and commentators said the affair called into question the competence of the FAA.[177]Several international airlines substituted different planes so they could avoid problems landing at scheduled airports, and about 2% of flights (320) were cancelled by the evening of January 19.[178]
A number of 5G networks deployed on the radio frequency band of 3.3–3.6 GHz are expected to cause interference withC-Bandsatellite stations, which operate by receiving satellite signals at 3.4–4.2 GHz frequency.[179]This interference can be mitigated withlow-noise block downconvertersandwaveguide filters.[179]
In regions like the US and EU, the 6 GHz band is to be opened up for unlicensed applications, which would permit the deployment of 5G-NR Unlicensed, 5G version ofLTE in unlicensed spectrum, as well asWi-Fi 6e. However, interference could occur with the co-existence of different standards in the frequency band.[180]
There have been concerns surrounding the promotion of 5G, questioning whether the technology is overhyped. There are questions on whether 5G will truly change the customer experience,[181]ability for 5G's mmWave signal to provide significant coverage,[182][183]overstating what 5G can achieve or misattributing continuous technological improvement to "5G",[184]lack of new use case for carriers to profit from,[185]wrong focus on emphasizing direct benefits on individual consumers instead of for Internet of Things devices or solving thelast mile problem,[186]and overshadowing the possibility that in some aspects there might be other more appropriate technologies.[187]Such sort of concerns have also led to consumers not trusting information provided by cellular providers on the topic.[188]
There is a long history of fear and anxiety surrounding wireless signals that predates 5G technology. The fears about 5G are similar to those that have persisted throughout the 1990s and 2000s. According to theUSCenters for Disease Control and Prevention(CDC) "exposure to intense, direct amounts of non-ionizing radiation may result in damage to tissue due toheat. This is not common and mainly of concern in the workplace for those who work on large sources of non-ionizing radiation devices and instruments."[189]Some advocates of fringe health claim the regulatory standards are too low and influenced by lobbying groups.[190]
There have been rumors that 5G mobile phone use can cause cancer, but this is a myth.[191]Many popular books of dubious merit have been published on the subject[additional citation(s) needed]including one byJoseph Mercolaalleging that wireless technologies caused numerous conditions fromADHDto heart diseases and brain cancer. Mercola has drawn sharp criticism for hisanti-vaccinationismduring theCOVID-19 pandemicand was warned by theFood and Drug Administrationto stop selling fake COVID-19 cures through his onlinealternative medicinebusiness.[190][192]
According toThe New York Times, one origin of the 5G health controversy was an erroneous unpublished study that physicist Bill P. Curry did for the Broward County School Board in 2000 which indicated that the absorption of external microwaves by brain tissue increased with frequency.[193]According to experts[vague]this was wrong, the millimeter waves used in 5G are safer than lower frequency microwaves because they cannot penetrate the skin and reach internal organs. Curry had confusedin vitroandin vivoresearch. However Curry's study was widely distributed on the Internet. Writing inThe New York Timesin 2019,William Broadreported thatRT Americabegan airing programming linking 5G to harmful health effects which "lack scientific support", such as "brain cancer, infertility, autism, heart tumors, and Alzheimer's disease". Broad asserted that the claims had increased. RT America had run seven programs on this theme by mid-April 2019 but only one in the whole of 2018. The network's coverage had spread to hundreds of blogs and websites.[194]
In April 2019, the city ofBrusselsinBelgiumblocked a 5G trial because of radiation rules.[195]InGeneva,Switzerland, a planned upgrade to 5G was stopped for the same reason.[196]The Swiss Telecommunications Association (ASUT) has said that studies have been unable to show that 5G frequencies have any health impact.[197]
According toCNET,[198]"Members of Parliament in theNetherlandsare also calling on the government to take a closer look at 5G. Several leaders in theUnited States Congresshave written to theFederal Communications Commissionexpressing concern about potential health risks. InMill Valley, California, the city council blocked the deployment of new 5G wireless cells."[198][199][200][201][202]Similar concerns were raised inVermont[203]andNew Hampshire.[198]The USFDAis quoted saying that it "continues to believe that the current safety limits for cellphone radiofrequency energy exposure remain acceptable for protecting the public health".[204]After campaigning by activist groups, a series of small localities in the UK, including Totnes, Brighton and Hove, Glastonbury, and Frome, passed resolutions against the implementation of further 5G infrastructure, though these resolutions have no impact on rollout plans.[205][206][207]
Low-level EMF does have some effects on other organisms.[208]Vianet al., 2006 finds an effect ofmicrowaveongene expressioninplants.[208]A meta-analysis of 95in vitroandin vivostudies showed that an average of 80% of thein vivoresearch showed effects of such radiation, as did 58% of thein vitroresearch, but that the results were inconclusive as to whether any of these effects pose a health risk.[209]
As the introduction of 5G technology coincided with the time of theCOVID-19 pandemic, several conspiracy theories circulating online posited a link betweenCOVID-19and 5G.[210]This has led to dozens ofarsonattacks being made on telecom masts in the Netherlands (Amsterdam, Rotterdam, etc.), Ireland (Cork,[211]etc.), Cyprus, the United Kingdom (Dagenham,Huddersfield,Birmingham,BelfastandLiverpool),[212][213]Belgium (Pelt), Italy (Maddaloni), Croatia (Bibinje)[214]and Sweden.[215]It led to at least 61 suspected arson attacks against telephone masts in the United Kingdom alone[216]and over twenty in The Netherlands.
In the early months of the pandemic, anti-lockdown protesters atprotests over responses to the COVID-19 pandemicin Australia were seen with anti-5G signs, an early sign of what became a wider campaign by conspiracy theorists to link the pandemic with 5G technology. There are two versions of the 5G-COVID-19 conspiracy theory:[190]
In various parts of the world, carriers have launched numerous differently branded technologies, such as "5G Evolution", which advertise improving existing networks with the use of "5G technology".[217]However, these pre-5G networks are an improvement on specifications of existing LTE networks that are not exclusive to 5G. While the technology promises to deliver higher speeds, and is described by AT&T as a "foundation for our evolution to 5G while the 5G standards are being finalized", it cannot be considered to be true 5G. When AT&T announced 5G Evolution, 4x4 MIMO, the technology that AT&T is using to deliver the higher speeds, had already been put in place byT-Mobilewithout being branded with the 5G moniker. It is claimed that such branding is a marketing move that will cause confusion with consumers, as it is not made clear that such improvements are not true 5G.[218]
With the rollout of 5G, 4G has become more available and affordable, with the world's most developed countries having >90% LTE coverage.[219]Because of this, 4G is still not obsolete even today.[220]4G plans are sold alongside 5G plans on US carriers,[221]with 4G being cheaper than 5G.[222]
In April 2008, NASA partnered with Geoff Brown andMachine-to-Machine Intelligence (M2Mi) Corpto develop a fifth generation communications technology approach, though largely concerned with working with nanosats.[223]That same year, the South Korean IT R&D program of "5G mobile communication systems based on beam-division multiple access and relays with group cooperation" was formed.[224]
In August 2012, New York University founded NYU Wireless, a multi-disciplinary academic research centre that has conducted pioneering work in 5G wireless communications.[225]On October 8, 2012, the UK'sUniversity of Surreysecured £35M for a new 5G research centre, jointly funded by the British government's UK Research Partnership Investment Fund (UKRPIF) and a consortium of key international mobile operators and infrastructure providers, includingHuawei,Samsung,TelefónicaEurope,FujitsuLaboratories Europe,Rohde & Schwarz, andAircom International. It will offer testing facilities to mobile operators keen to develop a mobile standard that uses less energy and less radio spectrum, while delivering speeds higher than current 4G with aspirations for the new technology to be ready within a decade.[226][227][228][229]On November 1, 2012, the EU project "Mobile and wireless communications Enablers for the Twenty-twenty Information Society" (METIS) started its activity toward the definition of 5G. METIS achieved an early global consensus on these systems. In this sense, METIS played an important role in building consensus among other external major stakeholders prior to global standardization activities. This was done by initiating and addressing work in relevant global fora (e.g. ITU-R), as well as in national and regional regulatory bodies.[230]That same month, the iJOIN EU project was launched, focusing on "small cell" technology, which is of key importance for taking advantage of limited and strategic resources, such as theradio wavespectrum. According toGünther Oettinger, the European Commissioner for Digital Economy and Society (2014–2019), "an innovative utilization of spectrum" is one of the key factors at the heart of 5G success. Oettinger further described it as "the essential resource for the wireless connectivity of which 5G will be the main driver".[231]iJOIN was selected by the European Commission as one of the pioneering 5G research projects to showcase early results on this technology at theMobile World Congress2015 (Barcelona, Spain).
In February 2013, ITU-R Working Party 5D (WP 5D) started two study items: (1) Study on IMT Vision for 2020 and beyond, and; (2) Study on future technology trends for terrestrial IMT systems. Both aiming at having a better understanding of future technical aspects of mobile communications toward the definition of the next generation mobile.[232]On May 12, 2013, Samsung Electronics stated that they had developed a "5G" system. The core technology has a maximum speed of tens of Gbit/s (gigabits per second). In testing, the transfer speeds for the "5G" network sent data at 1.056 Gbit/s to a distance of up to 2 kilometers with the use of an 8*8 MIMO.[233][234]In July 2013,IndiaandIsraelagreed to work jointly on development of fifth generation (5G) telecom technologies.[235]On October 1, 2013, NTT (Nippon Telegraph and Telephone), the same company to launch world's first 5G network in Japan, wins Minister of Internal Affairs and Communications Award atCEATECfor 5G R&D efforts.[236]On November 6, 2013,Huaweiannounced plans to invest a minimum of $600 million into R&D for next generation 5G networks capable of speeds 100 times higher than modern LTE networks.[237]
On April 3, 2019,South Koreabecame the first country to adopt 5G.[238]Just hours later, Verizon launched its 5G services in the United States, and disputed South Korea's claim of becoming the world's first country with a 5G network, because allegedly, South Korea's 5G service was launched initially for just six South Korean celebrities so that South Korea could claim the title of having the world's first 5G network.[239]In fact, the three main South Korean telecommunication companies (SK Telecom,KT, andLG Uplus) added more than 40,000 users to their 5G network on the launch day.[240]In June 2019, the Philippines became the first country in Southeast Asia to roll out a 5Gbroadbandnetwork after Globe Telecom commercially launched its 5G data plans to customers.[241]AT&T brings 5G service to consumers and businesses in December 2019 ahead of plans to offer 5G throughout the United States in the first half of 2020.[242][243][244]
In 2020,AISandTrueMove Hlaunched 5G services inThailand, making it the first country inSoutheast Asiato have commercial 5G.[245][246]A functional mockup of a Russian 5G base station, developed by domestic specialists as part of Rostec's digital division Rostec.digital, was presented in Nizhny Novgorod at the annual conference "Digital Industry of Industrial Russia".[247][248]5G speeds have declined in many countries since 2022, which has driven the development of 5.5G to increase connection speeds.[249]
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Intelecommunications,6Gis the designation for a futuretechnical standardof asixth-generationtechnology forwireless communications.
It is the planned successor to5G(ITU-RIMT-2020), and is currently in the early stages of the standardization process, tracked by theITU-Ras IMT-2030[1]with the framework and overall objectives defined in recommendation ITU-R M.2160-0.[2][3]Similar to previous generations of thecellulararchitecture, standardization bodies such as3GPPandETSI, as well as industry groups such as theNext Generation Mobile Networks(NGMN) Alliance, are expected to play a key role in its development.[4][5][6]
Numerous companies (Airtel,Anritsu,Apple,Ericsson, Fly,Huawei,Jio,Keysight,LG,Nokia,NTT Docomo,Samsung,Vi,Xiaomi), research institutes (Technology Innovation Institute, theInteruniversity Microelectronics Centre) and countries (United States, United Kingdom,European Unionmember states, Russia, China, India, Japan, South Korea, Singapore, Saudi Arabia, United Arab Emirates, Qatar, and Israel) have shown interest in 6G networks, and are expected to contribute to this effort.[7][8][9][10][11][12][13][14]
6G networks will likely be faster than previous generations,[15]thanks to further improvements in radio interface modulation and coding techniques,[2]as well as physical-layer technologies.[16]Proposals include a ubiquitous connectivity model which could include non-cellular access such as satellite and WiFi, precise location services, and a framework for distributed edge computing supporting more sensor networks, AR/VR and AI workloads.[5]Other goals include network simplification and increased interoperability, lower latency, and energy efficiency.[2][17]It should enable network operators to adopt flexible decentralizedbusiness modelsfor 6G, with localspectrum licensing, spectrum sharing, infrastructure sharing, and intelligent automated management. Some have proposed that machine-learning/AI systems can be leveraged to support these functions.[18][19][20][17][21]
The NGMN alliance have cautioned that "6G must not inherently trigger a hardware refresh of 5G RAN infrastructure", and that it must "address demonstrable customer needs".[17]This reflects industry sentiment about the cost of the 5G rollout, and concern that certain applications and revenue streams have not lived up to expectations.[22][23][24]6G is expected to begin rolling out in the early 2030s, but given such concerns it is not yet clear which features and improvements will be implemented first.[25][26][27]
6G networks are expected to be developed and released by the early 2030s.[28][29]The largest number of 6G patents have been filed inChina.[30]
Recent academic publications have been conceptualizing 6G and new features that may be included. Artificial intelligence (AI) is included in many predictions, from 6G supporting AI infrastructure to "AI designing and optimizing 6G architectures, protocols, and operations."[31]Another study inNature Electronicslooks to provide a framework for 6G research stating "We suggest that human-centric mobile communications will still be the most important application of 6G and the 6G network should be human-centric. Thus, high security, secrecy and privacy should be key features of 6G and should be given particular attention by the wireless research community."[32]
The frequency bands for 6G are undetermined. Initially, Terahertz was considered an important band for 6G, as indicated by theInstitute of Electrical and Electronics Engineerswhich stated that "Frequencies from 100 GHz to 3 THz are promising bands for the next generation of wireless communication systems because of the wide swaths of unused and unexploredspectrum."[33]
One of the challenges in supporting the required high transmission speeds will be the limitation of energy consumption and associated thermal protection in the electronic circuits.[34]
As of now, mid bands are being considered by WRC for 6G/IMT-2030.
In June 2021, according to Samsung white paper, using Sub-THz 6G spectrum, their indoor data rate was successful for 6 Gbps at 15 meters distance. The following year, in 2022, 12G at 30 meters distance, and 2.3G at 120 meters distance in 2022.[35]
In September 2023, LG successfully tested 6G transmission and reception at 500 meters distance outdoor.[36][37]
Millimeter waves(30 to 300 GHz) andterahertz radiation(300 to 3,000 GHz) might, according to some speculations, be used in 6G. However, the wave propagation of these frequencies is much more sensitive to obstacles than themicrowavefrequencies (about 2 to 30 GHz) used in5GandWi-Fi, which are more sensitive than theradio wavesused in1G,2G,3Gand4G. Therefore, there are concerns those frequencies may not be commercially viable, especially considering that 5G mmWave deployments are very limited due to deployment costs.
In October 2020, theAlliance for Telecommunications Industry Solutions(ATIS) launched a "Next G Alliance", an alliance consisting ofAT&T,Ericsson,Telus,Verizon,T-Mobile,Microsoft,Samsung, and others that "will advance North American mobile technology leadership in 6G and beyond over the next decade."[38]
In January 2022, Purple Mountain Laboratories of China claimed that its research team had achieved a world record of 206.25 gigabits per second (Gbit/s) data rate for the first time in a lab environment within the terahertz frequency band, which is supposed to be the base of 6G cellular technology.[39]
In February 2022, Chinese researchers stated that they had achieved a record data streaming speed usingvortex millimetre waves, a form of extremely high-frequency radio wave with rapidly changing spins, the researchers transmitted 1 terabyte of data over a distance of 1 km (3,300 feet) in a second. The spinning potential of radio waves was first reported by British physicistJohn Henry Poyntingin 1909, but making use of it proved to be difficult. Zhang and colleagues said their breakthrough was built on the hard work of many research teams across the globe over the past few decades. Researchers in Europe conducted the earliest communication experiments using vortex waves in the 1990s. A major challenge is that the size of the spinning waves increases with distance, and the weakening signal makes high-speed data transmission difficult. The Chinese team built a unique transmitter to generate a more focused vortex beam, making the waves spin in three different modes to carry more information, and developed a high-performance receiving device that could pick up and decode a huge amount of data in a split second.[40]
In 2023,Nagoya Universityin Japan reported successful fabrication of three-dimensional wave guides withniobiummetal,[41]asuperconductingmaterial that minimizes attenuation due to absorption and radiation, for transmission of waves in the100GHzfrequency band, deemed useful in 6G networking.
On November 6, 2020, China launched aLong March 6rocketwith a payload of thirteen satellites into orbit. One of the satellites reportedly served as an experimental testbed for 6G technology, which was described as "the world's first 6G satellite."[42]
During rollout of5G, China bannedEricssonin favour of Chinese suppliers, primarilyHuaweiandZTE.[43][failed verification]HuaweiandZTEwere banned in many Western countries over concerns of spying.[44]This creates a risk of 6G network fragmentation.[45]Many power struggles are expected during the development of common standards.[46]In February 2024, the U.S., Australia, Canada, the Czech Republic, Finland, France, Japan, South Korea, Sweden and the U.K. released a joint statement stating that they support a set of shared principles for 6G for "open, free, global, interoperable, reliable, resilient, and secure connectivity."[47][48]
6G is considered a key technology for economic competitiveness, national security, and the functioning of society. It is a national priority in many countries and is named as priority in China'sFourteenth five-year plan.[49][50]
Many countries are favouring the OpenRANapproach, where different suppliers can be integrated together and hardware and software are independent of supplier.[51]
In March 2025 Australia's largest telecommunications providerTelstraannounced that 6G is expected to be rolled out in the 2030s, with a budget of $800 million AUD to upgrade existing infrastructure over four years.[52]
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ANT(originates from Adaptive Network Topology) is a proprietary (butopen access)multicastwireless sensor networktechnology designed and marketed by ANT Wireless (a division ofGarminCanada).[1]It providespersonal area networks(PANs), primarily foractivity trackers. ANT was introduced by Dynastream Innovations in 2003, followed by the low-power standard ANT+ in 2004, before Dynastream was bought by Garmin in 2006.[2]
ANT defines a wireless communicationsprotocol stackthat enables hardware operating in the 2.4GHzISM bandto communicate by establishing standard rules for co-existence, data representation, signalling,authentication, anderror detection.[3]It is conceptually similar toBluetooth low energy, but is oriented towards use with sensors.
As of November 2020,[update]the ANT website lists almost 200 brands using ANT technology.[4]Samsungand, to a lesser part,Fujitsu,HTC,Kyocera,NokiaandSharpadded native support (without the use of a USB adapter) to their smartphones, with Samsung starting support with theGalaxy S4and ending support with theGalaxy S20line.[5][6][7]
ANT-powerednodesare capable of acting as sources or sinks within awireless sensor networkconcurrently. This means the nodes can act as transmitters, receivers, or transceivers to route traffic to other nodes. In addition, every node is capable of determining when to transmit based on the activity of its neighbors.[3]
ANT can be configured to spend long periods in a low-power sleep mode (drawing current on the order of microamperes), wake up briefly to communicate (when current rises to a peak of 22 milliamperes (at −5dB) during reception and 13.5 milliamperes (at −5 dB) during transmission)[8]and return to sleep mode. Average current draw for low message rates is less than 60 microamperes on the nRF24AP1 chip.[8]The newer nRF24AP2 has improved on these figures.[9]
ANT is considered a network/transport layer protocol. The underlying link layer protocol is Shockburst,[10]which is used in many otherNordic Semiconductor"NRF" chips such as those used withArduino.[11]ANT uses Shockburst at 1 Mbsp with GFSK modulation, translating to a 1 MHzbandwidth, resulting in 126 available radio channels over the ISM band.[10]
ANT channels are separate from the underlying Shockburst RF channels. They are identified simply by a channel number built into the packet,[12]and on the nRF24AP2 78 channels can be used.[9]Each ANT channel consists of one or more transmitting nodes and one or more receiving nodes, depending on the network topology. Any node can transmit or receive, so the channels are bi-directional.[13]Newer versions of ANT can back one ANT channel with several RF channels throughfrequency agility.[12]
The underlying RF channel is onlyhalf-duplex, meaning only one node can transmit at a time. The underlying radio chip can also only choose to transmit or receive at any given moment.[11]As a result, the ANF channel is controlled by aTime Division Multiple Accessscheme. A "master" node controls the timing, while the "slave" nodes use the master node's transmission to determine when they can transmit.[9]
ANT accommodates three types of messaging: broadcast, acknowledged, and burst.
ANT was designed for low-bit-rate and low-power sensor networks, in a manner conceptually similar to (but not compatible with)Bluetooth Low Energy.[3]This is in contrast with normalBluetooth, which was designed for relatively high-bit-rate applications such as streaming sound for low-power headsets.
ANT uses adaptive isochronous transmission[14]to allow many ANT devices to communicate concurrently without interference from one another, unlike Bluetooth LE, which supports an unlimited number of nodes throughscatternetsand broadcasting between devices.
Burst – 20 kbit/s[16]Advanced Burst – 60 kbit/s[16]
Bluetooth,Wi-Fi, andZigbeeemploydirect-sequence spread spectrum(DSSS) andFrequency-hopping spread spectrum(FHSS) schemes respectively to maintain theintegrityof the wireless link.[18]
ANT uses an adaptiveisochronousnetwork technology to ensure coexistence with other ANT devices. This scheme provides the ability for each transmission to occur in an interference-free time slot within the defined frequency band. The radio transmits for less than 150 μs per message, allowing a single channel to be divided into hundreds of time slots. The ANT messaging period (the time between each node transmitting its data) determines how many time slots are available.[citation needed]
ANT+, introduced in 2004 as "the first ultra low power wireless standard",[2]is an interoperability function that can be added to the base ANT protocol. This standardization allows the networking of nearby ANT+ devices to facilitate the open collection and interpretation of sensor data. For example, ANT+ enabled fitness monitoring devices such as heart-rate monitors, pedometers, speed monitors, and weight scales can all work together to assemble and track performance metrics.[19]
ANT+ is designed and maintained by the ANT+ Alliance, which is managed by ANT Wireless, a division of Dynastream Innovations, owned byGarmin.[20]ANT+ is used in Garmin's line of fitness monitoring equipment. It is also used by Garmin's Chirp, ageocachingdevice, for logging and alerting nearby participants.[21]
ANT+ devices require certification from the ANT+ Alliance to ensure compliance with standard device profiles. Each device profile has an icon which may be used to visually match interoperable devices sharing the same device profiles.[4]
The ANT+ specification is publicly available. AtDEF CON2019, hacker Brad Dixon demonstrated a tool to modify ANT+ data transmitted throughUSBfor cheating in virtual cycling.[22]
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ABluetooth stackissoftwarethat is animplementationof theBluetooth protocolstack.
Bluetoothstacks can be roughly divided into two distinct categories:
TheFreeBSDbluetooth stack is implemented using theNetgraphframework.[2]A broad variety of Bluetooth USB dongles are supported by the ng_ubt driver.[3]
The implementation was committed in 2002, and first released withFreeBSD 5.0.[4]
NetBSDhas its own Bluetooth implementation, committed in 2006, and first released withNetBSD § 4.0.[5]
OpenBSDhas had the implementation from NetBSD for some time, but it was removed in 2014 due lack of maintainership andcode rot.[6][7]
DragonFly BSDhas had NetBSD's Bluetooth implementation since 1.11 (2008), first released withDragonFly BSD § 1.12.[8]
Anetgraph-based implementation fromFreeBSDhas also been available in the tree since 2008, dating to an import ofNetgraphfrom the FreeBSD 7 timeframe into DragonFly, but was possibly disabled until 2014-11-15, and may still require more work.[9][10]
BlueALSAis a Bluetooth audioALSAbackend that allows the use of Bluetooth-connected audio devices without the use ofPulseAudioorPipeWire.[11][12]
BlueZ, initially developed byQualcomm,[13]is a Bluetooth stack, included with the officialLinux kerneldistributions,[14]forLinux kernel-based family of operating systems. Its goal is to program an implementation of the Bluetooth wireless standards specifications for Linux. As of 2006, the BlueZ stack supports all core Bluetooth protocols and layers.[citation needed]It was initially developed byQualcomm, and is available forLinux kernelversions 2.4.6 and up.[15]In addition to the basic stack, the bluez-utils and bluez-firmware packages contain low level utilities such as dfutool which can interrogate the Bluetooth adapter chipset to determine whether its firmware can be upgraded. BlueZ is licensed under theGNU General Public License(GPL), but reported to be on its way toward switching to theGNU Lesser General Public License(LGPL).[16]
hidd is the Bluetoothhuman interface device(HID)daemon.[17]
Androidswitched from BlueZ to its ownBlueDroidstack, created byBroadcom, in late 2012.[16]BlueDroid has been since renamed Fluoride.[18]Marcel Holtmann, from the Intel Open Source Technology Center, implied that Google made a poor choice in switching to BlueDroid, during a presentation forBlueZ for Androidat the Android Builders Summit in 2014.[16]
With Android 13, Google by default enabled the newly developed Bluetooth stackGabeldorsche.[19]
The nameGabeldorschevery indirectly relates toSweyn Forkbeard, the son and successor ofHarald Bluetooth.[20]
Since version 10.2,Apple Inc.'smacOShas contained an integrated Bluetooth stack.[21]Included profiles are DUN, SPP, FAX, HID, HSP, SYNC, PAN, BPP and OBEX. Mac OS X 10.5 added support for A2DP and AVRCP.
Prior to Windows 8, the Microsoft Bluetooth Stack only supports external or integrated Bluetooth dongles attached throughUSB. It does not support Bluetooth radio connections overPCI,I2C,serial,PC Cardor other interfaces.[22]It also only supports a single Bluetooth radio.[22]Windows 8 has an extensible transport model allowing support for Bluetooth radios on non-USB buses.[23]
Generally, only a single stack can be used at any time: switching usually requires uninstalling the current stack, although a trace of previous stacks remains in the Windows registry. However, there are some cases where two stacks can be used on the same Microsoft Windows system, each using their own separate Bluetooth radio hardware.
Windows versions:[24]
Note :The Windows XP/Vista Windows Vista/Windows 7 Bluetooth stack supports the following Bluetooth profiles natively: PANU, SPP, DUN, OPP, OBEX, HID, HCRP.[22][23][26]Windows 8 adds support for HFP, A2DP, GATT and AVRCP Profiles.[23]
The Windows 7/Vista/8/10 stack provides kernel-mode and user-mode APIs for its Bluetooth stack- so hardware and software vendors can implement additional profiles.[23]
Windows 10 (Version 1803) and later support Bluetooth version 5.0 and several Bluetooth profiles.[29]
Bluetooth profiles exposed by the device but unsupported by the Windows stack will show as "Bluetooth Peripheral Device" inDevice Manager.
WIDCOMM was the first Bluetooth stack for theWindowsoperating system. The stack was initially developed by a company named WIDCOMM Inc., which was acquired byBroadcom Corporationin April 2004.[30]Broadcom continues tolicensethe stack for inclusion with many Bluetooth-poweredend-userdevices like Qualcomm Atheros, Realtek, Ralink.
An API is available for interacting with the stack from a custom application. For developers there is also a utility namedBTServer Spy Litebundled with the stack (some vendor-tied versions excluded) which monitors Bluetooth activity on the stack at a very low level — although the category and level of trace is configurable. This stack also allows use ofRFCOMMwithout creating a virtual serial port in the operating system.
In 2001,Toshibafirst announced a notebook design that would integrate a Bluetooth antenna inside the lid. Toshiba then went on to release the first two notebook models to offer dual Bluetooth/Wi-Fiintegration.[31]
Toshiba has created its own Bluetooth stack for use on Microsoft Windows. Toshiba licenses their stack to otheroriginal equipment manufacturers(OEM) and has shipped with someFujitsu Siemens,ASUS,DellandSonylaptops. Anon-disclosure agreementmust be signed to obtain theAPI. The Toshiba stack is also available with certain non-OEM Bluetooth accessories such as USB Bluetooth dongles and PCMCIA cards from various vendors.
The Toshiba stack supports one of the more comprehensive list of Bluetooth profiles including:SPP,DUN,FAX,LAP,OPP,FTP,HID,HDP,HCRP,PAN,BIP,HSP,HFP(including Skype support),A2DP,AVRCP.
The latest version of the Toshiba stack is9.20.02(T), released on 30 September 2016.
In 2010CSR plc(formerly Cambridge Silicon Radio) created its own Bluetooth stack.[32]It was based on CSR Synergy BT host stack. CSR was acquired byQualcommin August 2015.[33]
BlueSoleil(marketed as1000MoonsinChina) is a product of IVT Corporation, which produces stacks for embedded devices and desktop systems. The stack is available in both standard and VOIP versions. It supports the profiles A2DP, DUN, FAX, HFP, HSP, LAP, OBEX, OPP, PAN, SPP, AV, BIP, FTP, HID and SYNC.
An SDK for third-party application developers is available for non-commercial use at theBlueSoleil download site, but this API will only work with the non-free version of the stack, BlueSoleil 6.4 and above.
As of April 2018, the latest version of the global BlueSoleil stack is 10.0.497.0, released on 8 January 2018. The Chinese 1000Moons stack is at version10.2.497.0, released on 9 January 2018.
BlueFRITZ! was the stack supplied with the USB Bluetooth dongles from the German manufacturerAVM GmbH. It supported the profiles SPP, DUN, FTP, FAX and some more. HID was not supported. This stack could be switched into a mode where it is off and the Microsoft stack is used instead. Development of this stack has been aborted.
Digianswer was a subsidiary ofMotorola, Inc.since 1999.[34]Digianswer Bluetooth Software Suite (BTSWS) was marketed and sold throughOEMcustomers such asMotorola,DellandIBM, which bundledPCMCIAandUSBproducts together with BTSWS. The product has been available since August 2000.[35]
Apache Mynewt NimBLE is a full-featured,open sourceBluetooth Low Energy 4.2 and 5.0 protocol stack written in C forembedded systems. NimBLE is one of the most complete protocol stacks, supporting 5.0 features including high data rate and extended advertising. The implementation supports all layers of the Bluetooth protocol. The first ports for the Controller part are tonRF51 seriesand nRF52 SoCs from Nordic Semiconductor. NimBLE also supports standard HCI interfaces to work with controllers, including ST, Dialog and Em Micro chipsets. It leverages the open sourceApache Mynewt OSwhich is designed to support multiple microcontroller architectures.[36]NimBLE can also run with FreeRTOS and is portable to other real-time operating systems. The implementation allows for the Mynewt NimBLE Controller part to be used with a non-Mynewt NimBLE Host.
BlueCode+ is the portable higher layer Bluetooth protocol stack from Stollmann E+V GmbH. BlueCode+ 4.0 is qualified to Bluetooth version 3.0.[37]The protocol stack is chipset and operating system independent and supports any Bluetooth HCI chips available. The APIs offer control of the profiles and stack functions, as well as direct access to lower level functions. BlueCode+ 4.0 supports the protocols L2CAP, eL2CAP, RFCOMM, SDP Server and Client, MCAP, HCI-Host Side and AVDTP. Supported profiles are Generic Access (GAP), Service Discovery Application (SDAP), Serial Port Profile (SPP), Health Device Profile (HDP), Device Identification Profile (DID), Dial-up Networking (DUN), Fax, Headset (HSP), Handsfree (HFP), SIM Access (SAP), Phone Book Access (PBAP), Advanced Audio Distribution Profile (A2DP), Audio/Video Remote Control (AVRCP) and OBEX. The stack has been ported to a wide range of different microcontrollers and operating systems.
CSR's BCHS or BlueCore Host Software (now called CSR Synergy) provides the upper layers of the Bluetooth protocol stack (above HCI, or optionally RFCOMM) - plus a large library of Profiles — providing a complete system software solution for embedded BlueCore applications. Current qualified Profiles available with BCHS: A2DP, AVRCP, PBAP, BIP, BPP, CTP, DUN, FAX, FM API, FTP GAP, GAVDP, GOEP, HCRP, Headset, HF1.5, HID, ICP, JSR82, LAP Message Access Profile, OPP, PAN, SAP, SDAP, SPP, SYNC, SYNC ML.[38]
Bluelet is a portable embedded Bluetooth protocol stack ofBarrot Technology Limitedwith efficient, reliable, and small features. Bluelet is perfectly compatible with BREDR/LE profiles. Bluelet can easily be ported to different platforms, i.e., Linux, RTOS, Android. This offering includes the latest full implementation of Bluetooth 5.3 host using ANSI C, implementing all LE Audio Profiles / Services (BAP, PACS, ASCS, BASS; CSIP/CSIS; CCP/TBS; MCP/MCS; MICP/MICS; VCP/VCS/VOCS/AICS; TMAP, HAP/HAS; CAP) and the MESH stack.[39]
BlueMagic 3.0 is Qualcomm's (formerlyOpen Interface North America's) highly portable embedded Bluetooth protocol stack which powers Apple's iPhone and Qualcomm-powered devices such as the Motorola RAZR. BlueMagic also ships in products by Logitech, Samsung, LG, Sharp, Sagem, and more. BlueMagic 3.0 was the first fully certified (all protocols and profiles) Bluetooth protocol stack at the 1.1 level.[40]
OpenSynergy's Bluetooth Protocol Stack (Blue SDK) currently provides A2DP, AVRCP, VDP, BIP, BPP, CTN, FTP, GPP, HFP, HSP, HCRP, HDP, HID, MAP, OPP, PAN, PBAP, SAP, DUN, FAX, DID, GATT profiles. It is licensed by the Bluetooth Special Interest Group (SIG) and meets the standards of safety and security expected in automotive-grade products. Bluetooth Software Development Kit (Blue SDK) can easily be integrated into any operating system. It supports both BR/EDR (Classic) and Low Energy operations, classic profiles and low energy profiles use the same underlying protocol stack software.[41]
Bluetopia isStonestreet One's implementation of the upper layers of the Bluetooth protocol stack above the HCI interface and has been qualified to version 4.0 and earlier versions of the Bluetooth specification. The Application Programming Interface (API) provides access to all of the upper-layer protocols and profiles and can interface directly to the most popular Bluetooth chips from Broadcom, CSR, TI, and others. Bluetopia has been ported to multiple operating systems such as Windows Mobile/Windows CE, Linux, QNX, Nucleus, uCOS, ThreadX, NetBSD, and others. Bluetopia is currently shipping in devices from companies such as Motorola, Kodak, Honeywell, Garmin, VTech, and Harris.
Stonestreet Onewas acquired by Qualcomm in 2014. Texas Instruments provides its version of the Bluetopia stack for use with TI Bluetooth chips.
BlueWiseLE is theBluetooth Low Energycertified protocol stack software product from Alpwise. It includes the Link Layer[42]and also the Host stack (i.e. upper layers above the HCI).[43]The Link Layer controls the radio and the timing of the Bluetooth communication in three possible chipset configurations: SoC, co-processor or HCI. Several proprietary BLE profiles are also available including Voice over BLE and Firmware update Over the Air (FOTA).[44]
Bluetooth host subsystem product of Clarinox Technologies. Support for Windows 7/8/10, WinCE, Linux/AGL Linux, Android, AutoSAR, Integrity, SafeRTOS, QNX, μITRON, FreeRTOS, μC/OS, Azure RTOS ThreadX, Nucleus, MQX, RTX, embOS, TI-RTOS, DSP/BIOS, eCos and μ-velOSity. Qualified for Bluetooth specification 5.2,5.0 and all previous specifications includes all Classic profiles/protocols and LE profiles/services including BT & LE Audio. ClarinoxBlue supports HCI transport for SDIO, UART 3-Wire, UART-BCSP, UART-H4, USB. The stack has been ported to many CPU and MCU families including NXP i.MX6/i.MX7/i.MX8/i.MX RT, Kinetis K6x/7x, LPC 18xx/43xx/54xxx STMicro; STM32F4x, STM32H7, STM32WB55, STM32MP157; Texas Instruments TI MSP432, DSP 5xxx, OMAP/Davinci, Tiva TM4C123x, Sitara 3xxx; Renesas Synergy S5/S7, RH850, R-Car M3/H3; Xilinx PowerPC, soft core SPARC LEON. ClarinoxBlue Bluetooth host system is provided with ClariFi debug tool, in-built protocol analyzer, supports faster debugging of complex wireless devices. ClariFi offers threading, memory usage, memory leak analysis and audio analysis to support the tuning of applications and aid in the communication of issues.[45]
dotstack, a dual mode Bluetooth stack by SEARAN, is a good fit for low cost and low power embedded devices, tested with iPhone (uses SEARAN's IAP), Android and other mobile platforms. dotstack is qualified as V2.1 + EDR, V4.1, V4.2 and 5.0, with SPP, GAP, HID, Headset, HFP, FTP, HDP, PBAP, Simple Secure Pairing, A2DP, AVRCP, PAN, MAP, BLE (GATT) with ANP/ANS, FMP, HIDS, HOGP, PASP/PASS, PXP, TIP, BAS, DIS, IAS, LLS, TPS, ANCS, BLP/BLS, GP, HTP, HRP/HRS. dotstack is ported to platforms from, ST Micro (STM32L1/4, STM32F0/1/2/3/4), Microchip (PIC24, dsPIC, PIC32), NXP (LPC), Energy Micro (EFM32), TI (MSP430, C5000 etc.), Renesas (RX, SH-2A, M2 ARM Cortex A15, R-Car), and tested with Bluetooth RF controllers, CSR8811/8311/8510, BlueCore 4 & 6, TI CC2560/2564, Intel/Infineon PMB8753, Marvell Avastar 88w8777, 88W8790, Toshiba TC35661, Microchip/ISSC IS1662. dotstack has FreeRTOS, uOS, Linux, Android, QNX, MQX, ThreadX, and no RTOS integration. Min RAM requirement for SPP 3KB with RTOS and app.[46]
EtherMindfrom MINDTREE Ltd is a BT-SIG qualified Bluetooth Stack and Profile IP offering.[47]
Mindtree's EtherMind Stack supports all popular versions of Bluetooth specifications (2.1+EDR, v4.0, v4.1, v4.2, 5.0, 5.1 and 5.2) and includes all mandatory and optional features of the core stack and all the adopted profiles are supported as part of EtherMind. The stack supports the latest adopted version of 23 Bluetooth Classic Profiles[48]such as A2DP, AVRCP, etc.; and 54 Bluetooth Low Energy Profiles & Services[49]such as Location and Navigation Profile, Weight Scale Profile/Service, etc. The offering includes the latestMesh[50]andIPv6Stack[51]over Bluetooth Smart capabilities.
Jungo's Bluetooth Protocol Stack BTware allows device manufacturers to easily incorporate standard Bluetooth connectivity in their designs, including mobile handsets,automotive infotainmentsystems, set top boxes and medical devices. BTware supports standard HCI as well as proprietary HCI. Supported protocols: L2CAP, RFCOMM, AVDTP, AVCTP, BNEP, MCAP. Supported profiles: GAP, A2DP, AVRCP, HSP, HFP, SPP, DUN, HID, PAN, HDP, PBAP, OPP, FTP, MAP and others.
Jungo has discontinued distributing BTware.
lwBT is anopen sourcelightweight Bluetooth protocol stack forembedded systemsby blue-machines. It acts as a network interface for the lwIP protocol stack.
It supports some Bluetooth protocols and layers, such as the H4 and BCSP UART layers. Supported higher layers include:HCI,L2CAP, SDP, BNEP,RFCOMMandPPP.
The supported profiles are: PAN (NAP, GN, PANU), LAP, DUN and Serial Port.
lwBT has been ported to the RenesasM16C, used on theMulle platform, line of microcontrollers, and Linux as well as Windows. The source code was also available for use.
A fork of lwBT can be found in theGitHubrepository because Googlecode is gone.[52]
MecelBetula is a Bluetooth stack aimed at the embedded automotive market. The stack has support for a wide range of CPUs including, ARM, Renesas V850, TI DSP 54xx and 55xx family and x86 compatible. It also ported to a wide range of operating systems, such asWindows,Linux,Androidor running without or with a custom OS. It has support for Bluetooth version 5.3, including the new Bluetooth Low Energy & mesh.[53]Supported profiles are HSP, DUN, FAX, HFP, PBAP, MAP, OPP, FTP, BIP, BPP, SYNC, GAVDP, A2DP, AVRCP, HID, SAP, PAN.
Silvair Mesh Stack is an implementation ofBluetooth MESH profile and Models, developed primarily forSmart lightingapplications. Apart from core mesh node features it implements Light Lightness Server model, Light Controller model and Sensor Server model so that it may be used to builddimmingluminaires anddaylight harvestingsensors.
It providesPWM/0-10Voutput for direct dimming control andUARTinterface for integration purposes.DALIoutput is marked as planned.[54]
Silvair Mesh Stack has been qualified byBluetooth SIGon 2017-07-18 with QDID 98880, as a first Bluetooth mesh node implementation.[55]
Siemens' implementation of theblue2netaccess point.
Symbian OSwas an operating system for mobile phones, which includes a Bluetooth stack.
All phones based onNokia'sS60 platformandUIQ Technology'sUIQ platformuse this stack.
The Symbian Bluetooth stack runs inuser spacerather than kernel space, and has public APIs for L2CAP, RFCOMM, SDP, AVRCP, etc.
Profiles supported in the OS include GAP, OBEX, SPP, AVRCP, GAVDP, PAN and PBAP.[56]Additional profiles supported in the OS + S60 platform combination include A2DP, HSP, HFP1.5, FTP, OPP, BIP, DUN, SIM access and device ID.[57][58]
TheZephyr Project RTOSincludes a complete,open sourceBluetooth Low Energy v5.3[59]compliant protocol stack written in C forembedded systems. It contains both a BLE Controller and a BLE and BR/EDR capable Host running onnRF51 Seriesand nRF52 SoCs from Nordic Semiconductor.
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In order to useBluetooth, a device must be compatible with the subset of Bluetoothprofiles(often called services or functions) necessary to use the desired services. A Bluetooth profile is a specification regarding an aspect of Bluetooth-based wireless communication between devices. It resides on top of the Bluetooth Core Specification and (optionally) additional protocols. While the profile may use certain features of the core specification, specific versions of profiles are rarely tied to specific versions of the core specification, making them independent of each other. For example, there are Hands-Free Profile (HFP) 1.5 implementations using both Bluetooth 2.0 and Bluetooth 1.2 core specifications.
The way a device uses Bluetooth depends on its profile capabilities. The profiles provide standards that manufacturers follow to allow devices to use Bluetooth in the intended manner. For the Bluetooth Low Energy stack, according to Bluetooth 4.0 a special set of profiles applies.
A hostoperating systemcan expose a basic set of profiles (namely OBEX, HID and Audio Sink) and manufacturers can add additional profiles to their drivers andstackto enhance what their Bluetooth devices can do. Devices such as mobile phones can expose additional profiles by installing appropriate apps.
At a minimum, each profile specification contains information on the following topics:
This article summarizes the current definitions of profiles defined and adopted by the Bluetooth SIG and possible applications of each profile.
This profile defines how multimedia audio can be streamed from one device to another over a Bluetooth connection (it is also called Bluetooth Audio Streaming). For example, music can be streamed from a mobile phone, laptop, or desktop to a wirelessheadset, hearing aid/cochlear implantstreamer, or car audio; voice can be streamed from a microphone device to a recorder on a mobile phone or computer.[1]The Audio/Video Remote Control Profile (AVRCP) is often used in conjunction with A2DP for remote control on devices such as headphones, car audio systems, or stand-alone speaker units. These systems often also implementHeadset(HSP) orHands-Free(HFP) profiles for telephone calls, which may be used separately.
Each A2DP service, of possibly many, is designed to uni-directionally transfer an audio stream in up to 2 channel stereo, either to or from the Bluetooth host.[2]This profile relies onAVDTPandGAVDP. It includes mandatory support for the low-complexitySBCcodec (not to be confused with Bluetooth's voice-signal codecs such asCVSDM), and supports optionallyMPEG-1 Part 3/MPEG-2 Part 3(MP2andMP3), MPEG-2 Part 7/MPEG-4 Part 3(AACandHE-AAC), andATRAC, and is extensible to support manufacturer-definedcodecs, such asaptX.[3]For an extended list of codecs, seeList of codecs § Bluetooth.
While designed for a one-way audio transfer -CSRhas developed a way to transfer a mono stream back (and enable use of headsets with microphones), and incorporated it intoFastStreamandaptX Low Latencycodecs. The patent has expired.
Some Bluetooth stacks enforce theSCMS-Tdigital rights management(DRM) scheme. In these cases, it is impossible to connect certain A2DP headphones for high quality audio, while some vendors disable the A2DP functionality altogether to avoid devices rejecting A2DP sink.
The ATT is a wire application protocol for theBluetooth Low Energyspecification. It is closely related to Generic Attribute Profile (GATT).
This profile is designed to provide a standard interface to control TVs,Hi-Fiequipment, etc. to allow a singleremote control(or other device) to control all of the A/V equipment to which a user has access. It may be used in concert with A2DP or VDP.[4]It is commonly used in car navigation systems to control streaming Bluetooth audio.
It also has the possibility for vendor-dependent extensions.
AVRCP has several versions with significantly increasing functionality:[5]
This profile is designed for sending images between devices and includes the ability to resize, and convert images to make them suitable for the receiving device. It may be broken down into smaller pieces:
This allows devices to send text, e-mails,vCards, or other items toprintersbased on print jobs. It differs from HCRP in that it needs no printer-specific drivers. This makes it more suitable for embedded devices such asmobile phonesanddigital cameraswhich cannot easily be updated with drivers dependent upon printer vendors.
This provides unrestricted access to the services, data and signalling thatISDNoffers.
This is designed forcordless phonesto work using Bluetooth. It is hoped that mobile phones could use a Bluetooth CTP gateway connected to alandlinewhen within the home, and the mobile phone network when out of range. It is central to theBluetooth SIG's "3-in-1 phone" use case.
This profile allows a device to be identified above and beyond the limitations of the Device Class already available in Bluetooth. It enables identification of the manufacturer, product id, product version, and the version of the Device ID specification being met. It is useful in allowing a PC to identify a connecting device and download appropriatedrivers. It enables similar applications to those thePlug-and-playspecification allows.
This is important in order to make best use of the features on the device identified. A few examples illustrating possible uses of this information are listed below:
This profile provides a standard to access theInternetand otherdial-upservices over Bluetooth by utilising avirtual COM portassociated with a virtualmodem.[15]The most common scenario is accessing the Internet from alaptopby dialing up on amobile phone, wirelessly. It is based onSerial Port Profile(SPP), and provides for relatively easy conversion of existing products, through the many features that it has in common with the existing wiredserial protocolsfor the same task. These include theAT commandset specified inEuropean Telecommunications Standards Institute(ETSI) 07.07, andPoint-to-Point Protocol(PPP).
DUN distinguishes the initiator (DUN Terminal) of the connection and the provider (DUN Gateway) of the connection. The gateway provides a modem interface and establishes the connection to a PPP gateway. The terminal implements the usage of the modem and PPP protocol to establish the network connection. In standard phones, the gateway PPP functionality is usually implemented by the access point of the Telco provider. In "always on" smartphones, the PPP gateway is often provided by the phone and the terminal shares the connection.
This profile is intended to provide a well-defined interface between a mobile phone orfixed-line phoneand a PC with Fax software installed. Support must be provided for ITU T.31 and / or ITU T.32AT commandsets as defined byITU-T. Data and voice calls are not covered by this profile.
GAVDP provides the basis forA2DPandVDP, the basis of the systems designed for distributing video and audio streams using Bluetooth technology.
The GAVDP defines two roles, that of an Initiator and an Acceptor:
Note: the roles are not fixed to the devices. The roles are determined when you initiate a signaling procedure, and they are released when the procedure ends. The roles can be switched between two devices when a new procedure is initiated.
The Baseband, LMP, L2CAP, and SDP are Bluetooth protocols defined in the Bluetooth Core specifications. AVDTP consists of a signaling entity for negotiation of streaming parameters and a transport entity that handles the streaming.
Provides the basis for all other profiles. GAP defines how two Bluetooth units discover and establish a connection with each other.
Provides profile discovery and description services forBluetooth Low Energyprotocol. It defines how ATT attributes are grouped together into sets to form services.[16]
Provides a basis for other data profiles. Based onOBEXand sometimes referred to as such.
This provides a simple wireless alternative to a cable connection between a device and a printer. Unfortunately it does not set a standard regarding the actual communications to the printer, sodriversare required specific to the printer model or range. This makes this profile less useful for embedded devices such as digital cameras and palmtops, as updating drivers can be problematic.
Health Thermometer profile (HTP) and Heart Rate Profile (HRP) fall under this category as well.
Profile designed to facilitate transmission and reception of Medical Device data. The APIs of this layer interact with the lower level Multi-Channel Adaptation Protocol (MCAP layer), but also performSDPbehavior to connect to remote HDP devices. Also makes use of the Device ID Profile (DIP).
This profile is used to allow car hands-free kits to communicate with mobile phones in the car. It commonly uses Synchronous Connection Oriented link (SCO) to carry amonauralaudio channel withcontinuously variable slope delta modulationorpulse-code modulation, and with logarithmica-laworμ-lawquantization. Version 1.6 adds optional support for wide band speech with the mSBC codec, a 16 kHz monaural configuration of theSBCcodec mandated by theA2DPprofile. Version 1.7 adds indicator support to report such things as headset battery level. Version 1.9 addsLC3-SBWcodec.
In 2002Audi, with theAudi A8, was the first motor vehicle manufacturer to install Bluetooth technology in a car, enabling the passenger to use a wireless in-car phone. The following yearDaimlerChryslerandAcuraintroduced Bluetooth technology integration with the audio system as a standard feature in the third-generationAcura TLin a system dubbed HandsFree Link (HFL). Later,BMWadded it as an option on its1 Series,3 Series,5 Series,7 SeriesandX5vehicles. Since then, other manufacturers have followed suit, with many vehicles, including theToyota Prius(since 2004), 2007Toyota Camry, 2006Infiniti G35, and theLexusLS 430 (since 2004). SeveralNissanmodels (Versa, X-Trail) include a built-in Bluetooth for the Technology option.Volvostarted introducing support in some vehicles in 2007, and as of 2009 all Bluetooth-enabled vehicles support HFP.[17]
Many car audio consumer electronics manufacturers like Kenwood, JVC, Sony, Pioneer and Alpine build car audio receivers that house Bluetooth modules all supporting various HFP versions.
Bluetooth car kits allow users with Bluetooth-equipped cell phones to make use of some of the phone's features, such as making calls, while the phone itself can be left in the user's pocket or hand bag. Companies likeVisteon Corp.,Peiker acustic,RAYTEL,Parrot SA,Novero, Dension, S1NN and Motorola manufacture Bluetooth hands-free car kits for well-known brand car manufacturers.
Most Bluetooth headsets implement both Hands-Free Profile and Headset Profile, because of the extra features in HFP for use with a mobile phone, such as last number redial, call waiting and voice dialing.
The mobile phone side of an HFP link is Audio Gateway or HFP Server. The automobile side of HFP link is Car Kit or HFP Client.
Provides support forHID devicessuch asmice,joysticks,keyboards, and simple buttons and indicators on other types of devices. It is designed to provide a lowlatencylink, with low power requirements.PlayStation 3controllers andWiiremotes also use Bluetooth HID.
Bluetooth HID is a lightweight wrapper of thehuman interface deviceprotocol defined forUSB. The use of the HID protocol simplifies host implementation (when supported by hostoperating systems) by re-use of some of the existing support forUSB HIDin order to support also Bluetooth HID.
Keyboard and keypads must be secure. For other HID devices, security is optional.[18]
A profile that defines how a device with Bluetooth low energy wireless communications can supportHID devicesover the Bluetooth using the low energy protocol stack using:Generic Attribute Profile.
This is the most commonly used profile, providing support for the popular Bluetooth headsets to be used with mobile phones and gaming consoles. It relies onSCOaudio encoded in 64 kbit/s CVSD or PCM and a subset ofAT commandsfrom GSM 07.07 for minimal controls including the ability to ring, answer a call, hang up and adjust the volume. This profile supportsmono audioonly.
iAP and later iAPv2 protocol are proprietary protocols developed byApple Inc.for communication with 3rd party accessories for iPhones, iPods and iPads. Most Bluetooth drivers and stacks for Windows do not support the iAP profile since using such protocols requires aMFi licensefrom Apple and thus is displayed as "Bluetooth Peripheral Device" or "Not Supported Bluetooth Function" inDevice Manager.
This is often referred to as thewalkie-talkieprofile. It is anotherTCSbased profile, relying onSCOto carry the audio. It is proposed to allow voice calls between two Bluetooth capable handsets, over Bluetooth.
The ICP standard was withdrawn on 10-June-2010.[19]
LAN Access profile makes it possible for a Bluetooth device to accessLAN,WANorInternetvia another device that has a physical connection to the network. It usesPPPoverRFCOMMto establish connections. LAP also allows the device to join an ad-hoc Bluetooth network.
The LAN Access Profile has been replaced by thePANprofile in the Bluetooth specification.
Mesh Profile Specification[20]allows for many-to-many communication over Bluetooth radio. It supports data encryption, message authentication and is meant for building efficient smart lighting systems and IoT networks.
Application layer for Bluetooth Mesh has been defined in a separate Mesh Model Specification.[21]As of release 1.0 lighting, sensors, time, scenes and generic devices has been defined.
Additionally, application-specific properties has been defined in Mesh Device Properties[22]Specification, which contains the definitions for all mesh-specific GATT characteristics and their descriptors.
Message Access Profile (MAP)[23]specification allows exchange of messages between devices. Mostly used for automotive handsfree use. The MAP profile can also be used for other uses that require the exchange of messages between two devices. The automotive Hands-Free use case is where an on-board terminal device (typically an electronic device as a Car-Kit installed in the car) can talk via messaging capability to another communication device (typically a mobile phone). For example, Bluetooth MAP is used by HP Send and receive text (SMS) messages from a Palm/HP smartphone to an HP TouchPad tablet.[24]Bluetooth MAP is used by Ford in select SYNC Generation 1-equipped 2011 and 2012 vehicles[25]and also by BMW with many of their iDrive systems. The Lexus LX and GS 2013 models both also support MAP as does the Honda CRV 2012, Acura 2013 and ILX 2013. Apple introduced Bluetooth MAP in iOS 6 for the iPhone and iPad. Android support was introduced in version 4.4 (KitKat).[26]
A basic profile for sending "objects" such as pictures,virtual business cards, orappointment details. It is called push because the transfers are always instigated by the sender (client), not the receiver (server).
OPP uses the APIs of OBEX profile and the OBEX operations which are used in OPP are connect, disconnect, put, get and abort. By using these API the OPP layer will reside over OBEX and hence follow the specifications of the Bluetooth stack.
This profile is intended to allow the use of Bluetooth Network Encapsulation Protocol onLayer 3protocols for transport over a Bluetooth link.
Phone Book Access (PBA).[27][28][29]or Phone Book Access Profile (PBAP) is a profile that allows exchange of Phone Book Objects between devices. It is likely to be used between a car kit and a mobile phone to:
The profile consists of two roles:
The Proximity profile (PXP) enables proximity monitoring between two devices. This feature is especially useful for unlocking devices such as a PC when a connected Bluetooth smartphone is nearby.
This profile is based onETSI07.10 and theRFCOMMprotocol. It emulates a serial cable to provide a simple substitute for existingRS-232, including the familiar control signals. It is the basis forDUN,FAX, HSP andAVRCP. SPP maximum payload capacity is 128 bytes.
Serial Port Profile defines how to set up virtual serial ports and connect two Bluetooth enabled devices.
SDAP describes how an application should use SDP to discover services on a remote device. SDAP requires that any application be able to find out what services are available on any Bluetooth enabled device it connects to.
This profile allows devices such as car phones with built-inGSMtransceivers to connect to aSIM cardin a Bluetooth enabled phone, thus the car phone itself does not require a separate SIM card and the car external antenna can be used.[30][31][32]This profile is sometimes referred to as rSAP (remote-SIM-Access-Profile),[31]though that name does not appear in the profile specification published by theBluetooth SIG. Information on phones that support SAP can be found below:
Currently[when?]the following cars by design can work with SIM-Access-Profile:
Many manufacturers of GSM based mobile phones offer support for SAP/rSAP. It is supported by theAndroid,Maemo, andMeeGophone OSs. Neither Apple'siOSnor Microsoft'sWindows Phonesupport rSAP; both use PBAP for Bluetooth cellphone-automobile integration.
based on Symbian OS:
based on Bada OS:
based on special/dedicated Systems:
This profile allowssynchronizationofPersonal Information Manager(PIM) items. As this profile originated as part of theinfraredspecifications but has been adopted by the Bluetooth SIG to form part of the main Bluetooth specification, it is also commonly referred to asIrMCSynchronization.
For Bluetooth, Synchronization is one of the most important areas. The Bluetooth specifications up to, and including 1.1, has Synchronization Profile that is based on IrMC. Later, many of the companies in the Bluetooth SIG already had proprietary synchronization solutions and they did not want to implement IrMC -based synchronization also, henceSyncMLemerged. SyncML is an open industry initiative for common data synchronization protocol. The SyncML protocol has been developed by some of the leading companies in their sectors, Lotus, Motorola, Ericsson, Matsushita Communication Industrial Co., Nokia, IBM, Palm Inc., Psion and Starfish Software; together with over 600 SyncML Supporter companies. SyncML is a synchronization protocol that can be used by devices to communicate the changes that have taken place in the data that is stored within them. However, SyncML is capable of delivering more than just basic synchronization; it is extensible, providing powerful commands to allow searching and execution.
This profile allows the transport of a video stream. It could be used for streaming a recorded video from a PC media center to a portable player, or a live video from a digital video camera to a TV. Support for theH.263baseline is mandatory. TheMPEG-4Visual Simple Profile, andH.263profiles 3 and 8 are optionally supported, and covered in the specification.1
This is a profile for carryingWireless Application Protocol (WAP)overPoint-to-Point Protocolover Bluetooth.
These profiles are still not finalised, but are currently proposed within the Bluetooth SIG:
Compatibility of products with profiles can be verified on theBluetooth Qualification Program website.
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https://en.wikipedia.org/wiki/List_of_Bluetooth_profiles
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Bluesnarfingis theunauthorized accessof information from awireless devicethrough aBluetoothconnection, often between phones, desktops, laptops, and PDAs (personal digital assistant).[1]This allows access to calendars, contact lists, emails and text messages, and on some phones, users can copy pictures and private videos. Both Bluesnarfing andBluejackingexploit others' Bluetooth connections without their knowledge. While Bluejacking is essentially harmless as it only transmits data to the target device, Bluesnarfing is thetheft of informationfrom the target device.[2]
For a Bluesnarfing attack to succeed, the attacker generally needs to be within a maximum range of 10 meters from the target device. In some cases, though, attackers can initiate a Bluesnarfing attack from a greater distance.[3]
Bluesnarfing exploits vulnerabilities in theOBject EXchangeprotocol used for Bluetooth device communication, involving hackers who use tools like Bluediving to detect susceptible devices. Once a vulnerable device is identified, hackers establish a connection and employ Bluesnarfing tools to extract data. These tools, available on thedark webor developed by hackers, enable attackers to access sensitive information from compromised devices.[3]
Any device with its Bluetooth connection turned on and set to "discoverable" (able to be found by other Bluetooth devices in range) may be susceptible to Bluejacking and possibly to Bluesnarfing if there is a vulnerability in the vendor's software. By turning off this feature, the potential victim can be safer from the possibility of being Bluesnarfed; although a device that is set to "hidden" may be Bluesnarfable by guessing the device'sMAC addressvia abrute force attack. As with all brute force attacks, the main obstacle to this approach is the sheer number of possible MAC addresses. Bluetooth uses a 48-bit unique MAC Address, of which the first 24 bits are common to a manufacturer.[4]The remaining 24 bits have approximately 16.8 million possible combinations, requiring anaverageof 8.4 million attempts to guess by brute force.
Attacks on wireless systems have increased along with the popularity ofwireless networks. Attackers often search forrogue access points, or unauthorized wireless devices installed in an organization's network and allow an attacker to circumventnetwork security. Rogue access points and unsecured wireless networks are often detected through war driving, which is using an automobile or other means of transportation to search for a wireless signal over a large area. Bluesnarfing is an attack to access information from wireless devices that transmit using the Bluetooth protocol. With mobile devices, this type of attack is often used to target theinternational mobile equipment identity(IMEI). Access to this unique piece of data enables the attackers to divert incoming calls and messages to another device without the user's knowledge.
Bluetooth vendors advise customers with vulnerable Bluetooth devices to either turn them off in areas regarded as unsafe or set them to undiscoverable.[5]This Bluetooth setting allows users to keep their Bluetooth on so that compatible Bluetooth products can be used but other Bluetooth devices cannot discover them.
Because Bluesnarfing is an invasion ofprivacy, it is illegal in many countries.
Bluesnipinghas emerged as a specific form of Bluesnarfing that is effective at longer ranges than normally possible. According toWiredmagazine, this method surfaced at theBlack Hat BriefingsandDEF CONhacker conferences of 2004 where it was shown on theG4techTVshowThe Screen Savers.[6]For example, a "rifle" with a directional antenna,Linux-powered embeddedPC, andBluetoothmodule mounted on aRuger 10/22folding stock has been used for long-range Bluesnarfing.[7]
In the TV seriesPerson of Interest, Bluesnarfing, often mistakenly referred to as Bluejacking in the show and at other times forced pairing and phone cloning, is a common element in the show used to spy on and track the people the main characters are trying to save or stop.
Mark Ciampa (2009), Security+ Guide to Network Security Fundamentals Third Edition. Printed in Canada.Roberto Martelloni'shome pageArchived2017-12-27 at theWayback Machinewith Linux source code of released Bluesnarfer proof-of-concept.
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https://en.wikipedia.org/wiki/Bluesniping
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BlueSoleilis aBluetoothsoftware/driver forMicrosoft Windows,LinuxandWindows CE. It supports Bluetooth chipsets fromCSR,Broadcom,Marvelletc. Bluetoothdongles,PCs,Laptops,PDAs,PNDsandUMPCsare sometimes bundled with a version of this software albeit with limited functionality and OEM licensing. The software is rarely needed on modern computers, as well-functioning Bluetooth drivers for the most widely used Bluetooth chips have been available throughWindows UpdatesinceWindows Vista.
BlueSoleil is developed by the Chinese firm IVT Corporation and the first version was released in 1999. In China, BlueSoleil is marketed as 1000Moons (千月).[1]
BlueSoleil features the following technologies:
A demonstration version of BlueSoleil is available, restricting the device after 2MB data transfer, approximately 1.5 minutes of high-quality audio or 2–4 hours of mouse use. The software must be purchased to enable unlimited use.
BlueSoleil has been distributed over 30 million copies. IVT has also established an interoperability testing centre where it has built up a large library of Bluetooth products which are on the market in order to perform interoperability testing.[2]
Various Bluetooth dongles are delivered with an obsolete or demonstration version of Bluesoleil. New versions are available as a standalone purchase from the vendor's website. Regardless of whether the bundled or the standalone version is purchased, the software enforces licensing restrictions which tie it to the address of a specific Bluetooth dongle.
Bluesoleil works with the main Bluetooth Silicon Vendors hardware, such as Accelsemi,Atheros,CSR, Conwise, 3DSP,Broadcom,Intel,Marvell,NSC,RFMD,SiRFas well as baseband IP such as RivieraWaves BT IP.
If there is no Bluetooth dongle attached to thePCthe Bluetooth logo will begrey,blueif a dongle is attached, andgreenwhen connected to another Bluetooth enabled device.
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https://en.wikipedia.org/wiki/BlueSoleil
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Bluetooth beaconsare hardware transmitters — a class ofBluetooth Low Energy(LE) devices that broadcast their identifier to nearbyportable electronicdevices. The technology enablessmartphones,tabletsand other devices to perform actions when in close proximity to a beacon.
Bluetooth beacons useBluetooth Low Energy proximity sensingto transmit auniversally unique identifier[1]picked up by a compatible app or operating system. The identifier and several bytes sent with it can be used to determine the device's physical location,[2]track customers, or trigger alocation-basedaction on the device such as acheck-in on social mediaor apush notification.
One application is distributing messages at a specificpoint of interest, for example a store, a bus stop, a room or a more specific location like a piece of furniture or a vending machine. This is similar to previously used geopush technology based onGPS, but with a much reduced impact on battery life and much extended precision.
Another application is anindoor positioning system,[3][4][5]which helps smartphones determine their approximate location or context. With the help of a Bluetooth beacon, a smartphone's software can approximately find its relative location to a Bluetooth beacon in a store.Brick and mortarretail stores use the beacons formobile commerce, offering customers special deals throughmobile marketing,[6]and can enablemobile paymentsthroughpoint of salesystems.
Bluetooth beacons differ from some other location-based technologies as the broadcasting device (beacon) is only a 1-way transmitter to the receiving smartphone or receiving device, and necessitates a specific app installed on the device to interact with the beacons. Thus only the installed app, and not the Bluetooth beacon transmitter, can track users.
Bluetooth beacon transmitters come in a variety of form factors, including small coin cell devices, USB sticks, and generic Bluetooth 4.0 capable USBdongles.[7]
The development of the "short-link" radio technology, later named Bluetooth, was initiated in 1989 by Dr. Nils Rydbeck CTO at Ericsson Mobile inLundand Dr.Johan Ullman. The purpose was to develop wireless headsets, according to two inventions byJohan Ullman, SE 8902098–6, issued 1989-06-12 and SE 9202239, issued 1992-07-24. Since its creation the Bluetooth standard has gone through many generations each adding different features. Bluetooth 1.2 allowed for faster speed up to ≈700 kbit/s. Bluetooth 2.0 improved on this for speeds up to 3 Mbit/s. Bluetooth 2.1 improved device pairing speed and security. Bluetooth 3.0 again improved transfer speed up to 24 Mbit/s. In 2010 Bluetooth 4.0 (Low Energy) was released with its main focus being reduced power consumption. Before Bluetooth 4.0 the majority of connections using Bluetooth were two way, both devices listen and talk to each other. Although this two way communication is still possible with Bluetooth 4.0, one way communication is also possible. This one way communication allows a bluetooth device to transmit information but not listen for it. These one way "beacons" do not require a paired connection like previous Bluetooth devices so they have new useful applications.
Bluetooth beacons operate using the Bluetooth 4.0 Low Energy standard so battery powered devices are possible. Battery life of devices varies depending on manufacturer. The Bluetooth LE protocol is significantly more power efficient than Bluetooth Classic. Several chipsets makers, includingTexas Instruments[8]andNordic Semiconductornow supply chipsets optimized for iBeacon use. Power consumption depends on iBeacon configuration parameters of advertising interval and transmit power. Battery life can range between 1–48 months. Apple's recommended setting of 100 ms advertising interval with a coin cell battery provides for 1–3 months of life, which increases to 2–3 years as advertising interval is increased to 900 ms.[9]
Battery consumption of the phones is a factor that must be taken into account when deploying beacon enabled apps. A recent report has shown that
older phones tend to draw more battery power in the vicinity of iBeacons, while the newer phones can be more efficient in the same environment.[10]In addition to the time spent by the phone scanning, number of scans and number of beacons in the vicinity are also significant factors for battery drain.
An energy efficient iBeacon application needs to consider these aspects in order to strike a good balance between app responsiveness and battery consumption.
Bluetooth beacons can also come in the form of USB dongles. These small USB beacons can be powered by a standard USB port which makes them ideal for long term permanent installations.
Bluetooth beacons can be used to send a packet of information that contains a Universally Unique Identifier (UUID). This UUID is used to trigger events specific to that beacon. In the case of Apple's iBeacon the UUID will be recognized by an app on the user device that will trigger an event. This event is fully customizable by the app developer but in the case of advertising the event might be a push notification with an ad. However, with a UID based system the users device must connect to an online server which is capable of understanding the beacons UUID. Once the UUID is sent to the server the appropriate message action is sent to a users device.
Other methods of advertising are also possible with beacons, URIBeacon and Google's Eddystone allow for a URI transmission mode that unlike iBeacons UID doesn't require an outside server for recognition. The URI beacons transmit a URI which could be a link to a webpage and the user will see that URI directly on their phone.[11]
Beacons can be associated with the artpieces in a museum to encourage further interaction. For example, a notification can be sent to user's mobile device when user is in the proximity to a particular artpiece. By sending user the notification, user is alerted with the artpiece in his proximity, and if user indicates their further interest, a specific app can be installed to interact with the encountered artpiece.[12]In general, a native app is needed for a mobile device to interact with the beacon if the beacon uses iBeacon protocol; whereas if Eddystone is employed, user can interact with the artpiece through a physical web URL broadcast by the Eddystone.
Indoor positioning with beacons falls into three categories. Implementations with many beacons per room, implementations with one beacon per room, and implementations with a few beacons per building. Indoor navigation with Bluetooth is still in its infancy but attempts have been made to find a working solution.
With multiple beacons per roomtrilaterationcan be used to estimate a users' position to within about 2 meters.[13]Bluetooth beacons are capable of transmitting their Received Signal Strength Indicator (RSSI) value in addition to other data. This RSSI value is calibrated by the manufacturer of the beacon to be the signal strength of the beacon at a known distance, typically one meter. Using the known output signal strength of the beacon and the signal strength observed by the receiving device an approximation can be made about the distance between the beacon and the device. However this approximation is not very reliable, so for more accurate position tracking other methods are preferred. Since its release in 2010 many studies have been connected using Bluetooth beacons for tracking. A few methods have been tested to find the best way of combining the RSSI values for tracking. Neural networks have been proposed as a good way of reducing the error in estimation.[13]AStigmergicapproach has also been tested, this method uses an intensity map to estimate a users location.[14]Bluetooth LE specification 5.1 added further more precise methods for position determination using multiple beacons.
With only one beacon per room, a user can use their known room position in conjunction with a virtual map of all the rooms in a building to navigate a building. A building with many separate rooms may need a different beacon configuration for navigation. With one beacon in each room a user can use an app to know the room they are in, and a simple shortest path algorithm can be used to give them the best route to the room they are looking for. This configuration requires a digital map of the building but attempts have been made to make this map creation easier.[15]
Beacons can be used in conjunction withpedestrian dead reckoningtechniques to add checkpoints to a large open space.[16]PDR uses a known last location in conjunction with direction and speed information provided by the user to estimate a person's location. This technique can be used to estimate a person's location as they walk through a building. Using Bluetooth beacons as checkpoints the user's location can be recalculated to reduce error. In this way a few Bluetooth beacons can be used to cover a large area like a mall.
Using the device tracking capabilities of Bluetooth beacons, in-home patient monitoring is possible. Using bluetooth beacons a person's movements and activities can be tracked in their home.[17]Bluetooth beacons are a good alternative to in house cameras due to their increased level of privacy. Additionally bluetooth beacons can be used in hospitals or other workplaces to ensure workers meet certain standards. For example, a beacon may be placed at a hand sanitizer dispenser in a hospital – the beacons can help ensure employees are using the station regularly.
One use of beacons is as a "key finder" where a beacon is attached to, for example, a keyring and a smartphone app can be used to track the last time the device came in range.
Another similar use is to track pets, objects (e.g. baggage) or people. The precision and range of BLE doesn't match GPS, but beacons are significantly less expensive. Several commercial and free solutions exist, which are based on proximity detection, not precise positioning. For example, Nivea launched the "kid-tracker" campaign in Brazil back in 2014.[18]
In mid-2013,AppleintroducediBeaconsand experts wrote about how it is designed to help the retail industry by simplifying payments and enabling on-site offers. On December 6, 2013, Apple activated iBeacons across its 254 US retail stores.[19]McDonald's has used the devices to give special offers to consumers in its fast-food stores.[6]As of May 2014, different hardware iBeacons can be purchased for as little as $5 per device to more than $30 per device.[20]Each of these different iBeacons have varying default settings for their default transmit power and iBeacon advertisement frequency. Some hardware iBeacons advertise at as low as 1 Hz while others can be as fast as 10 Hz.[21]
AltBeacon is an open source alternative to iBeacon created by Radius Networks.[22]
URIBeacons are different from iBeacons and AltBeacons because rather than broadcasting an identifier, they send an URL which can be understood immediately.[22]
Eddystoneis Google's standard for Bluetooth beacons. It supports three types of packets, Eddystone-UID, Eddystone-URL, and Eddystone-TLM.[11]Eddystone-UID functions in a very similar way to Apple's iBeacon, however, it supports additional telemetry data with Eddystone-TLM. The telemetry information is sent along with the UID data. The beacon information available includes battery voltage, beacon temperature, number of packets sent since last startup, and beacon uptime.[11]Using the Eddystone protocol, Google had built the now discontinued[23]Google Nearby that allowed Android users to receive beacon notifications without an app.
Although thenear-field communication(NFC) environment is very different and has many non-overlapping applications, it is still compared with iBeacons.
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https://en.wikipedia.org/wiki/Bluetooth_Low_Energy_beacon
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Beaconsare small devices that enable relatively accurate location within a narrow range. Beacons periodically transmit small amounts of data within a range of approximately 70 meters, and are often used for indoor location technology.[1]Compared to devices based onGlobal Positioning System(GPS), beacons provide more accurate location information and can be used for indoor location. Various types of beacons exist, which can be classified based on their type of Beacon protocol, power source and location technology.
In December 2013,AppleannouncediBeacon: the first beacon protocol in the market. iBeacon works with Apple's iOS and Google's Android. The beacon using the iBeacon protocol transmits a so-called UUID. The UUID is a string of 24 numbers, which communicate with an installed Mobile App.[2]
Advantages:
GoogleannouncedEddystonein July 2015, after it was renamed from its former name UriBeacon. Beacons with support from Eddystone are able to transmit three different frame-types, which work with both iOS and Android.[3]A single beacon can transmit one, two or all three frametypes. The three frametypes are:
Advantages:
Radius Networks announced AltBeacon in July 2014. This open source beacon protocol was designed to overcome the issue of protocols favouring one vendor over the other.[4]
Advantages:
The Web & Information Systems engineering lab (WISE) at the Vrije Universiteit Brussel (VUB) announced SemBeacon in September 2023. It is an open source[5]beacon protocol andontologybased on AltBeacon and Eddystone-URL to create
interoperable applications that do not require a local database.[6]
Advantages:
Tecno-World (Pitius Tec S.L., Manufacture-ID 0x015C) announced GeoBeacon in July 2017. This open source beacon protocol was designed for usage in GeoCaching applications due to the very compact type of data storage.[7]
Advantages:
In general, there are three types of power source for beacons:
Most beacons use bluetooth technology to communicate with other devices and retrieve thelocationinformation. Apart from bluetooth technology however, several other location technologies exist. The most common location technologies are the following:
The majority of beacon location devices rely onBluetooth low energy(BLE) technology. Compared to 'classic'Bluetoothtechnology, BLE consumes less power, has a lower range, and transmits less data. BLE is designed for periodic transfers of very small amounts of data.
In July 2015, theWi-Fi Allianceannounced Wi-Fi Aware. Similar to BLE, Wi-Fi Aware has a lower power consumption than regular Wi-Fi and is designed for indoor location purposes.
Whereas most beacon vendors focus on merely one technology, some vendors combine multiple location technologies.
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https://en.wikipedia.org/wiki/Types_of_beacons#AltBeacon_(Radius_Networks)
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iBeaconis a protocol developed byAppleand introduced at theApple Worldwide Developers Conferencein 2013.[1]Various vendors have since made iBeacon-compatible hardware transmitters – typically calledbeacons– a class ofBluetooth Low Energy(BLE) devices that broadcast their identifier to nearbyportable electronicdevices. The technology enablessmartphones,tabletsand other devices to perform actions when in proximity to an iBeacon.[2][3]
iBeacon is based onBluetooth low energy proximity sensingby transmitting auniversally unique identifier[4]picked up by a compatible app or operating system. The identifier and several bytes sent with it can be used to determine the device's physical location,[5]track customers, or trigger alocation-basedaction on the device such as acheck-in on social mediaor apush notification.
iBeacon can also be used with an application as anindoor positioning system,[6][7][8]which helps smartphones determine their approximate location or context. With the help of an iBeacon, a smartphone's software can approximately find its relative location to an iBeacon in a store.Brick and mortarretail stores use the beacons formobile commerce, offering customers special deals throughmobile marketing,[9]and can enablemobile paymentsthroughpoint of salesystems.
Another application is distributing messages at a specificPoint of Interest, for example a store, a bus stop, a room or a more specific location like a piece of furniture or a vending machine. This is similar to previously used geopush technology based onGPS, but with a much reduced impact on battery life and better precision.
iBeacon differs from some other location-based technologies as the broadcasting device (beacon) is only a 1-way transmitter to the receiving smartphone or receiving device, and necessitates a specific app installed on the device to interact with the beacons. This ensures that only the installed app (not the iBeacon transmitter) can track users as they walk around the transmitters.
iBeacon compatible transmitters come in a variety of form factors, including small coin cell devices, USB sticks, and generic Bluetooth 4.0 capable USBdongles.[10]
An iBeacon deployment consists of one or more iBeacon devices that transmit their own unique identification number to the local area. Software on a receiving device may then look up the iBeacon and perform various functions, such as notifying the user. Receiving devices can also connect to the iBeacons to retrieve values from iBeacon's GATT (generic attribute profile) service. iBeacons do not push notifications to receiving devices (other than their own identity). However, mobile software can use signals received from iBeacons to trigger their own push notifications.[11]
Region monitoring (limited to 20 regions on iOS) can function in the background (of the listening device) and has different delegates to notify the listening app (and user) of entry/exit in the region - even if the app is in the background or the phone is locked. Region monitoring also allows for a small window in which iOS gives a closed app an opportunity to react to the entry of a region.
As opposed to monitoring, which enables users to detect movement in-and-out of range of the beacons, ranging provides a list of beacons detected in a given region, along with the estimated distance from the user's device to each beacon.[12]Ranging works only in the foreground but will return (to the listening device) an array (unlimited) of all iBeacons found along with their properties (UUID, etc.)[13]
An iOS device receiving an iBeacon transmission can approximate the distance from the iBeacon. The distance (between transmitting iBeacon and receiving device) is categorized into 3 distinct ranges:[14]
An iBeacon broadcast has the ability to approximate when a user has entered, exited, or lingered in region. Depending on a customer's proximity to a beacon, they are able to receive different levels of interaction at each of these three ranges.[15]
The maximum range of an iBeacon transmission will depend on the location and placement, obstructions in the environment and where the device is being stored (e.g. in a leather handbag or with a thick case). Standard beacons have an approximate range of 70 meters. Long range beacons can reach up to 450 meters.
The frequency of the iBeacon transmission depends on the configuration of the iBeacon and can be altered using device specific methods. Both the rate and the transmit power have an effect on the iBeacon battery life. iBeacons come with predefined settings and several of them can be changed by the developer, including the rate, the transmit power, and the Major and Minor values. The Major and Minor values are settings which can be used to connect to specific iBeacons or to work with more than one iBeacon at the same time. Typically, multiple iBeacon deployment at a venue will have the same UUID, and use the major and minor pairs to segment and distinguish subspaces within the venue. For example, the Major values of all the iBeacons in a specific store can be set to the same value and the Minor value can be used to identify a specific iBeacon within the store.
The Bluetooth LE protocol is significantly more power efficient than Bluetooth Classic. Several chipsets makers, includingTexas Instruments[17]andNordic Semiconductornow supply chipsets optimized for iBeacon use. Power consumption depends on iBeacon configuration parameters of advertising interval and transmit power. A study on 16 different iBeacon vendors reports that battery life can range between 1–24 months. Apple's recommended setting of 100 ms advertising interval with a coin cell battery provides for 1–3 months of life, which increases to 2–3 years as advertising interval is increased to 900 ms.[18]
Battery consumption of the phones is a factor that must be taken into account when deploying beacon-enabled apps. A recent report has shown that
older phones tend to draw more battery in the vicinity of iBeacons, while the newer phones can be more efficient in the same environment.[19]In addition to the time spent by the phone scanning, number of scans and number of beacons in the vicinity are also significant factors for battery drain, as pointed out by theAislelabsreport.[20]In a follow-up report, Aislelabs found a drastic improvement in battery consumption for iPhone 5s, iPhone 5c versus the older model iPhone 4s.
At 10 surrounding iBeacons, iPhone 4s can consume up to 11% of battery per hour whereas iPhone 5s consumes a little less than 5% battery per hour.[21]An energy efficient iBeacon application needs to consider these aspects in order to strike a good balance between app responsiveness and battery consumption.
In mid-2013Appleintroduced iBeacons and experts wrote about how it is designed to help the retail industry by simplifying payments and enabling on-site offers. On December 6, 2013, Apple activated iBeacons across its 254 US retail stores.[22]McDonald'shas used the devices to give special offers to consumers in its fast-food stores.[9]
As of May 2014, different hardware iBeacons can be purchased for as little as $5 per device to more than $30 per device.[23]Each of these different iBeacons have varying default settings for their default transmit power and iBeacon advertisement frequency. Some hardware iBeacons advertise at frequencies as low as 1 Hz while others can be as high as 10 Hz.
iBeacon technology is still in its infancy. One well-reported software quirk exists on 4.2 and 4.3 Android systems whereby the system's bluetooth stack crashes when presented with many iBeacons.[24]This was reportedly fixed in Android 4.4.4.[25]
Bluetooth low energydevices can operate in an advertisement mode to notify nearby devices of their presence.[26]In the simplest form, an iBeacon is a Bluetooth low energy device emitting advertisements following a strict format, that being an Apple-defined iBeacon prefix, followed by a variable UUID, and a major, minor pair.[27]An example iBeacon advertisement frame could look like:
wherefb0b57a2-8228-44cd-913a-94a122ba1206is the UUID.
Since iBeacon advertising is just an application of the general Bluetooth Low Energy advertisement, the above iBeacon can be emitted by issuing the following commands on Linux to a supported Bluetooth 4 Low Energy device on a modern kernel:[28]
For the retransmission interval setting (first of above commands) to work again, the transmission must be stopped with:
Devices running theAndroid operating systemprior to version 4.3 can only receive iBeacon advertisements but cannot emit iBeacon advertisements. Android 5.0 ("Lollipop") added the support for both central and peripheral modes.[29]
Byte 0-2: Standard BLE Flags (Not necessary but standard)
Byte 3-29: Apple Defined iBeacon Data
Unlike iOS, Android does not have native iBeacon support. Due to this, to use iBeacon on Android, a developer either has to use an existing library or create code that parses BLE packets to find iBeacon advertisements.
BLE support was introduced inAndroid Jelly Beanwith major bug fixes inAndroid KitKat. Stability improvements and additional BLE features have been progressively added there after, with a major stability improvement in version 6.01 ofAndroid Marshmallowthat prevents inter-app connection leaking.
By design, the iBeacon advertisement frame is plainly visible.
This leaves the door open for interested parties to capture, copy and reproduce the iBeacon advertisement frames at different physical locations.
This can be done simply by issuing the right sequence of commands to compatible Bluetooth 4.0 USB dongles.
Successful spoofing of Apple store iBeacons was reported in February 2014.[30]This is not a security flaw in the iBeacon per se, but application developers must keep this in mind when designing their applications with iBeacons.
PayPalhas taken a more robust approach, where the iBeacon is purely the start of a complex security negotiation (Challenge–response authentication). This is not likely to be hacked, nor is it likely that it would be disrupted by copies of beacons.[31]
Listening for iBeacon can be achieved using the following commands with a modern Linux distribution:
On another terminal, launch the protocol dump program:
See Bluetooth Core Spec. Volume 4, Part E, 7.7.65.2: LE Meta Event::LE Advertising Report Sub-Event, for details on the hcidump output.
TheMAC addressof the iBeacon along with its iBeacon payload is clearly identifiable. The sequence of commands intechnical detailscan then be used to reproduce the iBeacon frame.
Even though theNFCenvironment is very different, and has many non-overlapping applications, it still compares with iBeacons.
The NFC range is up to 20 cm (7.87 inches) but the optimum range is less than 4 cm (1.57 inches). iBeacons have a significantly higher range.
Not all phones carry NFC chips. Apple's first iPhone model containing NFC chips was the iPhone 6, introduced September 2014, but most modern phones have had Bluetooth 4.0 or later capability for several years prior to this.
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Eddystonewas aBluetooth Low Energy beaconprofile released byGooglein July 2015. In December 2018 Google stopped delivering both Eddystone and Physical Web beacon notifications. TheApache 2.0-licensed,cross-platform, and versioned profile contained several frame types, includingEddystone-UID,Eddystone-URL, andEddystone-TLM.[1]Eddystone-URLwas used by thePhysical Webproject, whereasEddystone-UIDwas typically used by native apps on a user's device, including Google's first party apps such asGoogle Maps.[2]
The format was named after theEddystone Lighthousein the UK, motivated by the simplicity of a lighthouse-signal and its one-directional nature.[3]
Though similar to theiBeaconprofile released byApplein 2013, Eddystone can be implemented without restriction. Eddystone also contains a telemetry frame (Eddystone-TLM) designed for reporting on a beacon's health, including, for example, battery level. Like other beacon technology, beacons with Eddystone can give devices a better indication of what objects and places are around them.[4]Importantly, beacons do not generally accept connections from other devices, meaning that the beacon itself cannot record what devices are in its vicinity. In many cases, the simplicity of the beacon frame means that an app (for exampleGoogle Chrome) is required in order to interpret the beacon's signal.
Nearby Messages is the API that can be used off of this protocol to receive data that is stored within beacons. Differing from iBeacon, Google beacons use not only Bluetooth but also WiFi and near ultrasonic sounds to communicate between devices.[5]
Eddystone has 4 frame types.
In tandem with the Eddystone, Google launched the Google beacon platform. The platform includes the Proximity Beacon API designed to associate content with individual beacons.[11]The Proximity Beacon API fronts a registry of beacons where extra information (known as "attachments"), useful to developers' applications, can be associated with individual beacon IDs. Several attachments can be associated with a single beacon. Attachments can be updated in real-time and can be retrieved by an app using the Nearby API inAndroid(throughGoogle Play Services) and the Nearby library foriOS.
Google's navigation platformWazehas deployed Eddystone beacons in tunnels around the world (where GPS would not work)[12]
They transmit the following data:
They will ignore this information from any beacons that do not use an ID number belonging to Waze.[13]
In 2018, the security of the platform came under scrutiny from privacy advocates with concerns over how the audio component of the beacon is recorded, stored and ultimately filtered to just the ultrasonic portion of the signal.[14]Without proper informed consent, users may find their conversations are illegally being recorded by beacons using the Eddystone protocol in collaboration with the Nearby Messages API.
In December 2018, Google stopped delivering both Eddystone and Physical Web beacon notifications.[15]The low number of users and the poor user experience were the reasons to discontinued the Eddystone beacons. Google continues to enable access to the beacon dashboard and can deliver proximity-based experiences similar to Nearby Notifications via third-party apps using the Proximity Beacons API.
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Bluetooth Meshis a computermesh networkingstandardbased onBluetooth Low Energythat allows for many-to-many communication over Bluetooth radio. The Bluetooth Mesh specifications were defined in the Mesh Profile[1]and Mesh Model[2]specifications by theBluetooth Special Interest Group(Bluetooth SIG). Bluetooth Mesh was conceived in 2014[3]and adopted on July 13, 2017(2017-07-13).[4]
Bluetooth Mesh is amesh networkingstandard that operates on aflood networkprinciple. It's based on the nodes relaying the messages: every relay node that receives a network packet that
can be retransmitted with TTL = TTL - 1. Message caching is used to prevent relaying recently seen messages.
Communication is carried in the messages that may be up to 384 bytes long, when using Segmentation and Reassembly (SAR) mechanism, but most of the messages fit in one segment, that is 11 bytes. Each message starts with an opcode, which may be a single byte (for special messages), 2 bytes (for standard messages), or 3 bytes (for vendor-specific messages).
Every message has a source and a destination address, determining which devices process messages. Devices publish messages to destinations which can be single things / groups of things / everything.
Each message has a sequence number that protects the network against replay attacks.
Each message is encrypted and authenticated. Two keys are used to secure messages: (1) network keys – allocated to a single mesh network, (2) application keys – specific for a given application functionality, e.g. turning the light on vs reconfiguring the light.
Messages have atime to live(TTL). Each time message is received and retransmitted, TTL is decremented which limits the number of "hops", eliminating endless loops.
Bluetooth Mesh has a layered architecture, with multiple layers as below.
Nodes that support the various features can be formed into a particular mesh network topology.
to enable larger networks.
advertising bearers.
duty cycles only in conjunction with a node supporting the Friend feature.
messages destined for those nodes.
The practical limits of Bluetooth Mesh technology are unknown. Some limits that are built into the specification include:
Number of virtual groups is 2128.
As of version 1.0 of Bluetooth Mesh specification,[2]the following standard models and model groups have been defined:
Foundation models have been defined in the core specification. Two of them are mandatory for all mesh nodes.
Provisioning is a process of installing the device into a network. It is a mandatory step to build a Bluetooth Mesh network.
In the provisioning process, a provisioner securely distributes a network key and a unique address space for a device. The provisioning protocol uses P256 Elliptic CurveDiffie-HellmanKey Exchange to create a temporary key to encrypt network key and other information. This provides security from a passive eavesdropper.
It also provides various authentication mechanisms to protect network information, from an active eavesdropper who usesman-in-the-middle attack, during provisioning process.
A key unique to a device known as "Device Key" is derived from elliptic curve shared secret on provisioner and device during the provisioning process. This device key is used by the provisioner to encrypt messages for that specific device.
The security of the provisioning process has been analyzed in a paper presented during theIEEE CNS2018 conference.[5]
The provisioning can be performed using a Bluetooth GATT connection or advertising using the specific bearer.[1]
Free softwareandopen source softwareimplementations include the following:
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https://en.wikipedia.org/wiki/Bluetooth_mesh_networking
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Continua Health Allianceis an international non-profit, open industry group of nearly 240 healthcare providers, communications, medical, and fitness device companies.
Continua was a founding member of Personal Connected Health Alliance which was launched in February 2014 with other founding members mHealth SUMMIT andHIMSS.
Continua Health Alliance is an international not-for-profit industry organization enabling end-to-end, plug-and-play connectivity of devices and services for personal health management and healthcare delivery. Its mission is to empower information-driven health management and facilitate the incorporation of health and wellness into the day-to-day lives of consumers. ts activities include a certification and brand support program, events and collaborations to support technology and clinical innovation, as well as outreach to employers, payers, governments and care providers. With nearly 220 member companies reaching across the globe, Continua comprises technology, medical device and healthcare industry leaders and service providers dedicated to making personal connected health a reality.
Continua Health Alliance is working toward establishing systems ofinteroperabletelehealth devices and services in three major categories: chronicdisease management, aging independently, and health andphysical fitness.
Continua Health Alliance version 1 design guidelines are based on proven connectivitytechnical standardsand includeBluetoothfor wireless andUSBfor wired device connection. The group released the guidelines to the public in June 2009.[1]
The group is establishing aproduct certificationprogram using its recognizablelogo, the Continua Certified Logo program, signifying that the product is interoperable with other Continua-certified products. Products made under Continua Health Alliance guidelines will provide consumers with increased assurance of interoperability between devices, enabling them to more easily share information with caregivers and service providers.
Through collaborations withgovernment agenciesand other regulatory bodies, Continua works to provide guidelines for the effective management of diverse products and services from a global network of vendors. Continua Health Alliance products make use of theISO/IEEE 11073 Personal Health Data (PHD) Standards.
Continua design guidelines are not available to the public without signing aNon-disclosure agreement. Continua's guidelines help technology developers build end-to-end, plug-and-play systems more efficiently and cost effectively.
Continua Health Alliance was founded on June 6, 2006[2]
Continua Health alliance performed its first public demonstration of interoperability on October 27, 2008 at the Partners Center for Connected Health 5th Annual Connected Health Symposium in Boston.[3]
Continua Health Alliance certified its first product, the Nonin 2500 PalmSAT handheld pulse oximeter with USB, on January 26, 2009.[4]
By the end of December 2014 there are more than 100 certified products.[5]
Continua selectedBluetooth Low EnergyandZigbeewireless protocols as the wireless standards for its Version 2 Design Guidelines which have been released. Bluetooth Low Energy is to be used for low-power mobile devices. Zigbee will be used for networked low-power sensors such as those enabling independent living.[6]
Beginning in 2012, Continua invites non-members to request a copy of its Design Guidelines after signing a non-disclosure agreement.[7]
Continua has working groups and operations in the U.S., EU, Japan, India and China.
Continua Health Alliance currently has nearly 220 member companies.[8]
Continua's Board of Directors is currently composed of the following companies:[9]
The organisation is primarily staffed by volunteers from the member organisations that are organised into working groups that address the goals of the alliance. Below the board of directors sit the following main working groups:[10]
The Continua Alliance website contains a full listing of member organisations, a directory of qualified products, and a clear statement of their mission.
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https://en.wikipedia.org/wiki/Continua_Health_Alliance
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DASH7 Alliance Protocol(D7A) is an open-source wireless sensor and actuator network protocol, which operates in the 433 MHz, 868 MHz and 915 MHz unlicensedISM/SRD band. DASH7 provides multi-yearbattery life, range of up to 2 km, low latency for connecting with moving things, a very small open-sourceprotocol stack,AES128-bit shared-key encryption support, and data transfer of up to 167 kbit/s. The DASH7 Alliance Protocol is the name of the technology promoted by the non-profit consortium called the DASH7 Alliance.
DASH7 Alliance Protocol originates from theISO/IEC 18000-7standard describing a 433 MHzISM bandair interface for active RFID. This standard was mainly used for military logistics.
The DASH7 Alliance re-purposed the original 18000-7 technology in 2011 and made it evolve toward a wireless sensor network technology for commercial applications. The DASH7 Alliance Protocol covers all sub-GHz ISM bands, making it available globally. The name of the new protocol was derived from the section seven denoted as -7 (/dæʃˈsɛvən/) of the original standard document.
The current version of the DASH7 Alliance protocol is no longer compliant with the ISO/IEC 18000-7 standard.[1]
In January 2009, theU.S. Department of Defenseannounced the largest RFID award in history, a $429 million contract for DASH7 devices, to four prime contractors, namelySavi Technology,Northrop Grumman Information Technology,UnisysandSystems & Processes Engineering Corp. (SPEC).[2]
In March 2009, the DASH7 Alliance, a non-profit industry consortium to promote interoperability among DASH7-compliant devices, was announced, and as of July 2010 has more than 50 participants in 23 countries. It was meant to be similar to what theWi-Fi Alliancedoes forIEEE 802.11, forwireless sensor networking.
In April 2011, the DASH7 Allianceannouncedadoption of DASH7 Mode 2, based on the ISO 18000-7 standard that makes better use of modern silicon to achieve faster throughput, multi-hop, lower latency, better security, sensor support, and a built-in query protocol.
In March 2012, the DASH7 Allianceannouncedthat it was making the DASH7 Mode 2 specification available to non-members.
In July 2013, the DASH7 Alliance announced the DASH7 Alliance Protocol Draft 0.2.
In May 2015, the DASH7 Alliancepublicly releasedv1.0 of the DASH7 Alliance Protocol.
In January 2017, the DASH7 Alliance publicly released the v1.1 of the DASH7 Alliance Protocol. The version constitutes a major update of v1.0, in particular in the area of security and interoperability.
Compared with other wireless data technologies:[3]
868/915 MHz: +27dBm
166.667 kbit/s / 9.6 kbit/s, 55.55 kbit/s or
166.667 kbit/s
Tree
Regulations (from 1 mW to 1 W)
Aggregation), up to
65,535 Bytes (with
Aggregation)
per Sector (Assumes 8
channel Access Point)/AP aggregates to 156 kbit/s
per Sector (Assumes 8
channel Access Point)
supported with an RPMA
extender
typical
US:<+27 dBm
US:900bit/s-100 kbit/s/900bit/s-100 kbit/s
30 km (rural)
20 byte payload
10 km (urban)
messages/day/max. 4 messages of 8
bytes/day
10 Mbit/s/1 kbit/s to
10 Mbit/s
100 kbit/s/200 bit/s to
100 kbit/s
Networks based on DASH7 differ from typical wire-line and wireless networks utilizing a "session". DASH7 networks serve applications in which low power usage is essential and data transmission is typically much slower and/or sporadic, like basictelemetry. Thus, instead of replicating a wire-line "session", DASH7 was designed with the concept ofB.L.A.S.T.:
D7A utilizes the 433, 868 and 916 MHz frequencies,[6]which are globally available and license-free.
Sub 1-GHz is ideal for wirelesssensornetworking applications, since it penetrates concrete and water, but also has the ability to propagate over very long ranges without requiring a large power draw on a battery. The low input current of typical tag configurations allows operating on coin cell orthin-filmbatteries.
Unlike most activeRFIDorLPWANtechnologies, DASH7 supports tag-to-tag communications.
Localization techniques can be applied to DASH7 endpoints. An accuracy of 1 m using DASH7 beacons at 433 MHz has been achieved in a lab experiment.[7]
DASH7 supports a built-in query protocol that minimizes "round trips" for most messaging applications that results in lower latency and higher network throughput.
DASH7 provides a link budget of up to 140 dB with 27 dBm transmission power, which positions the technology as medium-range, compared to short-range (Bluetooth,Wi-Fi, ...) and long-range (LoRaWAN, SigFox). Note that higher ranges are always obtained at the expense of per-bit power consumption and transmission duration. Low-power long-range technologies are generally not truly bi-directional, as the regular scanning duty is pretty high. In this context, DASH7 is a very good compromise between range, power consumption, and bi-directionality and is very suitable for industrial applications with effective range of 100 to 500 m.
In line-of-sight situations, DASH7 devices today advertise read ranges of 1 kilometer or more, however, ranges of up to 10 km have been tested bySavi Technologyand are easily achievable in theEuropean Union, where governmental regulations are less constrained than in the USA.
The DASH7 Alliance is currently working on a certification program that functionally tests the DASH7 devices. The certification is composed of a set of test scenarios covering transactions in different stack configurations (channel, QoS, security). The physical wireless interface is not covered by the certification and will have to comply to local radio regulations.
The DASH7 Alliance policy forbids the addition of proprietary or licensable modulation techniques in the official DASH7 Alliance Protocol. However, the layered structure of the protocol allows simple integration of alternative modulations, such as LoRa, under thenetwork layer(D7ANL).
Similar to other networking technologies that began with the defense sector,e.g., the Defense Advanced Research Projects Agency (DARPA) funding ARPANET, the precursor to the Internet, DASH7 is similarly suited to a wide range of applications in development or being deployed, including:
The goal of the project is to provide a reference implementation of theDASH7 Alliance protocol.[10]This implementation should focus on completeness, correctness and being easy to understand. Performance and code size are less important aspects. For clarity, a clear separation between the ISO layers is maintained in the code. The project is available on GitHubWelcomeand is licensed under the Apache License, version 2.0.
DASH7 Mode 2developers benefit from the open-source firmware library calledOpenTag, which provides developers with a "C"-based environment in which to develop DASH7 applications quickly. So in addition to DASH7 (ISO 18000-7) being an open source, ISO standard, OpenTag is an open-source stack that is quite unique relative to other wireless sensor networking (e.g. ZigBee) and active RFID (e.g. proprietary) options elsewhere in the marketplace today. Even though OpenTag is an open-source project, people may not be able to use it free of charge. As of August 2015, there is no evidence to suggest that OpenTag bears a royalty, although current versions ofOpenTag licenseArchived2013-12-31 at theWayback Machinedo include a provision permittingRANDlicensing.
DASH7 developers receive support from thesemiconductorindustry including multiple options, withTexas Instruments,ST Microelectronics,Silicon Labs,SemtechandAnalog Devicesall offering DASH7-enabled hardware development kits or system-on-a-chip products.
Many companies are members of the DASH7 Alliance to produce DASH7-compliant hardware products:
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https://en.wikipedia.org/wiki/DASH7
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Aheadsetis a combination ofheadphoneandmicrophone. Headsets connect over atelephoneor to acomputer, allowing the user to speak and listen while keeping both hands free. They are commonly used in customer service and technical support centers, where employees can converse with customers whiletypinginformation into a computer. They are also common amongcomputer gamersand let them talk with each other and hear others while using theirkeyboardsandmiceto play the game.
Telephone headsets generally useloudspeakerswith a narrowerfrequency rangethan those also used for entertainment.[1]Stereo computer headsets, on the other hand, use 32-ohm speakers with a broader frequency range.
Headsets are available in single-earpiece and double-earpiece designs. Double-earpiece headsets may supportstereosound or use the samemonauralaudio channel for both ears. Single-earpiece headsets free up one ear, allowing better awareness of surroundings.Telephoneheadsets are monaural, even for double-earpiece designs, because telephone offers only single-channel input and output.
The microphone arm of headsets may carry an external microphone or be of the voice tube type. External microphone designs have the microphone housed in the front end of the microphone arm. Voicetube designs are also called internal microphone design, and have the microphone housed near the earpiece, with a tube carrying sound to the microphone.
Most external microphone designs are of eitheromnidirectionalornoise-cancelingtype. Noise-canceling microphone headsets use abi-directional microphoneas elements. A bi-directional microphone's receptive field has two angles only. Its receptive field is limited to only the front and the direct opposite back of the microphone. This creates an "8" shape field, and this design is the best method for picking up sound only from a close proximity of the user, while not picking up most surrounding noises.
Omni-directional microphones pick up the complete 360-degree field, which may include much extraneous noise.
Standard headsets with a headband worn over the head are known asover-the-head headsets. Headsets with headbands going over the back of the user's neck are known asbackwear-headsetsorbehind-the-neck headsets. Headsets worn over the ear with a soft ear-hook are known asover-the-ear headsetsorearloop headsets. Convertible headsets are designed so that users can change the wearing method by re-assembling various parts. There are alsounder-the-chin headsetssimilar to the headphones that stenographers wear.
Headsets earpieces may be for either one or both ears. They generally come with one of 3 styles:
Telephone headsets connect to afixed-linetelephone system. A telephone headset functions by replacing thehandsetof a telephone. Headsets for standard corded telephones are fitted with a standard4P4Ccommonly called an RJ-9 connector. Headsets are also available with 2.5mm jack sockets for many DECT phones and other applications. Cordlessbluetoothheadsets are available and often used withmobile telephones. Headsets are widely used for telephone-intensive jobs, in particular bycall centreworkers. They are also used by anyone wishing to hold telephone conversations with both hands free.
Not all telephone headsets are compatible with all telephone models. Because headsets connect to the telephone via the standard handset jack, the pin-alignment of the telephone handset may be different from the default pin-alignment of the telephone headset. To ensure a headset can properly pair with a telephone, telephone adapters or pin-alignment adapters are available. Some of these adapters also provide mute function and switching between handset and headset.
For older models of telephones, the headset microphoneimpedanceis different from that of the original handset, requiring a telephone amplifier to impedance-match the telephone headset. A telephone amplifier provides basic pin-alignment similar to a telephone headset adapter, but it also offers soundamplificationfor the microphone as well as the loudspeakers. Most models of telephone amplifiers offer volume control for the loudspeaker as well as a microphone, mute function and switching between handset and headset. Telephone amplifiers are powered through batteries orAC adapters.
Most telephone headsets have a Quick Disconnect (QD) cable, allowing fast and easy disconnection of the headset from the telephone without having to remove the headset.
AHandset lifteris a device that automatically lifts or replaces ahandsetoff/on atelephone. It is usually connected to awireless headsetand allows cordless headset use on technically primitive desk phones.
Some phones only have a mechanical means of switchhook operation. The lifter allows cordless headsets to be used remotely with such phones. The phone user presses the appropriate headset button to either answer a call or terminate a call. The headset's base station's interface with the handset lifter will take the appropriate action - lift or replace the handset.[2]
The use of a handset lifter is considered archaic by most technical professionals. Technology from decades ago eliminated the need for such device, however many phones, including modern IP phones, still do not have discrete circuitry for switchhook operation.
Computer headsets generally come in two connection types: standard 3.5 mm andUSBconnection. General 3.5 mm computer headsets come with two 3.5 mm connectors: one connecting to the microphone jack and one connecting to the headphone/speaker jack of the computer. 3.5 mm computer headsets connect to the computer via asound card, which converts thedigital signalof the computer to ananalog signalfor the headset. USB computer headsets connect to the computer via a USB port, and the audio conversion occurs in the headset or in the control unit of the headset.
Gaming headsets for computers are specifically designed for gaming and provide some additional features that can be beneficial for gamers. These features include game-specific sound modes, aesthetic designs inspired by popular games or themes, detachable microphones, and RGB lighting.[3]
Mobile (cellular) phone headsets are often referred to ashandsfree. Older mobile phones used a single earphone with a microphone module connected in the cable. For music-playing mobile phones, manufacturers may bundle stereo earphones with a microphone. There are also third-party brands which may provide better sound quality or wireless connectivity.
Mobile headsets come in a range of wearing-styles, including behind-the-neck, over-the-head, over-the-ear, and lightweight earbuds. Some aftermarket mobile headsets come with a standard 2.5 mm plug different from the phone's audio connector, so users have to purchase an adapter. A USB headset for a computer also cannot be directly plugged into a phone's orportable media player's micro-USB slot.Smartphonesoften use a standard 3.5 mm jack, so users may be able to directly connect the headset to it. There are however different pin-alignment to the 3.5mm plug, mainly OMTP and CTIA, so a user should find out which settings their device uses before buying a headphone/headset.
Many wireless mobile headsets useBluetoothtechnology, supported by many phones and computers, sometimes by connecting a Bluetooth adapter to a USB port. Since version 1.1 Bluetooth devices can transmit voice calls and play several music and video formats, but audio will not be played in stereo unless the cell phone or media device, and the headset, both have theA2DPprofile.
In 2019,wirelessheadsets were a new trend for business and consumer communications. There are a number of wireless products, and they usually differ according to application and power management. The first wireless headsets were jointly invented byNASAandPlantronicsduringApollo programto improve astronaut's communications during mission.[4][5]
Digital Enhanced Cordless Telecommunications(DECT) is one of the most common standards for cordless telephones. It uses 1.88 to 1.90 GHzRF(European Version) or 1.92 to 1.93 GHz RF (US Version). Different countries have regulations for the bandwidth used in DECT, but most have pre-set this band for wireless audio transmission. The most common profile of DECT isGeneric access profile(GAP), which is used to ensure common communication between base station and its cordless handset. This common platform allows communication between the two devices even if they are from different manufacturers. For example, a Panasonic DECT base-station theoretically can connect to a Siemens DECT Handset. Based on this profile, developers such asPlantronics,JabraorAccutonehave launched wireless headsets which can directly pair with any GAP-enabled DECT telephones. So, users with a DECT Wireless Headset can pair it with their home DECT phones and enjoy wireless communication.[6]
Because DECT specifications are different between countries, developers who use the same product across different countries have launched wireless headsets which use2.4GHzRF as opposed to the 1.89 or 1.9 GHz in DECT. Almost all countries in the world have the 2.4 GHz band open for wireless communications, so headsets using this RF band is sellable in most markets. However, the 2.4 GHz frequency is also the base frequency for many wireless data transmissions, i.e.,Wireless LAN,Wi-Fi,Bluetooth..., the bandwidth may be quite crowded, so using this technology may be more prone to interference.
Because 2.4 GHz Wireless Headsets cannot directly "talk" to any standard cordless telephones, an extra base-unit is required for this product to function. Most 2.4 GHz Wireless Headsets come in two units, a wireless headset and a wireless base-station, which connects to your original telephone unit via the handset jack. The wireless headset communicates with the base-station via 2.4 GHz RF, and the voice signals are sent or received via the base unit to the telephone unit. Some products will also offer an automatichandset lifter, so the user can wirelessly lift the handset off the telephone by pressing the button on the wireless headset.
Bluetoothtechnology is widely used for short-range voice transmission. While it can be and is used for data transmission, the short range (due to using low power to reduce battery drain) is a limiting factor. A very common application is a hands-free Bluetooth earpiece for a phone which may be in a user's pocket.
There are two types of Bluetooth headsets. Headsets using Bluetooth v1.0 or v1.1 generally consist of a single monaural earpiece, which can only access Bluetooth's headset/handsfree profile. Depending on the phone's operating system, this type of headset will either play music at a very low quality (suitable for voice) or will be unable to play music at all.
Headsets with theA2DPprofile can play stereo music with acceptable quality.[7]Some A2DP-equipped headsets automatically de-activate the microphone function while playing music; if these headsets are paired to a computer via Bluetooth connection, the headset may disable either the stereo or the microphone function. ModernAirPodsalso have[8]a microphone to use for calls and interactions withSiridigital assistant.
Desktop devices usingBluetoothtechnology are available. With a base station that connects via cables to the fixed-line telephone and also the computer via sound card, users with any Bluetooth headset can pair their headset to the base station, enabling them to use the same headset for both fixed-line telephone and computer VoIP communication. This type of device, when used together with a multiple-point Bluetooth headset, enables a single Bluetooth headset to communicate with a computer and both mobile and landline telephones.
Some Bluetooth office headsets incorporate Class 1 Bluetooth into the base station so that, when used with a Class 1 Bluetooth headset, the user can communicate from a greater distance, typically around 100 feet compared to the 33 feet of the more usual Class 2 Bluetooth headset. Many headsets supplied with these base stations connect to cellphones via Class 2 Bluetooth, however, restricting the range to about 33 feet.
Bone conductionheadphones/setstransmitsoundto theinner earprimarily through thebonesof theskull, allowing the hearer to perceive audio content without blocking theear canal. Bone conduction transmission occurs constantly as sound waves vibrate bone, specifically the bones in the skull, although it is hard for the average individual to distinguish sound being conveyed through the bone as opposed to the sound being conveyed through the air via the ear canal. Intentional transmission of sound through bone can be used with individuals with normal hearing — as with bone-conduction headphones — or as a treatment option for certain types of hearing impairment. Bone generally conveys lower-frequency sounds better than higher frequency sound. These headsets/phones can be wired or wireless.[9][10]
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Ahotspotis a physical location where people can obtainInternet access, typically usingWi-Fitechnology, via awireless local-area network(WLAN) using arouterconnected to anInternet service provider.
Public hotspots may be created by a business for use by customers, such ascoffee shopsor hotels. Public hotspots are typically created fromwireless access pointsconfigured to provide Internet access, controlled to some degree by the venue. In its simplest form, venues that havebroadband Internet accesscan create public wireless access by configuring anaccess point(AP), in conjunction with a router to connect the AP to the Internet. A single wireless router combining these functions may suffice.[1]
A private hotspot, often calledtethering, may be configured on a smartphone or tablet that has anetworkdata plan, to allow Internet access to other devices viapassword,Bluetooth pairing, or through themoeexprotocol overUSB, or even when both the hotspot device and the device[s] accessing it are connected to the same Wi-Fi network but one which does not provide Internet access. Similarly, a Bluetooth orUSB OTGcan be used by a mobile device to provide Internet access via Wi-Fi instead of a mobile network, to a device that itself has neither Wi-Fi nor mobile network capability passwords.
The public can use alaptopor other suitable portable device to access the wireless connection (usuallyWi-Fi) provided. The iPass 2014 interactive map, that shows data provided by the analysts Maravedis Rethink, shows that in December 2014 there are 46,000,000 hotspots worldwide and more than 22,000,000 roamable hotspots. More than 10,900 hotspots are on trains, planes and airports (Wi-Fi in motion) and more than 8,500,000 are "branded" hotspots (retail, cafés, hotels). The region with the largest number of public hotspots is Europe, followed by North America and Asia.[2]
Libraries throughout the United States are implementing hotspot lending programs to extend access to online library services to users at home who cannot afford in-home Internet access or do not have access to Internet infrastructure. TheNew York Public Librarywas the largest program, lending out 10,000 devices to library patrons.[3]Similar programs have existed in Kansas,[4]Maine,[5]and Oklahoma;[6]and many individual libraries are implementing these programs.[7]
Wi-Fi positioningis a method forgeolocationbased on the positions of nearby hotspots.[8]
Security is a serious concern in connection with public and private hotspots. There are three possible attack scenarios. First, there is the wireless connection between the client and the access point, which needs to beencrypted, so that the connection cannot be eavesdropped or attacked by aman-in-the-middle attack. Second, there is the hotspot itself. The WLAN encryption ends at the interface, then travels its network stack unencrypted and then, third, travels over the wired connection up to theBRASof the ISP.
Depending upon the setup of a public hotspot, the provider of the hotspot has access to the metadata and content accessed by users of the hotspot. The safest method when accessing the Internet over a hotspot, with unknown security measures, isend-to-end encryption. Examples of strong end-to-end encryption areHTTPSandSSH.
Some hotspotsauthenticateusers; however, this does not prevent users from viewing network traffic usingpacket sniffers.[9]
Some vendors provide a download option that deploysWPAsupport. This conflicts with enterprise configurations that have solutions specific to their internalWLAN.
TheOpportunistic Wireless Encryption(OWE) standard providesencrypted communicationin open Wi-Fi networks, alongside theWPA3standard,[10]but is not yet widely implemented.
New York City introduced a Wi-Fi hotspot kiosk calledLinkNYCwith the intentions of providing modern technology for the masses as a replacement to a payphone.[11]Businesses complained they were a homeless magnet and CBS news observed transients with wires connected to the kiosk lingering for an extended period.[12]It was shut down following complaints about transient activity around the station and encampments forming around it.[11]Transients/panhandlerswere the most frequent users of the kiosk since its installation in early 2016 spurring complaints about public viewing of pornography and masturbation.[13]
Public hotspots are often found atairports,bookstores, coffee shops,department stores,fuel stations,hotels,hospitals,libraries, publicpay phones,restaurants,RV parksand campgrounds,supermarkets,train stations, and other public places. Additionally, manyschoolsanduniversitieshavewireless networkson their campuses.
According to statista.com, in the year 2022, there are approximately 550 million free Wi-Fi hotspots around the world.[14]TheU.S. NSAwarns against connecting to free public Wi-Fi.[15]
Free hotspots operate in two ways:
A commercial hotspot may feature:
Many services provide payment services to hotspot providers, for a monthly fee or commission from the end-user income. For example,Amazingportscan be used to set up hotspots that intend to offer both fee-based and free internet access, andZoneCDis aLinux distributionthat provides payment services for hotspot providers who wish to deploy their own service.[citation needed]
Roamingservices are expanding among major hotspot service providers. With roaming service the users of a commercial provider can have access to other providers' hotspots, either free of charge or for extra fees, which users will usually be charged on an access-per-minute basis.[citation needed]
Many Wi-Fi adapters built into or easily added to consumer computers and mobile devices include the functionality to operate as private or mobile hotspots, sometimes referred to as "mi-fi".[18]The use of a private hotspot to enable other personal devices to access theWAN(usually but not always theInternet) is a form ofbridging, and known as tethering. Manufacturers andfirmwarecreators can enable this functionality in Wi-Fi devices on many Wi-Fi devices, depending upon the capabilities of the hardware, and most modern consumer operating systems, includingAndroid,Apple OS X10.6 and later,[19]Windows,[20]andLinux[citation needed]include features to support this. Additionally wireless chipset manufacturers such asAtheros,Broadcom,Inteland others, may add the capability for certain Wi-FiNICs, usually used in a client role, to also be used for hotspot purposes. However, some service providers, such as AT&T,[21]Sprint,[22]and T-Mobile[23]charge users for this service or prohibit and disconnect user connections if tethering is detected.[citation needed]
Third-party software vendors offer applications to allow users to operate their own hotspot, whether to access the Internet when on the go, share an existing connection, or extend the range of another hotspot.
Hotspot 2.0, also known as HS2 and Wi-Fi Certified Passpoint,[24]is an approach to public access Wi-Fi by theWi-Fi Alliance. The idea is for mobile devices to automatically join a Wi-Fi subscriber service whenever the user enters a Hotspot 2.0 area, in order to provide better bandwidth and services-on-demand to end-users and relieve carrier infrastructure of some traffic.
Hotspot 2.0 is based on theIEEE 802.11ustandard, which is a set of protocols published in 2011 to enable cellular-like roaming. If the device supports 802.11u and is subscribed to a Hotspot 2.0 service it will automatically connect and roam.[25][26][27]
The "user-fairness model" is a dynamic billing model, which allows volume-based billing, charged only by the amount of payload (data, video, audio). Moreover, the tariff is classified by net traffic and user needs.[31][citation needed]
If the net traffic increases, then the user has to pay the next higher tariff class. The user can be prompted to confirm that they want to continue the session in the higher traffic class.[dubious–discuss]A higher class fare can also be charged for delay sensitive applications such as video and audio, versus non time-critical applications such as reading Web pages and sending e-mail.
The "User-fairness model" can be implemented with the help of EDCF (IEEE 802.11e). An EDCF user priority list shares the traffic in 3 access categories (data, video, audio) and user priorities (UP).[31]
SeeService-oriented provisioningfor viable implementations.
Depending upon the set up of a public hotspot, the provider of the hotspot has access to the metadata and content accessed by users of the hotspot, and may have legal obligations related to privacy requirements and liability for use of the hotspot for unlawful purposes.[32]In countries where the internet is regulated orfreedom of speechmore restricted, there may be requirements such as licensing, logging, or recording of user information.[citation needed]Concerns may also relate tochild safety, andsocial issuessuch as exposure to objectionable content, protection againstcyberbullyingand illegal behaviours, and prevention of perpetration of such behaviors by hotspot users themselves.
TheData Retention Directivewhich required hotspot owners to retain key user statistics for 12 months was annulled by the Court of Justice of the European Union in 2014. TheDirective on Privacy and Electronic Communicationswas replaced in 2018 by theGeneral Data Protection Regulation, which imposes restrictions on data collection by hotspot operators.
Public access wirelesslocal area networks(LANs) were first proposed by Henrik Sjoden at the NetWorld+Interop conference in TheMoscone Centerin San Francisco in August 1993.[33]Sjoden did not use the term "hotspot" but referred to publicly accessible wireless LANs.
The first commercial venture to attempt to create a public local area access network was a firm founded in Richardson, Texas known as PLANCOM (Public Local Area Network Communications). The founders of the venture, Mark Goode, Greg Jackson, and Brett Stewart dissolved the firm in 1998, while Goode and Jackson createdMobileStar Networks. The firm was one of the first to sign such public access locations as Starbucks,[34]American Airlines,[35]and Hilton Hotels.[36]The company was sold to Deutsche Telecom in 2001, who then converted the name of the firm into "T-Mobile Hotspot". It was then that the term "hotspot" entered the popular vernacular as a reference to a location where a publicly accessible wireless LAN is available.
ABI Researchreported there was a total of 4.9 million global Wi-Fi hotspots in 2012.[37]In 2016 theWireless Broadband Alliancepredicted a steady annual increase from 5.2m public hotspots in 2012 to 10.5m in 2018.[38]
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Java APIs forBluetoothWireless Technology (JABWT) is aJ2MEspecification forAPIsthat allowsJavaMIDletsrunning on embedded devices such as mobile phones to use Bluetooth for short-range wireless communication. JABWT was developed as JSR-82 under theJava Community Process.[1]
JSR 82 implementations forJava 2 Platform Standard Edition(J2SE) are also available.
The original Java Specification Request (JSR-82) was submitted byMotorolaandSun Microsystems,[2]and approved by the Executive Committee for J2ME in September 2000. JSR-82 provided the first standardized Java API for Bluetooth protocols, allowing developers to write applications using Bluetooth that work on all devices conforming to the specification. The first version of JSR-82 was released in March 2002. The most recent update to JSR-82, Maintenance Draft Review 4, was released in March 2010. The specification, reference implementation, andTechnology Compatibility Kit(TCK) are maintained at Motorola Open Source.[3]
JABWT provides support for discovery of nearby Bluetooth devices.[4]Java applications can use the API to scan for discoverable devices, identify services provided by discovered devices, and search for devices that the device frequently contacts.
JABWT provides an object exchange API for transfer of data objects between devices. For example, two devices conforming to the OBEX protocol could exchange virtual business cards or calendar appointments.
JABWT allows management of the local device’s state.[5]JABWT applications are able to access information about the host device (such as Bluetooth address), mark their host device as discoverable to other Bluetooth devices, and register to provide services.
JABWT supports connections with different levels of security. Applications using the APIs can pass parameters to the Connector.open() method indicating the level of security required to establish a connection to another device.
Hundreds of mobile devices from different manufacturers comply with the JSR-82 specification.[6]Google maintains alistof devices that conform to the JSR-82 specification.
Several open-source implementations of the JSR-82 specification are available:
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Key finders, also known askeyfinders,key locators, orelectronic finders, are smallelectronic devicesfitted to objects to locate them when misplaced or stolen, such askeys, luggage, purses, wallets, pets, laptop computers, toddlers, cellphones, equipment, or tools, and to transmit alerts, e.g., that one's restaurant table is ready or a nurse is needed. Some key finders beep or flash lights on demand.
Early models of key finder were sound-based, and listened for a clap orwhistle(or a sequence of same), then beeped for the user to find them. Determining what was a clap or a whistle proved difficult, resulting in poor performance and false alarms. Because of this low quality and unreliability, these early key finders were soon discarded and were unpopular for serious needs.
As electronics became smaller and cheaper, andbattery lifeimproved, radio became viable to locate the keys, which were fitted with a small receiver. A separate transmitter is used to activate one or more receivers. All wireless key finders have to "listen" for a searching transmission, resulting in battery replacement at intervals ranging from three months to a year. Using a radio signal removes the risk of false alarms.
Some distributors include a cost-effective key-return service that assists in returning the keys should they be lost in a taxi, bus or other public place, provided the customer registered their devices and contact information. Thetransmittercan also contain information to help return it to its rightful owner.
Peer-to-peerkey finders no longer require a separate "base"; they are all functionally identical and based on acommunication systemwherein each device can find all the others individually. The user can, for example, use adigital walletto find misplacedkeysand vice versa, or amobile phoneto find a lost TV remote control or eyeglasses. In addition, since the keyfinders have their own transmitters, they can reply to each other by radio as well as by beeping and flashing a light to attract attention. The seeking unit can then follow this beacon to find even a buried set of keys. Having a transmitter in each unit also means that, unlike second-generation units, losing a single transmitter does not result in total loss of the ability to find other items it tracks.
Bluetooth Low Energy (BLE) beaconsare crucial in the functionality of key finders. These beacons, characterized by their efficient energy usage, emit signals that can be detected by compatible devices, usually smartphones, for location tracking purposes. Key finders withBLEbeacon technology primarily aid in locating personal items. The beacon attached to an item like keys emits signals that, when in range, are detected by a smartphone app, indicating the item's location.
BLE beacons transmit signals that are detected by a compatible device, enabling the device to determine the beacon's location. This technology is widely used in key finders, where the beacon is attached to items such as keys or wallets, facilitating their location through a smartphone application.[1]
Tracking devices have been implicated in criminal activity, such asstalking[4]and identifying when properties are empty.[5]Safeguards built in to some tracking devices to notify a person when they are being tracked, are compromised because devices can be turned off once tracking is undertaken sufficiently, can be muffled or hidden out of view, or require an app to notify of illicit tracking, which is not usually in use by a victim.[4]
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Li-Fi(also written asLiFi) is awireless communicationtechnology which utilizes light to transmit data and position between devices. The term was first introduced byHarald Haasduring a 2011TEDGlobaltalk inEdinburgh.[1]
Li-Fi is a light communication system that is capable of transmittingdataat high speeds over thevisible light,ultraviolet, andinfraredspectrums. In its present state, onlyLED lampscan be used for the transmission of data in visible light.[2]
In terms of itsend user, the technology is similar toWi-Fi– the key technical difference being that Wi-Fi usesradio frequencyto induce an electric tension in an antenna to transmit data, whereas Li-Fi uses the modulation of light intensity to transmit data. Li-Fi is able to function in areas otherwise susceptible toelectromagnetic interference(e.g.aircraft cabins, hospitals, or the military).[3]
Li-Fi is a derivative ofoptical wireless communications(OWC) technology, which uses light fromlight-emitting diodes(LEDs) as a medium to deliver network, mobile, high-speed communication in a similar manner toWi-Fi.[4]The Li-Fi market was projected to have acompound annual growth rateof 82% from 2013 to 2018 and to be worth over $6 billion per year by 2018.[5]However, the market has not developed as such and Li-Fi remains a niche technology.[6]
Visible light communications(VLC) works by switching the current to the LEDs off and on at a very high speed, beyond the human eye's ability to notice.[7]Technologies that allow roaming between various Li-Fi cells, also known as handover, may allow seamless transition between such cells. The light waves cannot penetrate walls which translates to a much shorter range, and a lowerhackingpotential, relative to Wi-Fi.[8][9]Direct line of sight is not always necessary for Li-Fi to transmit a signal and light reflected off walls can achieve 70Mbit/s.[10][11]
Li-Fi can potentially be useful in electromagnetic sensitive areas without causingelectromagnetic interference.[8][12][9]Both Wi-Fi and Li-Fi transmit data over theelectromagnetic spectrum, but whereas Wi-Fi utilizes radio waves, Li-Fi uses visible, ultraviolet, and infrared light.[13]Researchers have reached data rates of over 224 Gbit/s,[14]which was much faster than typical fastbroadbandin 2013.[15][16]Li-Fi was expected to be ten times cheaper than Wi-Fi.[17]The first commercially available Li-Fi system was presented at the 2014Mobile World Congressin Barcelona.
Although Li-Fi LEDs would have to be kept on to transmit data, they could be dimmed to below human visibility while still emitting enough light to carry data.[17]This is also a major bottleneck of the technology when based on the visible spectrum, as it is restricted to the illumination purpose and not ideally adjusted to a mobile communication purpose, given that other sources of light, for example the sun, will interfere with the signal.[18]
Since Li-Fi's short wave range is unable to penetrate walls, transmitters would need to be installed in every room of a building to ensure even Li-Fi distribution. The high installation costs associated with this requirement to achieve a level of practicality of the technology is one of the potential downsides.[5][7][19]
The initial research on Visible Light Communication (VLC) was published bythe Fraunhofer Institute for Telecommunicationsin September 2009, showcasing data rates of 125 Mbit/s over a 5 m distance using a standard white LED.[20]In 2010, transmission rates were already increased to 513 Mbit/s using the DMT modulation format.[21]
During his 2011 TED Global Talk, ProfessorHarald Haas, a Mobile Communications expert at theUniversity of Edinburgh, introduced the term "Li-Fi" while discussing the concept of "wireless data from every light".[22]
The general term "visible light communication" (VLC), whose history dates back to the 1880s, includes any use of the visible light portion of the electromagnetic spectrum to transmit information. The D-Light project, funded from January 2010 to January 2012 at Edinburgh's Institute for Digital Communications, was instrumental in advancing this technology, with Haas also contributing to the establishment of a company for its commercialization.[23][24]
In October 2011, theFraunhoferIPMS research organization and industry partners formed theLi-Fi Consortium, to promote high-speed optical wireless systems and to overcome the limited amount of radio-based wireless spectrum available by exploiting a completely different part of the electromagnetic spectrum.[25]
The practical demonstration of VLC technology using Li-Fi[26]took place in 2012, with transmission rates exceeding 1 Gbit/s achieved under laboratory conditions.[27]In 2013, laboratory tests achieved speed of up to 10 Gbit/s. By August 2013, data rates of approximately 1.6 Gbit/s were demonstrated over a single color LED.[28]A significant milestone was reached in September 2013 when it was stated that Li-Fi, or VLC systems in general, did not absolutely require line-of-sight conditions.[29]In October 2013, it was reported Chinese manufacturers were working on Li-Fi development kits.[30]
In April 2014, the Russian company Stins Coman announced the BeamCaster Li-Fi wireless local network, capable of data transfer speeds up to 1.25gigabytesper second (GB/s). They foresee boosting speeds up to 5 GB/s in the near future.[31]In the same year, Sisoft, a Mexican company, set a new record by transferring data at speeds of up to 10 GB/s across a light spectrum emitted by LED lamps.[32]
The advantages of operating detectors such as APDs inGeiger-modeassingle photon avalanche diode(SPAD) were demonstrated in May 2014, highlighting enhanced energy efficiency and receiver sensitivity .[33]This operational mode also facilitatedquantum-limitedsensitivity, enabling receivers to detect weak signals from considerable distances.[34]
In June 2018, Li-Fi successfully underwent testing at aBMWplant inMunichfor industrial applications under the auspices of the Fraunhofer Heinrich-Hertz-Institute.[35]
In August 2018,Kyle AcademyinScotland, piloted the usage within its premises, enabling students to receive data through rapid on–off transitions of room lighting.[36]
In June 2019, Oledcomm, a French company, showcased its Li-Fi technology at the 2019Paris Air Show.[37]
Like Wi-Fi, Li-Fi is wireless and usessimilar 802.11 protocols, but it also usesultraviolet,infrared, andvisible light communication.[38]
One part of VLC is modeled after communication protocols established by theIEEE802 workgroup. However, theIEEE 802.15.7 standard is out-of-date: it fails to consider the latest technological developments in the field of optical wireless communications, specifically with the introduction of opticalorthogonal frequency-division multiplexing(O-OFDM) modulation methods which have been optimized for data rates, multiple-access, and energy efficiency.[39]The introduction of O-OFDM means that a new drive for standardization of optical wireless communications is required.[citation needed]
Nonetheless, the IEEE 802.15.7 standard defines thephysical layer(PHY) andmedia access control(MAC) layer. The standard is able to deliver enough data rates to transmit audio, video, and multimedia services. It takes into account optical transmission mobility, its compatibility with artificial lighting present in infrastructures, and the interference which may be generated by ambient lighting.
The MAC layer permits using the link with the other layers as with theTCP/IPprotocol.[citation needed]
The standard defines three PHY layers with different rates:
The modulation formats recognized for PHY I and PHY II areon–off keying(OOK) and variablepulse-position modulation(VPPM). TheManchester codingused for the PHY I and PHY II layers includes the clock inside the transmitted data by representing a logic 0 with an OOK symbol "01" and a logic 1 with an OOK symbol "10", all with a DC component. The DC component avoids light extinction in case of an extended run of logic 0's.[citation needed]
In July 2023, the IEEE published the802.11bbstandard for light-based networking, intended to provide a vendor-neutral standard for the Li-Fi market.
Many experts foresee a movement towards Li-Fi in homes because it has the potential for faster speeds and its security benefits with how the technology works. Because the light sends the data, the network can be contained in a single physical room or building reducing the possibility of a remote network attack. Though this has more implications in enterprise and other sectors, home usage may be pushed forward with the rise of home automation that requires large volumes of data to be transferred through the local network.[41]
Mostremotely operated underwater vehicles(ROVs) are controlled by wired connections. The length of their cabling places a hard limit on their operational range, and other potential factors such as the cable's weight and fragility may be restrictive. Since light can travel through water, Li-Fi based communications could offer much greater mobility.[42][unreliable source]Li-Fi's utility is limited by the distance light can penetrate water. Significant amounts of light do not penetrate further than 200 meters. Past 1000 meters, no light penetrates.[43]
Efficient communication of data is possible in airborne environments such as a commercialpassenger aircraftutilizing Li-Fi. Using this light-based data transmission will not interfere with equipment on the aircraft that relies onradio wavessuch as itsradar lifi connectivity.[44]
Increasingly, medical facilities are using remote examinations and even procedures. Li-Fi systems could offer a better system to transmit low latency, high volume data across networks.[citation needed]Besides providing a higher speed, light waves also have reduced effects onmedical instruments. An example of this would be the possibility of wireless devices being used inMRIssimilar radio sensitive procedures.[44]Another application of LiFi in hospitals is localisation of assets and personnel.[45]
Vehiclescould communicate with one another via front and back lights to increase road safety. Street lights and traffic signals could also provide information about current road situations.[46]
Due to the specific properties of light, the optical beams can be bundled especially well in comparison to radio-based devices, allowing highly directional Li-Fi systems to be implemented. Devices have been developed for outdoor use that make it more difficult to access the data due to their low beam angle, thus increasing the security of the transmission. These can be used, for example, for building-to-building communication or for networking small radio cells.
Anywhere in industrial areas data has to be transmitted, Li-Fi is capable of replacingslip rings, sliding contacts, and short cables, such asIndustrial Ethernet. Due to the real-time of Li-Fi (which is often required for automation processes), it is also an alternative to common industrialWireless LANstandards. Fraunhofer IPMS, a research organization inGermanystates that they have developed a component which is very appropriate for industrial applications with time-sensitive data transmission.[47]
Street lampscan be used to display advertisements for nearby businesses or attractions oncellular devicesas an individual passes through. A customer walking into a store and passing through the store's front lights can show current sales and promotions on the customer's cellular device.[48]
In warehousing, indoor positioning and navigation is a crucial element. 3D positioning helpsrobotsto get a more detailed and realistic visual experience. Visible light from LED bulbs is used to send messages to the robots and other receivers and hence can be used to calculate the positioning of the objects.[49]
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The wireless data exchange standardBluetoothuses a variety ofprotocols. Core protocols are defined by the trade organizationBluetooth SIG. Additional protocols have been adopted from other standards bodies. This article gives an overview of the core protocols and those adopted protocols that are widely used.
The Bluetooth protocol stack is split in two parts: a "controller stack" containing the timing critical radio interface, and a "host stack" dealing with high level data. The controller stack is generally implemented in a low cost silicon device containing the Bluetooth radio and a microprocessor. The host stack is generally implemented as part of an operating system, or as an installable package on top of an operating system. For integrated devices such as Bluetooth headsets, the host stack and controller stack can be run on the same microprocessor to reduce mass production costs; this is known as ahostlesssystem.
The normal type of radio link used for general data packets using a pollingTDMAscheme to arbitrate access. It can carry packets of several types, which are distinguished by:
A connection must be explicitly set up and accepted between two devices before packets can be transferred.
ACL packets are retransmitted automatically if unacknowledged, allowing for correction of a radio link that is subject to interference. Forisochronousdata, the number of retransmissions can be limited by a flush timeout; but without using L2PLAY retransmission and flow control mode or EL2CAP, a higher layer must handle the packet loss.
ACL links are disconnected if there is nothing received for the supervision timeout period; the default timeout is 20 seconds, but this may be modified by the master.
The type of radio link used for voice data. A SCO link is a set of reserved time slots separated by the SCO interval Tscowhich is determined during logical link establishment by the Central device. Each device transmits encoded voice data in the reserved timeslot. There are no retransmissions, but forward error correction can be optionally applied. SCO packets may be sent every 1, 2, or 3 time slots.
Enhanced SCO (eSCO) links allow greater flexibility in setting up links: they may use retransmissions to achieve reliability, allow for a wider variety of packet types and for greater intervals between packets than SCO, thus increasing radio availability for other links.
Used for control of the radio link between two devices, mobile dmv, querying device abilities and power control. Implemented on the controller.
Standardized communication between the host stack (e.g., a PC or mobile phone OS) and the controller (the Bluetooth integrated circuit (IC)). This standard allows the host stack or controller IC to be swapped with minimal adaptation.
There are several HCI transport layer standards, each using a different hardware interface to transfer the same command, event and data packets. The most commonly used areUSB(in PCs) andUART(in mobile phones and PDAs).
In Bluetooth devices with simple functionality (e.g., headsets), the host stack and controller can be implemented on the same microprocessor. In this case the HCI is optional, although often implemented as an internal software interface.
This is the LMP equivalent forBluetooth Low Energy(LE), but is simpler. It is implemented on the controller and manages advertisement, scanning, connection and security from a low-level, close to the hardware point of view fromBluetooth perspective.
L2CAPis used within the Bluetooth protocol stack. It passes packets to either the Host Controller Interface (HCI) or, on a hostless system, directly to the Link Manager/ACL link.
L2CAP's functions include:
L2CAP is used to communicate over the host ACL link. Its connection is established after the ACL link has been set up.
In basic mode, L2CAP provides packets with a payload configurable up to 64 kB, with 672 bytes as the default MTU, and 48 bytes as the minimum mandatory supported MTU. In retransmission and flow control modes, L2CAP can be configured for reliable or asynchronous data per channel by performing retransmissions and CRC checks. Reliability in either of these modes is optionally and/or additionally guaranteed by the lower layer Bluetooth BDR/EDR air interface by configuring the number of retransmissions and flush timeout (time after which the radio will flush packets). In-order sequencing is guaranteed by the lower layer.
The EL2CAP specification adds an additionalenhanced retransmission mode(ERTM) to the core specification, which is an improved version of retransmission and flow control modes. ERTM is required when using an AMP (Alternate MAC/PHY), such as 802.11abgn.
BNEP[1]is used for delivering network packets on top of L2CAP. This protocol is used by thepersonal area networking (PAN)profile. BNEP performs a similar function toSubnetwork Access Protocol(SNAP) in Wireless LAN.
In the protocol stack, BNEP is bound to L2CAP.
The Bluetooth protocol RFCOMM is a simple set of transport protocols, made on top of the L2CAP protocol, providing emulatedRS-232serial ports(up to sixty simultaneous connections to a Bluetooth device at a time). The protocol is based on the ETSI standard TS 07.10.
RFCOMM is sometimes calledserial port emulation. The Bluetoothserial port profile(SPP) is based on this protocol.
RFCOMM provides a simple reliable data stream to the user, similar to TCP. It is used directly by many telephony related profiles as a carrier for AT commands, as well as being a transport layer for OBEX over Bluetooth.
Many Bluetooth applications use RFCOMM because of its widespread support and publicly available API on most operating systems. Additionally, applications that used a serial port to communicate can be quickly ported to use RFCOMM.
In the protocol stack, RFCOMM is bound to L2CAP.
Used to allow devices to discover what services each other support, and what parameters to use to connect to them. For example, when connecting a mobile phone to a Bluetooth headset, SDP will be used to determine whichBluetooth profilesare supported by the headset (headset profile,hands free profile,advanced audio distribution profile, etc.) and the protocol multiplexer settings needed to connect to each of them. Each service is identified by aUniversally Unique Identifier(UUID), with official services (Bluetooth profiles) assigned a short form UUID (16 bits rather than the full 128).
In the protocol stack, SDP is bound to L2CAP.
Also referred to astelephony control protocol specification binary(TCS binary)
Used to set up and control speech and data calls between Bluetooth devices. The protocol is based on the ITU-T standardQ.931, with the provisions of Annex D applied, making only the minimum changes necessary for Bluetooth.
TCS is used by theintercom(ICP) andcordless telephony(CTP) profiles. The telephone control protocol specification is not called TCP, to avoid confusion with transmission control protocol (TCP) used for Internet communication.
Used by the remote control profile to transferAV/Ccommands over an L2CAP channel. The music control buttons on a stereo headset use this protocol to control the music player.
In the protocol stack, AVCTP is bound to L2CAP.
Used by the advanced audio distribution profile to stream music to stereo headsets over an L2CAP channel. Intended to be used by video distribution profile.
In the protocol stack, AVDTP is bound to L2CAP.
Object exchange(OBEX; also termedIrOBEX) is a communications protocol that facilitates the exchange of binary objects between devices. It is maintained by theInfrared Data Associationbut has also been adopted by theBluetooth Special Interest Groupand theSyncMLwing of theOpen Mobile Alliance(OMA).
In Bluetooth, OBEX is used for many profiles that require simple data exchange (e.g., object push, file transfer, basic imaging, basic printing, phonebook access, etc.).
Similar in scope to SDP but specially adapted and simplified for Low Energy Bluetooth. It allows a client to read and/or write certain attributes exposed by the server in a non-complex, low-power friendly manner.
In the protocol stack, ATT is bound to L2CAP.
This is used by Bluetooth Low Energy implementations for pairing and transport specific key distribution.
In the protocol stack, SMP is bound to L2CAP.
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MyriaNedis awireless sensor network (WSN)platform developed byDevLab. It uses an epidemic communication style based on standardradio broadcasting. This approach reflects the way humans interact, which is calledgossiping.[1]Messages are sent periodically and received by adjoining neighbours. Each message is repeated and duplicated towards allnodesthat span the network; it spreads like avirus(hence the term epidemic communication).
This is a very efficient and robust[2][3]protocol, mainly for two reasons:
Nodes can be added, removed or may be physically moving without the need to reconfigure the network. TheGOSSIP protocolis a self-configuring network solution. The network may even be heterogeneous, where several types of nodes communicate different pieces of information with each other at the same time. This is possible due to the fact that no interpretation of the message content is required in order to be able to forward it to other nodes.
Message communication is fully transparent, providing a seamless communication platform, where new functionality can be added later, without the need to change the installed base. Furthermore, MyriaNed is enabled to update the wireless sensor nodes software by means of “over the air” programming of a deployed network.
Traditionallyradio communicationis organized according to themaster-slavephilosophy. The way two nodes communicate ispoint-to-point. A command is senttop-downand a confirmation is sentbottom-upbetween twohierarchicallevels.
However, inbiologythis is organized differently. For instanceadrenalinein the human body works completely different. This message (hormoneandneurotransmitter) is sent to different types ofcells. Every cell knows what to do with this message (increase heart rate, constrict blood vessels, dilate air passages) and does not sent a confirmation. This is theinspirationfor MyriaNed in a nutshell.
Another inspiration is the basicradio broadcastingprinciple. A radio with an antenna is made to send and receive a message to and from every direction. Implicitly it is not optimized to perform point-to-point communication. Wires are ideally suitable for that because they always link two devices. Looking at wireless communication, it should be structured in such a way that it uses the potential of radio transmission.
The third inspiration is that of humangossiping. The term is sometimes associated with spreadingmisinformationof trivial nature but the way information is disseminated is one of the oldest and most common in nature. Information is generated by a source and gossiped to its neighbours. They spread the message to their neighbours, thereby exponentially increasing the number of people familiar with the information.
Together these three inspirations led to the development of the MyriaNed platform. There is no master-slave structure in the network rather each node ishierarchicallyequal. MyriaNed uses biological routing which is random and independent of the function of the node. Each node decides what to do with a message. Furthermore, it sends the message to all its neighbours thereby using the basic radio communication characteristics.
In potential the complete set of information (e.g. sensor values, control data) is available to every node in the network. By using an intelligent strategy, called shared state, this information is stored as adistributed databasein the network. Nodes that are newly added to the network can utilize this shared state to instantaneously adapt and contribute to the network functionality.
When it comes to caching the messages there are two scenarios. The first scenario, if a message is new to the receiving node (meaning the data was not received in previous communication rounds), the node will store the message in cache and transmit this message to its own neighbours. Secondly, if the message is old (meaning the data was already received before, i.e. through another neighbour), the message is discarded. If the cache is full, different strategies can be employed in order to make room for new messages.
Since there is notop-downstructure imposed on the network and data dissemination is transparent, the network is naturally scalable. On the communication level no identification administration is necessary and messages have a standard structure. This makes it possible that a MyriaNed network can scale far beyond the limits of currently available WSN technologies. Also different functionality can be integrated and executed on a single network.
In order to reduce the energy consumption of the nodes in the networkduty cyclingis used. This means that nodes communicate periodically, and go to standby mode in a large part of the period in order to preserve energy. In order to communicate the nodes need to wake up at the same time, therefore they have a built-in synchronization mechanism.
During radio communication aTDMA(time-division multiple access)[4]scheme is used to overcome collisions during broadcast communication.
Current implementations run on 2.4 GHz and 868 MHz radios. The concept of MyriaNed is however not restricted to these frequencies.
From the previous characteristics of MyriaNed it can be derived that it uses a truemeshtopology. The advantage of such a topology is reliability, and coping with mobility, because of the redundant communication paths in the network.
Setup and configuration is kept to a bare minimum because of thebottom-up approachutilized in the self-organizing network. There is no notion of a coordinator or network manager entity compared to technologies such asZigbeeorWirelessHART. This reduces the effort spent on setup and maintenance.
When MyriaNed is used for specific applications, the ultimate implementation is based on a large set of autonomous devices which make their own autonomous decisions (e.g. controlling actuators) based on the available information that travels through the network by gossiping dissemination. The sum of all individual behaviors of the network nodes reflect the emergent behavior of the system as a whole, which is the systems application.
MyriaNed has an extremely small stack, uses low calculation power and does not need a large amount of energy. Therefore, it can be run on a simplemicrocontrollerand small sized battery. This makes the costs of a single node very low.
DevLabmembers work with a single chip solution in which theradioandmicrocontrollerare integrated. This chip with an attached battery is smaller than a 2 euro coin.
Installation and expansion of networks using the MyriaNed protocol is very cost efficient as well. There is no need for addressing and the information in the network is synchronized over time with added nodes. Therefore, no additional costs have to be made (like gateways/setup/bridges) in order to install or expand the network.
Because of the structure of MyriaNed there is no need for different profiles for market applications. Different applications can run next to each other without interfering. Instead they will only help each other by increasing the density of the network. EveryDevLab memberis free to use MyriaNed in whatever market they want. This has resulted in many interoperable devices in completely different applications.
Chess Wise, one of the companies behind DEVLAB, used the MyriaNED technology as an early base for Mymesh, their network protocol. This technology is used to connect, control and analyze thousands of devices simultaneously within demanding environments.[5]
EP application 2301302, van der Wateren, Frits, "Broadcast-only distributed wireless network", published 2009-06-22, assigned to CHESS
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Near-field communication(NFC) is a set ofcommunication protocolsthat enablescommunicationbetween two electronic devices over a distance of4 cm (1+1⁄2in) or less.[1]NFC offers a low-speed connection through a simple setup that can be used for thebootstrappingof capable wireless connections.[2]Like otherproximity cardtechnologies, NFC is based oninductive couplingbetween twoelectromagnetic coilspresent on a NFC-enabled device such as asmartphone. NFC communicating in one or both directions uses a frequency of 13.56 MHz in the globally available unlicensedradio frequencyISM band, compliant with theISO/IEC 18000-3air interface standard at data rates ranging from 106 to 848 kbit/s.
TheNFC Forumhas helped define and promote the technology, setting standards for certifying device compliance.[3][4]Secure communications are available by applying encryption algorithms as is done for credit cards[5]and if they fit the criteria for being considered apersonal area network.[6]
NFC standards cover communications protocols and data exchange formats and are based on existingradio-frequency identification(RFID) standards includingISO/IEC 14443andFeliCa.[7]The standards include ISO/IEC 18092[8]and those defined by the NFC Forum. In addition to the NFC Forum, theGSMAgroup defined a platform for the deployment of GSMA NFC Standards[9]within mobile handsets. GSMA's efforts include Trusted Services Manager,[10][11]Single Wire Protocol, testing/certification and secure element.[12]NFC-enabled portable devices can be provided withapplication software, for example to read electronic tags or make payments when connected to an NFC-compliant system. These are standardized to NFC protocols, replacing proprietary technologies used by earlier systems.
A patent licensing program for NFC is under deployment by France Brevets, a patent fund created in 2011. This program was under development by Via Licensing Corporation, an independent subsidiary ofDolby Laboratories, and was terminated in May 2012.[13]A platform-independentfree and open sourceNFC library,libnfc, is available under theGNU Lesser General Public License.[14][15]
Present and anticipated applications include contactless transactions, data exchange and simplified setup of more complex communications such asWi-Fi.[16]In addition, when one of the connected devices has Internet connectivity, the other can exchange data with online services.[citation needed]
Near-field communication (NFC) technology not only supports data transmission but also enables wireless charging, providing a dual-functionality that is particularly beneficial for small, portable devices. The NFC Forum has developed a specific wireless charging specification, known as NFC Wireless Charging (WLC), which allows devices to charge with up to 1W of power over distances of up to2 cm (3⁄4in).[17]This capability is especially suitable for smaller devices like earbuds, wearables, and other compact Internet of Things (IoT) appliances.[17]
Compared to the more widely knownQi wireless chargingstandard by theWireless Power Consortium, which offers up to 15W of power over distances up to4 cm (1+5⁄8in), NFC WLC provides a lower power output but benefits from a significantly smaller antenna size.[17]This makes NFC WLC an ideal solution for devices where space is at a premium and high power charging is less critical.[17]
The NFC Forum also facilitates a certification program, labeled as Test Release 13.1 (TR13.1), ensuring that products adhere to the WLC 2.0 specification. This certification aims to establish trust and consistency across NFC implementations, minimizing risks for manufacturers and providing assurance to consumers about the reliability and functionality of their NFC-enabled wireless charging devices.[17]
NFC is rooted inradio-frequency identificationtechnology (known as RFID) which allows compatible hardware to both supply power to and communicate with an otherwise unpowered and passive electronic tag using radio waves. This is used for identification, authentication andtracking. Similar ideas in advertising and industrial applications were not generally successful commercially, outpaced by technologies such asQR codes,barcodesandUHFRFIDtags.[citation needed]
Ultra-wideband(UWB) another radio technology has been hailed as a future possible alternatives to NFC technology due to further distances of data transmission, as well as Bluetooth and wireless technology.[55]
NFC is a set of short-range wireless technologies, typically requiring a separation of10 cm (3+7⁄8in) or less. NFC operates at 13.56MHzonISO/IEC 18000-3air interface and at rates ranging from 106 kbit/s to 424 kbit/s. NFC always involves an initiator and a target; the initiator actively generates anRFfield that can power a passive target. This enables NFC targets to take very simple form factors such as unpowered tags, stickers, key fobs, or cards. NFC peer-to-peer communication is possible, provided both devices are powered.[56]
NFC tags contain data and are typically read-only, but may be writable. They can be custom-encoded by their manufacturers or use NFC Forum specifications. The tags can securely store personal data such as debit and credit card information, loyalty program data, PINs and networking contacts, among other information. The NFC Forum defines five types of tags that provide different communication speeds and capabilities in terms of configurability, memory, security,data retentionand write endurance.[57]
As withproximity cardtechnology, NFC usesinductive couplingbetween two nearbyloop antennaseffectively forming an air-coretransformer. Because the distances involved are tiny compared to thewavelengthofelectromagnetic radiation(radio waves) of that frequency (about 22 metres), the interaction is described asnear field. An alternatingmagnetic fieldis the main coupling factor and almost no power is radiated in the form ofradio waves(which are electromagnetic waves, also involving an oscillatingelectric field); that minimises interference between such devices and any radio communications at the same frequency or with other NFC devices much beyond its intended range. NFC operates within the globally available and unlicensedradio frequencyISM bandof 13.56 MHz. Most of the RF energy is concentrated in the ±7 kHz bandwidth allocated for that band, but the emission'sspectral widthcan be as wide as 1.8 MHz[58]in order to support high data rates.
Working distance with compact standard antennas and realistic power levels could be up to about20 cm (7+7⁄8in) (but practically speaking, working distances never exceed10 cm or3+7⁄8in). Note that because the pickup antenna may be quenched in aneddy currentby nearby metallic surfaces, the tags may require a minimum separation from such surfaces.[59]
The ISO/IEC 18092 standard supports data rates of 106, 212 or 424kbit/s.
The communication takes place between an active "initiator" device and a target device which may either be:
NFC employs two differentcodingsto transfer data. If an active device transfers data at 106 kbit/s, a modifiedMiller codingwith 100 percentmodulationis used. In all other casesManchester codingis used with a modulation ratio of 10 percent.
Every active NFC device can work in one or more of three modes:
NFC tags are passive data stores which can be read, and under some circumstances written to, by an NFC device. They typically contain data (as of 2015[update]between 96 and 8,192 bytes) and are read-only in normal use, but may be rewritable. Applications include secure personal data storage (e.g.debitorcredit cardinformation,loyalty programdata,personal identification numbers(PINs), contacts). NFC tags can be custom-encoded by their manufacturers or use the industry specifications.
Although the range of NFC is limited to a few centimeters, standard plain NFC is not protected againsteavesdroppingand can be vulnerable to data modifications. Applications may use higher-layercryptographic protocolsto establish a secure channel.
The RF signal for the wireless data transfer can be picked up with antennas. The distance from which an attacker is able to eavesdrop the RF signal depends on multiple parameters, but is typically less than 10 meters.[60]Also, eavesdropping is highly affected by the communication mode. A passive device that doesn't generate its own RF field is much harder to eavesdrop on than an active device. An attacker can typically eavesdrop within 10 m of an active device and 1 m for passive devices.[61]
Because NFC devices usually includeISO/IEC 14443protocols,relay attacksare feasible.[62][63][64][page needed]For this attack the adversary forwards the request of the reader to the victim and relays its answer to the reader in real time, pretending to be the owner of the victim's smart card. This is similar to aman-in-the-middle attack.[62]Onelibnfccode example demonstrates a relay attack using two stock commercial NFC devices. This attack can be implemented using only two NFC-enabled mobile phones.[65]
NFC standards cover communications protocols and data exchange formats, and are based on existing RFID standards includingISO/IEC 14443andFeliCa.[7]The standards include ISO/IEC 18092[8]and those defined by the NFC Forum.
NFC is standardized in ECMA-340 and ISO/IEC 18092. These standards specify the modulation schemes, coding, transfer speeds and frame format of the RF interface of NFC devices, as well as initialization schemes and conditions required for data collision-control during initialization for both passive and active NFC modes. They also define thetransport protocol, including protocol activation and data-exchange methods. The air interface for NFC is standardized in:
NFC incorporates a variety of existing standards includingISO/IEC 14443Type A and Type B, andFeliCa(also simply named F or NFC-F). NFC-enabled phones work at a basic level with existing readers. In "card emulation mode" an NFC device should transmit, at a minimum, a unique ID number to a reader. In addition, NFC Forum defined a common data format calledNFC Data Exchange Format(NDEF) that can store and transport items ranging from anyMIME-typed object to ultra-short RTD-documents,[68]such asURLs. The NFC Forum added theSimple NDEF Exchange Protocol(SNEP) to the spec that allows sending and receiving messages between two NFC devices.[69]
TheGSM Association (GSMA)is a trade association representing nearly 800 mobile telephony operators and more than 200 product and service companies across 219 countries. Many of its members have led NFC trials and are preparing services for commercial launch.[70]
GSM is involved with several initiatives:
StoLPaN (Store Logistics and Payment with NFC) is a pan-European consortium supported by theEuropean Commission'sInformation Society Technologiesprogram. StoLPaN will examine the potential for NFC local wireless mobile communication.[74]
NFC Forum is a non-profit industry association formed on March 18, 2004, byNXP Semiconductors,SonyandNokiato advance the use of NFC wireless interaction in consumer electronics, mobile devices and PCs. Its specifications include the five distinct tag types that provide different communication speeds and capabilities covering flexibility, memory, security, data retention and write endurance. NFC Forum promotes implementation and standardization of NFC technology to ensure interoperability between devices and services. As of January 2020, the NFC Forum had over 120 member companies.[75]
NFC Forum promotes NFC and certifies device compliance[5]and whether it fits in apersonal area network.[5]
GSMA defined a platform for the deployment of GSMA NFC Standards[9]within mobile handsets. GSMA's efforts include,[76]Single Wire Protocol, testing and certification and secure element.[12]The GSMA standards surrounding the deployment of NFC protocols (governed byNFC Forum) on mobile handsets are neither exclusive nor universally accepted. For example, Google's deployment ofHost Card EmulationonAndroid KitKatprovides for software control of a universal radio. In this HCE Deployment[77]the NFC protocol is leveraged without the GSMA standards.
Other standardization bodies involved in NFC include:
NFC allows one- and two-way communication between endpoints, suitable for many applications.
NFC devices can act as electronicidentity documentsandkeycards.[2]They are used incontactless paymentsystems and allowmobile paymentreplacing or supplementing systems such as credit cards andelectronic ticketsmart cards. These are sometimes calledNFC/CTLSorCTLS NFC, withcontactlessabbreviated asCTLS. NFC can be used to share small files such as contacts and for bootstrapping fast connections to share larger media such as photos, videos, and other files.[78]
NFC devices can be used in contactless payment systems, similar to those used in credit cards andelectronic ticketsmart cards, and allow mobile payment to replace/supplement these systems.
InAndroid4.4, Google introduced platform support for secure NFC-based transactions throughHost Card Emulation(HCE), for payments, loyalty programs, card access, transit passes and other custom services. HCE allows any Android 4.4 app to emulate an NFC smart card, letting users initiate transactions with their device. Apps can use a new Reader Mode to act as readers for HCE cards and other NFC-based transactions.
On September 9, 2014,Appleannounced support for NFC-powered transactions as part ofApple Pay.[79]With the introduction of iOS 11, Apple devices allow third-party developers to read data from NFC tags.[80]
As of 2022, there are five major NFC apps available in the UK: Apple Pay, Google Pay, Samsung Pay, Barclays Contactless Mobile and Fitbit Pay. The UK Finance's UK Payment Markets Summary 2021 looked at Apple Pay, Google Pay and Samsung Pay and found 17.3 million UK adults had registered for mobile payment (up 75% from the year before) and of those, 84% had made a mobile payment.[81]
NFC offers a low-speed connection with simple setup that can be used tobootstrapmore capablewireless connections.[2]For example,Android Beamsoftware uses NFC to enable pairing and establish a Bluetooth connection when doing a file transfer and then disabling Bluetooth on both devices upon completion.[82]Nokia, Samsung, BlackBerry and Sony[83]have used NFC technology to pair Bluetooth headsets, media players and speakers with one tap.[84]The same principle can be applied to the configuration of Wi-Fi networks.Samsung Galaxydevices have a feature namedS-Beam—an extension of Android Beam that uses NFC (to shareMAC addressandIP addresses) and then usesWi-Fi Directto share files and documents. The advantage of using Wi-Fi Direct over Bluetooth is that it permits much faster data transfers, running up to 300 Mbit/s.[56]
NFC can be used forsocial networking, for sharing contacts, text messages and forums, links to photos, videos or files[78]and entering multiplayermobile games.[85]
NFC-enabled devices can act as electronicidentity documentsfound in passports and ID cards, andkeycardsfor the use infare cards,transit passes,login cards, car keys andaccess badges.[2]NFC's short range and encryption support make it more suitable than less private RFID systems.
NFC-equipped smartphones can be paired withNFC Tagsor stickers that can be programmed by NFC apps. These programs can allow a change of phone settings, texting, app launching, or command execution.
Such apps do not rely on a company or manufacturer, but can be utilized immediately with an NFC-equipped smartphone and an NFC tag.[86]
The NFC Forum published theSignature Record Type Definition(RTD) 2.0 in 2015 to add integrity and authenticity for NFC Tags. This specification allows an NFC device to verify tag data and identify the tag author.[87]
NFC has been used invideo gamesstarting withSkylanders: Spyro's Adventure.[88]These are customizable figurines which contain personal data with each figure, so no two figures are exactly alike. Nintendo'sWii U GamePadwas the first console system to include NFC technology out of the box. It was later included in theNintendo 3DSrange (being built into the New Nintendo 3DS/XL and in a separately sold reader which usesInfraredto communicate to older 3DS family consoles) and theNintendo Switchrange (being built within the rightJoy-Concontroller and directly in the Nintendo Switch Lite). Theamiiborange of accessories utilize NFC technology to unlock features.
Adidas Telstar 18is a soccer ball that contains an NFC chip within.[89]The chip enables users to interact with the ball using a smartphone.[90]
NFC and Bluetooth are both relatively short-range communication technologies available onmobile phones. NFC operates at slower speeds than Bluetooth and has a much shorter range, but consumes far less power and doesn't require pairing.[91]
NFC sets up more quickly than standard Bluetooth, but has a lower transfer rate thanBluetooth low energy. With NFC, instead of performing manual configurations to identify devices, the connection between two NFC devices is automatically established in less than .1 second. The maximum data transfer rate of NFC (424 kbit/s) is slower than that of Bluetooth V2.1 (2.1 Mbit/s).
NFC's maximum working distance of less than20 cm (7+7⁄8in) reduces the likelihood of unwanted interception, making it particularly suitable for crowded areas that complicate correlating a signal with its transmitting physical device (and by extension, its user).[92]
NFC is compatible with existing passive RFID (13.56 MHz ISO/IEC 18000-3) infrastructures. It requires comparatively low power, similar to the Bluetooth V4.0 low-energy protocol. However, when NFC works with an unpowered device (e.g. on a phone that may be turned off, a contactless smart credit card, a smart poster), the NFC power consumption is greater than that of Bluetooth V4.0 Low Energy, since illuminating the passive tag needs extra power.[91]
In 2011, handset vendors released more than 40 NFC-enabled handsets with theAndroidmobile operating system.BlackBerrydevices support NFC using BlackBerry Tag on devices running BlackBerry OS 7.0 and greater.[93]
MasterCardadded further NFC support for PayPass for the Android and BlackBerry platforms, enabling PayPass users to make payments using their Android or BlackBerry smartphones.[94]A partnership betweenSamsungandVisaadded a 'payWave' application on the Galaxy S4 smartphone.[95]
In 2012,Microsoftadded native NFC functionality in theirmobile OSwithWindows Phone 8, as well as theWindows 8operating system. Microsoft provides the "Wallet hub" in Windows Phone 8 for NFC payment, and can integrate multiple NFC payment services within a single application.[96]
In 2014,iPhone 6was released fromAppleto support NFC.[97]and since September 2019 iniOS 13Apple now allows NFC tags to be read out as well as labeled using an NFC app.[citation needed]
As of April 2011 hundreds of NFC trials had been conducted. Some firms moved to full-scale service deployments, spanning one or more countries. Multi-country deployments includeOrange's rollout of NFC technology to banks, retailers, transport, and service providers in multiple European countries,[42]andAirtel AfricaandOberthur Technologiesdeploying to 15 countries throughout Africa.[98]
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NearLink(Chinese:星闪; also known asSparkLinkand formerlyGreentooth) is a short-rangewirelesstechnology protocol, which was developed by the NearLink Alliance, led byHuaweito set up on September 22, 2020.[1][2]As of September 2023, the Alliance has more than 300 enterprises and institutions on board, which includeautomotivemanufacturers,chipand module manufacturers,applicationdevelopers,ICTcompanies, andresearchinstitutions.[3][4]
On November 4, 2022, the Alliance released theSparkLink Short-range Wireless Communications Standard 1.0, which incorporates two modes of access, namely, SparkLink Low Energy (SLE) and SparkLink Basic (SLB),[5][6]to integrate the features of traditional wireless technologies, such asBluetoothandWi-Fi, with enhanced prerequisites forlatency, power consumption, coverage, and security.[7][4][8]
The Alliance unveiled the Standard 2.0 on March 30, 2024, which enhances end-to-end protocol system and extends application standards, supporting native audio and video capabilities, human-computer interaction, and positioning applications.[9]
NearLink employs theCyclic Prefix-Orthogonal Frequency Division Multiplexing(Cyclic Prefix-OFDM) waveform to addresslatencyissues in various applications. The waveform features an ultra-short frame structure and a flexible scheduling scheme oftime-domainresources, reducing transmission latency to approximately 20 microseconds. In addition, NearLink appliespolar codesand adoptsHybrid Automatic Repeat-reQuest(HARQ) schemes to support applications with high reliability requirements, such as industrialclosed-loop controlapplications for automated assembly lines, where reliability requirements are at least 99.999%.[1]
The first product to feature NearLink technology was theHuawei Mate 60 seriessmartphone introduced by Huawei on August 29, 2023,[10][11]followed by FreeBuds Pro 3 on November 25, 2023, M-Pencil 3rd gen with the MatePad 13.2 tablet on 14 December 2023,[12][13]and thePura 70 serieson April 18, 2024.[14][15]
On September 22, 2020, the SparkLight Alliance was established to formulate the NearLink short-range wireless technology standard.[16]
By the end of 2021, the NearLink 1.0 standards were finalized, establishing a core end-to-end architecture that includes the NearLink access layer, basic service layer, and basic application layer.[17]
On November 4, 2022, the SparkLink Alliance officially released theSparkLink Short-range Wireless Communications Standard 1.0, which covers two modes of access: SLB (SparkLink Basic) and SLE (SparkLink Low Energy). They also unveiled "The White Paper for Promotion of SparkLink Short-Range Wireless Communication (SparkLink 1.0) for Industrial Use."[18][19]
On August 4, 2023, Huawei officially unveiled the NearLink short-range wireless communication technology at the Developer Conference, providing a new wireless communication method forHarmonyOS.[20][21]
On August 29, 2023, Huawei released the Huawei Mate 60 series smartphones, which are equipped with NearLink technology.[10]
On September 25, 2023, at Huawei's Autumn Full-Scenario New Products Launch event, a new range of products supporting NearLink technology were unveiled. These products include theHuawei MatePad Pro13.2-inch tablet, the third-generation M-Pencilstylus, and theFreeBuds Pro 3earbuds.[22][23][24]
On March 30, 2024, the Intelligent Car Connectivity Industry Ecosystem Alliance ("ICCE Alliance") and the NearLink Alliance jointly released theICCE Alliance Digital Key System Part 6: NearLink System Requirementsduring the 2024 International NearLink Alliance Industry Summit". The Requirements were formulated by various parties includingHuawei,BYD,Changan,GAC,FAW, etc.[25]
On November 12, 2024, Huawei released a beta version of HarmonyOS 5.0.1 targeted for developers that has full support of native NearLink Kit API integration of the operating system for third party applications support.[26]
The system structure of NearLink technology mainly consists of three layers: the physical layer, the data link layer, and the network layer.[27][28]
NearLink incorporates two access modes, namely SparkLink Low Energy ("SLE")[Note 1]and SparkLink Basic ("SLB").[Note 2][5][6]
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RuBee(IEEE standard 1902.1) is a two-way activewirelessprotocoldesigned for harsh environments and high-security asset visibility applications. RuBee utilizeslongwavesignals to send and receive short (128byte) data packets in a local regional network. The protocol is similar to theIEEE 802protocols in that RuBee is networked by using on-demand, peer-to-peer and active radiating transceivers. RuBee is different in that it uses a low frequency (131 kHz) carrier.
1902.1 is the "physical layer" workgroup with 17 corporate members. The work group was formed in late 2006. The final specification was issued as anIEEE standardin March 2009. The standard includes such things as packet encoding and addressing specifications. The protocol has already been in commercial use by several companies, in asset visibility systems and networks.[1]However, IEEE 1902.1 will be used in many sensor network applications, requiring this physical layer standard in order to establish interoperability between manufacturers. A second standard has been drafted 1902.2 for higher level data functions required in Visibility networks. Visibility networks provide the real-time status, pedigree, and location of people, livestock, medical supplies or other high-value assets within a local network. The second standard will address the data-link layers based on existing uses of the RuBee protocol. This standard, which will be essential for the widespread use of RuBee in visibility applications, will support the interoperability of RuBee tags, RuBee chips, RuBee network routers, and other RuBee equipment at the data-link layer.
A RuBee tag has a 4 bitCPU, 1 to 5 kB ofsRAM, acrystal, and alithiumbattery with an expected life of five years. It can optionally have sensors, displays, and buttons. The RuBee protocol is bidirectional, on-demand, and peer-to-peer. It can operate at other frequencies (e.g. 450 kHz) but 131 kHz is the most widely used one. The RuBee protocol uses anIP Address(Internet Protocol Address). A tag may hold data in its own memory (instead or in addition to having data stored on a server). RuBee functions successfully in harsh environments (one or both ends of the communication are near steel or water), with networks consisting of many thousands of tags, and has a range of 1 to 30 m (3 to 100 ft) depending on the antenna configuration. This allows RuBee radio tags function in environments where other radio tags and RFID may have problems. RuBee networks are in use in many visibility applications, including exit-entry detection in high-security government facilities, weapons and small arms in high-security armories, mission-critical specialized tools, smart shelves and racks for high-value assets; and smart entry/exit portals.
The major disadvantage RuBee has over other protocols is speed and packet size. The RuBee protocol is limited to 1,200baudin existing applications. The IEEE 1902.1 specifies 1,200 baud. The protocol could go to 9,600 baud with some loss of range. However, most visibility applications work well at 1,200 baud. Packet size is limited to tens to hundreds of bytes. RuBee's design forgoes high bandwidth, and high-speed communication because most visibility applications do not require them.
The use of LW magnetic energy brings about a number of advantages:
This protocol is similar at the physical level toNFC(13.56 MHz carrier, basically an air-core transformer pair) and alsoQi's inductive energy transfer (100 kHz-300 kHz carrier). Both modulate the receiver's coil load to communicate with the sender. Some NFC tags can support simple processors and a handful of storage like this protocol. NFC also shares the physical security properties of "magnetic" communications like RuBee, however, NFC signals can be detected miles from the source. RuBee signals are detectable at a maximum distance of 20 metres (66 ft) from the source.
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https://en.wikipedia.org/wiki/RuBee
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Tetheringorphone-as-modem (PAM)is the sharing of a mobile device'scellulardata connection with other connected computers. It effectively turns the transmitting device into amodemto allow others to use its cellular network as agatewayforInternetaccess.[1][2]The sharing can be done wirelessly overwireless LAN(Wi-Fi),Bluetooth,IrDAor by physical connection using a cable likeUSB. If tethering is done over Wi-Fi, the feature may be branded as apersonal hotspotormobile hotspot, and the transmitting mobile device would also act as a portable wirelessaccess point(AP)[3]which may also beprotectedusing a password.[4]Tethering over Bluetooth may use the Personal Area Networking (PAN)profilebetween paired devices, or alternatively the Dial-Up Networking (DUN) profile where the receiving device virtually dials the cellular networkAPN, typically using thenumber*99#.[5][6]
Many mobile devices are equipped with software to offer tethered Internet access.Windows Mobile 6.5,Windows Phone 7,Android(starting from version 2.2), andiOS3.0 (or later) offer tethering over a BluetoothPANor a USB connection. Tethering over Wi-Fi, also known as Personal Hotspot, is available on iOS starting withiOS 4.2.5(or later) oniPhone 4oriPad (3rd gen), certain Windows Mobile 6.5 devices like theHTC HD2, Windows Phone 7, 8 and 8.1 devices (varies by manufacturer and model), and certain Android phones (varies widely depending on carrier, manufacturer, and software version).[7]
For PCs, Windows added support for USB tethering devices sinceWindows 7.
For IPv4 networks, the tethering normally works viaNATon the handset's existing data connection, so from the network point of view, there is just one device with a singleIPv4 network address, though it is technically possible to attempt to identify multiple machines.
On somemobile network operators, this feature is contractually unavailable by default, and may be activated only by paying to add a tethering package to a data plan or choosing a data plan that includes tethering. This is done primarily because with a computer sharing the network connection, there is typically substantially more network traffic.
Some network-provided devices have carrier-specific software that may deny the inbuilt tethering ability normally available on the device, or enable it only if the subscriber pays an additional fee. Some operators have askedGoogleor any mobile device producer using Android to completely remove tethering capability from the operating system on certain devices.[8]Handsets purchased SIM-free, without a network provider subsidy, are often unhindered with regard to tethering.
There are, however, several ways to enable tethering on restricted devices without paying the carrier for it, including third-party USB tethering apps such as PDAnet,rooting Android devicesorjailbreaking iOS devicesand installing a tethering application on the device.[9]Tethering is also available as a downloadable third-party application on mostSymbianmobile phones[10]as well as on theMeeGoplatform[11]and onWebOSmobiles phones.[12]
Depending on the wireless carrier, a user'scellulardevice may have restricted functionality. While tethering may be allowed at no extra cost, some carriers impose a one-time charge to enable tethering and others forbid tethering or impose added data charges. Contracts that advertise "unlimited" data usage often have limits detailed in afair usage policy.
Since 2014, all pay-monthly plans from theThreenetwork in the UK include a "personal hotspot" feature.[13]
Earlier, two tethering-permitted mobile plans offered unlimited data:The Full Monty[14]onT-Mobile, andThe One PlanonThree. Three offered tethering as a standard feature until early 2012, retaining it on selected plans. T-Mobile dropped tethering on its unlimited data plans in late 2012.[15]
As cited inSprint Nextel's "Terms of Service":
"Except with Phone-as-Modem plans, you may not use a phone (including a Bluetooth phone) as a modem in connection with a computer, PDA, or similar device. We reserve the right to deny or terminate service without notice for any misuse or any use that adversely affects network performance."[16]
T-Mobile UShas a similar clause in its "Terms & Conditions":
"Unless explicitly permitted by your Data Plan, other uses, including for example, using your Device as a modem or tethering your Device to a personal computer or other hardware, are not permitted."[17]
T-Mobile's Simple Family or Simple Business plans offer "Hotspot" from devices that offer that function (such as Apple iPhone) to up to five devices. Since March 27, 2014, 1000 MB per month is free in the US with cellular service.[18]The host device has unlimited slow internet for the rest of the month, and all month while roaming in 100 countries, but with no tethering. For US$10 or $20 per month more per host device, the amount of data available for tethering can be increased markedly.[19]The host device cellular services can be canceled, added, or changed at any time; pro-rated, data tethering levels can be changed month-to-month; and T-Mobile no longer requires any long-term service contracts, allowing users to bring their own devices or buy devices from them, independent of whether they continue service with them.
As of 2013[update]Verizon WirelessandAT&T Mobilityoffer wired tethering to their plans for a fee, while Sprint Nextel offers a Wi-Fi connected "mobile hotspot" tethering feature at an added charge. However, actions by theFederal Communications Commission(FCC) and a small claims court in California may make it easier for consumers to tether. On July 31, 2012, the FCC released an unofficial announcement of Commission action, decreeing Verizon Wireless must pay $1.25 million to resolve the investigation regarding compliance of the C Block Spectrum (seeUS Wireless Spectrum Auction of 2008).[20]The announcement also stated that "(Verizon) recently revised its service offerings such that consumers on usage-based pricing plans may tether, using any application, without paying an additional fee." After that judgement, Verizon released "Share Everything" plans that enable tethering, however users must drop old plans they were grandfathered under (such as the Unlimited Data plans) and switch, or pay a tethering fee.
In another instance, Judge Russell Nadel of the Ventura Superior Court awarded AT&T customer Matt Spaccarelli $850, despite the fact that Spaccarelli had violated his terms of service byjailbreakinghis iPhone in order to fully utilize his iPhone's hardware. Spaccarelli demonstrated that AT&T had unfairly throttled his data connection. His data shows that AT&T had been throttling his connection after approximately 2 GB of data was used.[21]Spaccarelli responded by creating a personal web page in order to provide information that allows others to file a similar lawsuit, commenting:
"Hopefully with all this concrete data and the courts on our side, AT&T will be forced to change something. Let's just hope it chooses to go the way of Sprint, not T-Mobile."[22]
While T-Mobile did eventually allow tethering, on August 31, 2015, the company announced it will punish users who abuse its unlimited data by violating T-Mobile's rules on tethering (which unlike standard data does carry a 7GBcap beforethrottlingtakes effect) by permanently kicking them off the unlimited plans and making users sign up for tiered data plans.[23]T-Mobile mentioned that it was only a small handful of users who abused the tethering rules by using anAndroidapp that masks T-Mobile's tethering monitoring and uses as much as 2TBsper month, causing speed issues for most customers who do not abuse the rules.[24]
Germany has three major cellular providers. The biggest provider, Deutsche Telekom, only states that "[...] cellular services are only provided when used together with a mobile cellular device".[25]Moreover under point 11.5 of the cellular price list it is very much prohibited to make a private cellular connection commercially or publicly available. However, the price list of cellular contracts specifically states that using your own device as a modem or personal Hotspot for personal and private use is permitted.[26]
The next biggest cellular provider, Vodafone, also states in their mobile price list that they don't allow making the personal connection publicly available. A personal hotspot and especially tethering is on all mentioned contracts allowed. For example, the "Vodafone Red 2016 S" with 2 GB up to the "Vodafone Young 2020 XL" with unlimited data encourage their users to share their data with another personal device[27]
The third-largest provider, Telefonica O2, generally sells cheaper contracts than the larger providers. With their "o2 free unlimited contract", they explicitly stated that stationary non-battery-operated WiFi access points aren't allowed to be used the contract. Therefore, the German society of consumer rights sued Telefonica O2. This clause conflicts with net neutrality, which was confirmed by the European Court of Justice.[28]Germany's highest justice court also confirmed the illegality of contract clauses that would forbid WiFi hotspots, tethering and in this case cellular routers.[29]
"Wi-Fi sharing" or "Wi-Fi repeating" is a form of tethering through wireless LAN but with a separate use case similar to awireless repeater/extender. It allows a compatible device to tether its active Wi-Fi connection, without the involvement of cellular networks. It can be useful for example when travelling with multiple devices and not needing to register every device on a public network.[30]Samsung and LG have released smartphones with this ability starting with theGalaxy S7andV20. It is calledWi-Fi sharingon Samsung Galaxy andOne UI.[31][32]Google have also added this feature for the first time on thePixel 3.[33]
Microsoft Windowscomputers also allow the sharing of an active Wi-Fi (orEthernet) connection through tethering.[34]See alsoInternet Connection Sharing(ICS).
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https://en.wikipedia.org/wiki/Tethering
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Threadis anIPv6-based, low-powermesh networkingtechnology forInternet of things(IoT) products.[1]The Thread protocol specification is available at no cost; however, this requires agreement and continued adherence to anend-user license agreement(EULA), which states "Membership in Thread Group is necessary to implement, practice, and ship Thread technology and Thread Group specifications."[2]
Often used as a transport forMatter(the combination being known asMatter over Thread), the protocol has seen increased use for connectinglow-powerand battery-operatedsmart-homedevices.[3]
In July 2014, the Thread Group alliance was formed as an industry group to develop, maintain and drive adoption of Thread as an industry networking standard for IoT applications.[4]Thread Group provides certification for components and products to ensure adherence to the spec. Initial members wereARM Holdings,Big Ass Solutions,NXP Semiconductors/Freescale,Google-subsidiaryNest Labs,OSRAM,Samsung,Silicon Labs,Somfy,Tyco International,Qualcomm, and theYalelock company. In August 2018,Applejoined the group,[5]and released its first Thread product, theHomePod Mini, in late 2020.[6]
Thread uses6LoWPAN, which, in turn, uses theIEEE 802.15.4wireless protocol with mesh communication (in the2.4 GHzspectrum), as doZigbeeand other systems. However, Thread isIP-addressable, withcloudaccess andAES encryption. ABSD-licensedopen-source implementation of Thread calledOpenThreadis available from and managed by Google.[7]
The OpenThreadnetwork simulator, a part of the OpenThread implementation, simulates Thread networks using OpenThreadPOSIXinstances.[8]The simulator utilisesdiscrete-event simulationand allows for visualisation of communications through a web interface.[relevant?][9]
In 2019, the Connected Home over IP (CHIP) project, subsequently renamed toMatter, led by the Zigbee Alliance, now theConnectivity Standards Alliance(CSA), Google, Amazon, and Apple, announced a broad collaboration to create aroyalty-freestandard andopen-sourcecode base to promote interoperability in home connectivity, leveraging Thread, Wi-Fi, andBluetooth Low Energy.[10][11]
Apple TV 4K (2nd generation)
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https://en.wikipedia.org/wiki/Thread_(network_protocol)
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IEEE 802.11ahis awireless networkingprotocol published in 2017[1]calledWi-Fi HaLow[2][3][4](/ˈheɪˌloʊ/) as an amendment of theIEEE 802.11-2007wireless networking standard. It uses900 MHzlicense-exempt bandsto provide extended-rangeWi-Finetworks, compared to conventional Wi-Fi networks operating in the2.4 GHz,5 GHzand6 GHzbands. It also benefits from lower energy consumption, allowing the creation of large groups of stations or sensors that cooperate to share signals, supporting the concept of theInternet of things(IoT).[5]The protocol's low power consumption competes withBluetooth,LoRa,Zigbee, andZ-Wave,[6][7]and has the added benefit of higherdata ratesand wider coverage range.[2]
A benefit of 802.11ah is extended range, making it useful for rural communications and offloadingcell phone towertraffic.[8]The other purpose of the protocol is to allow low rate 802.11 wireless stations to be used in the sub-gigahertz spectrum.[5]The protocol is one of the IEEE 802.11 technologies which is the most different from theLANmodel, especially concerning medium contention. A prominent aspect of 802.11ah is the behavior of stations that are grouped to minimize contention on the air media, use relay to extend their reach, use little power thanks to predefined wake/doze periods, are still able to send data at high speed under some negotiated conditions and use sectored antennas. It uses the 802.11a/g specification that is down sampled to provide 26 channels, each of them able to provide 100 kbit/sthroughput. It can cover a one-kilometer radius.[9]It aims at providing connectivity to thousands of devices under anaccess point. The protocol supportsmachine to machine(M2M) markets, likesmart metering.[10]
Data rates up to 347 Mbit/s are achieved only with the maximum of four spatial streams using one 16 MHz-wide channel. Variousmodulationschemes andcodingrates are defined by the standard and are represented by aModulation and Coding Scheme(MCS) index value. The table below shows the relationships between the variables that allow for the maximum data rate. TheGuard interval(GI) is defined as the timing betweensymbols.
2 MHz channel uses anFFTof 64, of which: 56OFDMsubcarriers, 52 are for data and 4 arepilot toneswith a carrier separation of 31.25 kHz (2 MHz/64) (32 μs). Each of these subcarriers can be aBPSK,QPSK, 16-QAM, 64-QAMor 256-QAM. The total bandwidth is 2 MHz with an occupied bandwidth of 1.78 MHz. Total symbol duration is 36 or 40microseconds, whichincludesa guard interval of 4 or 8 microseconds.[9]
A RelayAccess Point(AP) is an entity that logically consists of a Relay and anetworking station(STA), or client. The relay function allows an AP and stations to exchange frames with one another by the way of a relay. The introduction of a relay allows stations to use higher MCSs (Modulation and Coding Schemes) and reduce the time stations will stay in Active mode. This improves battery life of stations. Relay stations may also provide connectivity for stations located outside the coverage of the AP. There is an overhead cost on overall network efficiency and increased complexity with the use of relay stations. To limit this overhead, the relaying function shall be bi-directional and limited to two hops only.
Power-saving stations are divided into two classes: TIM stations and non-TIM stations. TIM stations periodically receive information about traffic buffered for them from the access point in the so-called TIM information element, hence the name. Non-TIM stations use the new Target Wake Time mechanism which enables reducing signaling overhead.[11]
Target Wake Time (TWT) is a function that permits an AP to define a specific time or set of times for individual stations to access the medium. The STA (client) and the AP exchange information that includes an expected activity duration to allow the AP to control the amount of contention and overlap among competing STAs. The AP can protect the expected duration of activity with various protection mechanisms. The use of TWT is negotiated between an AP and an STA. Target Wake Time may be used to reduce network energy consumption, as stations that use it can enter a doze state until their TWT arrives.
Restricted Access Window allows partitioning of the stations within aBasic Service Set(BSS) into groups and restricting channel access only to stations belonging to a given group at any given time period. It helps to reduce contention and to avoid simultaneous transmissions from a large number of stations hidden from each other.[12][13]
Bidirectional TXOP allows an AP and non-AP (STA or client) to exchange a sequence of uplink and downlink frames during a reserved time (transmit opportunity or TXOP). This operation mode is intended to reduce the number of contention-based channel accesses, improve channel efficiency by minimizing the number of frame exchanges required for uplink and downlink data frames, and enable stations to extend battery lifetime by keeping Awake times short. This continuous frame exchange is done both uplink and downlink between the pair of stations. In earlier versions of the standard Bidirectional TXOP was called Speed Frame Exchange.[14]
The partition of the coverage area of a Basic Service Set (BSS) into sectors, each containing a subset of stations, is called sectorization. This partitioning is achieved through a set of antennas or a set of synthesized antenna beams to cover different sectors of the BSS. The goal of the sectorization is to reduce medium contention or interference by the reduced number of stations within a sector and/or to allow spatial sharing among overlapping BSS (OBSS) APs or stations.
Another WLAN standard for sub-1 GHz bands isIEEE 802.11afwhich, unlike 802.11ah, operates in licensed bands. More specifically, 802.11af operates in the TVwhite space spectrumin theVHFandUHFbands between 54 and 790 MHz usingcognitive radiotechnology.[15]
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https://en.wikipedia.org/wiki/IEEE_802.11ah
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Zigbeeis anIEEE 802.15.4-basedspecificationfor a suite of high-levelcommunication protocolsused to createpersonal area networkswith small, low-powerdigital radios, such as forhome automation, medical device data collection, and other low-power low-bandwidth needs, designed for small scale projects which need wireless connection. Hence, Zigbee is a low-power, low-data-rate, and close proximity (i.e., personal area)wireless ad hoc network.
The technology defined by the Zigbee specification is intended to be simpler and less expensive than other wirelesspersonal area networks(WPANs), such asBluetoothor more general wireless networking such asWi-Fi(orLi-Fi). Applications include wireless light switches,home energy monitors, traffic management systems, and other consumer and industrial equipment that requires short-range low-rate wireless data transfer.
Its low power consumption limits transmission distances to 10–100 meters (33–328 ft)line-of-sight, depending on power output and environmental characteristics.[1]Zigbee devices can transmit data over long distances by passing data through amesh networkof intermediate devices to reach more distant ones. Zigbee is typically used in low data rate applications that require long battery life and secure networking. (Zigbee networks are secured by 128-bitsymmetric encryptionkeys.) Zigbee has a defined rate of up to250kbit/s, best suited for intermittent data transmissions from a sensor or input device.
Zigbee was conceived in 1998, standardized in 2003, and revised in 2006. The name refers to thewaggle danceof honey bees after their return to the beehive.[2]
Zigbee is a low-powerwireless mesh networkstandard targeted at battery-powered devices in wireless control and monitoring applications. Zigbee delivers low-latency communication. Zigbee chips are typically integrated with radios and withmicrocontrollers.
Zigbee operates in the industrial, scientific and medical (ISM) radio bands, with the2.4GHzband being primarily used for lighting and home automation devices in most jurisdictions worldwide. While devices for commercial utility metering and medical device data collection often usesub-GHzfrequencies, (902-928MHzin North America, Australia, and Israel, 868-870 MHz in Europe, 779-787 MHz in China, even those regions and countries still using the 2.4 GHz for most globally sold Zigbee devices meant for home use. With data rates varying from around 20 kbit/s for sub-GHz bands to around 250 kbit/s for channels on the 2.4 GHz band range).
Zigbee builds on thephysical layerandmedia access controldefined inIEEE standard 802.15.4for low-rate wireless personal area networks (WPANs). The specification includes four additional key components:network layer,application layer,Zigbee Device Objects(ZDOs) and manufacturer-defined application objects. ZDOs are responsible for some tasks, including keeping track of device roles, managing requests to join a network, and discovering and securing devices.
The Zigbee network layer natively supports bothstarandtreenetworks, and genericmesh networking. Every network must have one coordinator device. Within star networks, the coordinator must be the central node. Both trees and meshes allow the use of Zigbeeroutersto extend communication at the network level. Another defining feature of Zigbee is facilities for carrying out secure communications, protecting the establishment and transport of cryptographic keys, ciphering frames, and controlling devices. It builds on the basic security framework defined in IEEE 802.15.4.
Zigbee-style self-organizingad hoc digital radio networkswere conceived in the 1990s. The IEEE 802.15.4-2003 Zigbee specification was ratified on December 14, 2004.[3]TheConnectivity Standards Alliance(formerly Zigbee Alliance) announced availability of Specification 1.0 on June 13, 2005, known as theZigBee 2004 Specification.
In September 2006, theZigbee 2006 Specificationwas announced, obsoleting the 2004 stack[4]The 2006 specification replaces the message andkey–value pairstructure used in the 2004 stack with acluster library. The library is a set of standardised commands, attributes and global artifacts organised under groups known as clusters with names such as Smart Energy, Home Automation, andZigbee Light Link.[5]
In January 2017, Connectivity Standards Alliance renamed the library toDotdotand announced it as a new protocol to be represented by an emoticon (||:).They also announced it will now additionally run over other network types usingInternet Protocol[6]and will interconnect with other standards such asThread.[7]Since its unveiling, Dotdot has functioned as the default application layer for almost all Zigbee devices.[8]
Zigbee Pro, also known as Zigbee 2007, was finalized in 2007.[9]A Zigbee Pro device may join and operate on a legacy Zigbee network and vice versa. Due to differences in routing options, a Zigbee Pro device must become a non-routing Zigbee End Device (ZED) on a legacy Zigbee network, and a legacy Zigbee device must become a ZED on a Zigbee Pro network.[10]It operates using the 2.4 GHz ISM band, and adds a sub-GHz band.[11]
Zigbee protocols are intended for embedded applications requiringlow power consumptionand tolerating lowdata rates. The resulting network will use very little power—individual devices must have a battery life of at least two years to pass certification.[12][13][dubious–discuss]
Typical application areas include:
Zigbee is not for situations with high mobility among nodes. Hence, it is not suitable for tactical ad hoc radio networks in the battlefield, where high data rate and high mobility is present and needed.[citation needed][18]
The first Zigbee application profile, Home Automation, was announced November 2, 2007.[citation needed]Additional application profiles have since been published.
TheZigbee Smart Energy 2.0specifications define anInternet Protocol-basedcommunication protocolto monitor, control, inform, and automate the delivery and use of energy and water. It is an enhancement of the Zigbee Smart Energy version 1 specifications.[19]It adds services forplug-in electric vehiclecharging, installation, configuration and firmware download, prepay services, user information and messaging, load control,demand responseand common information and application profile interfaces for wired and wireless networks. It is being developed by partners including:
Zigbee Smart Energy relies on Zigbee IP, a network layer that routes standard IPv6 traffic over IEEE 802.15.4 using6LoWPANheader compression.[20][21]
In 2009, the Radio Frequency for Consumer Electronics Consortium (RF4CE) and Connectivity Standards Alliance (formerly Zigbee Alliance) agreed to deliver jointly a standard for radio frequency remote controls. Zigbee RF4CE is designed for a broad range of consumer electronics products, such as TVs and set-top boxes. It promised many advantages over existing remote control solutions, including richer communication and increased reliability, enhanced features and flexibility, interoperability, and no line-of-sight barrier.[22]The Zigbee RF4CE specification uses a subset of Zigbee functionality allowing to run on smaller memory configurations in lower-cost devices, such as remote control of consumer electronics.
The radio design used by Zigbee has fewanalogstages and usesdigital circuitswherever possible. Products that integrate the radio and microcontroller into a single module are available.[23]
The Zigbee qualification process involves a full validation of the requirements of the physical layer. All radios derived from the same validatedsemiconductor mask setwould enjoy the same RF characteristics. Zigbee radios have very tight constraints on power and bandwidth. An uncertified physical layer that malfunctions can increase the power consumption of other devices on a Zigbee network. Thus, radios are tested with guidance given by Clause 6 of the 802.15.4-2006 Standard.[24]
This standard specifies operation in the unlicensed 2.4 to 2.4835 GHz[25](worldwide), 902 to 928 MHz (Americas and Australia) and 868 to 868.6 MHz (Europe)ISM bands. Sixteen channels are allocated in the 2.4 GHz band, spaced 5 MHz apart, though using only 2 MHz of bandwidth each. The radios usedirect-sequence spread spectrumcoding, which is managed by the digital stream into the modulator.Binary phase-shift keying(BPSK) is used in the 868 and 915 MHz bands, andoffset quadrature phase-shift keying(OQPSK) that transmits two bits per symbol is used in the 2.4 GHz band.
The raw, over-the-air data rate is 250kbit/sperchannelin the 2.4 GHz band, 40 kbit/s per channel in the 915 MHz band, and 20 kbit/s in the 868 MHz band. The actual data throughput will be less than the maximum specified bit rate because of thepacket overheadand processing delays. For indoor applications at 2.4 GHz transmission distance is 10–20 m, depending on the construction materials, the number of walls to be penetrated and the output power permitted in that geographical location.[26]The output power of the radios is generally 0–20dBm(1–100 mW).
There are three classes of Zigbee devices:
The current Zigbee protocols support beacon-enabled and non-beacon-enabled networks.
In non-beacon-enabled networks, an unslottedCSMA/CAchannel access mechanism is used. In this type of network, Zigbee routers typically have their receivers continuously active, requiring additional power.[29]However, this allows for heterogeneous networks in which some devices receive continuously while others transmit when necessary. The typical example of a heterogeneous network is awireless light switch: The Zigbee node at the lamp may constantly receive since it is reliably powered by the mains supply to the lamp, while a battery-powered light switch would remain asleep until the switch is thrown. In this case, the switch wakes up, sends a command to the lamp, receives an acknowledgment, and returns to sleep. In such a network the lamp node will be at least a Zigbee router, if not the Zigbee coordinator; the switch node is typically a Zigbee end device.
In beacon-enabled networks, Zigbee routers transmit periodic beacons to confirm their presence to other network nodes. Nodes may sleep between beacons, thus extending their battery life. Beacon intervals depend on data rate; they may range from 15.36 milliseconds to 251.65824 seconds at 250 kbit/s, from 24 milliseconds to 393.216 seconds at 40 kbit/s and from 48 milliseconds to 786.432 seconds at 20 kbit/s. Long beacon intervals require precise timing, which can be expensive to implement in low-cost products.
In general, the Zigbee protocols minimize the time the radio is on, so as to reduce power use. In beaconing networks, nodes only need to be active while a beacon is being transmitted. In non-beacon-enabled networks, power consumption is decidedly asymmetrical: Some devices are always active while others spend most of their time sleeping.
Except for Smart Energy Profile 2.0, Zigbee devices are required to conform to the IEEE 802.15.4-2003 Low-rate Wireless Personal Area Network (LR-WPAN) standard. The standard specifies the lowerprotocol layers—thephysical layer(PHY), and themedia access controlportion of thedata link layer. The basic channel access mode iscarrier-sense multiple access with collision avoidance(CSMA/CA). That is, the nodes communicate in a way somewhat analogous to how humans converse: a node briefly checks to see that other nodes are not talking before it starts. CSMA/CA is not used in three notable exceptions:
The main functions of thenetwork layerare to ensure correct use of theMAC sublayerand provide a suitable interface for use by the next upper layer, namely the application layer. The network layer deals with network functions such as connecting, disconnecting, and setting up networks. It can establish a network, allocate addresses, and add and remove devices. This layer makes use of star, mesh and tree topologies.
The data entity of the transport layer creates and managesprotocol data unitsat the direction of the application layer and performs routing according to the current topology. The control entity handles the configuration of new devices and establishes new networks. It can determine whether a neighboring device belongs to the network and discovers new neighbors and routers.
The routing protocol used by the network layer isAODV.[30]To find a destination device, AODV is used to broadcast a route request to all of its neighbors. The neighbors then broadcast the request to their neighbors and onward until the destination is reached. Once the destination is reached, a route reply is sent via unicast transmission following the lowest cost path back to the source. Once the source receives the reply, it updates its routing table with the destination address of the next hop in the path and the associated path cost.
The application layer is the highest-level layer defined by the specification and is the effective interface of the Zigbee system to its end users. It comprises the majority of components added by the Zigbee specification: both ZDO (Zigbee device object) and its management procedures, together with application objects defined by the manufacturer, are considered part of this layer. This layer binds tables, sends messages between bound devices, manages group addresses, reassembles packets, and transports data. It is responsible for providing service to Zigbee device profiles.
TheZDO(Zigbee device object), a protocol in the Zigbee protocol stack, is responsible for overall device management, security keys, and policies. It is responsible for defining the role of a device as either coordinator or end device, as mentioned above, but also for the discovery of new devices on the network and the identification of their offered services. It may then go on to establish secure links with external devices and reply to binding requests accordingly.
The application support sublayer (APS) is the other main standard component of the stack, and as such it offers a well-defined interface and control services. It works as a bridge between the network layer and the other elements of the application layer: it keeps up-to-datebinding tablesin the form of a database, which can be used to find appropriate devices depending on the services that are needed and those the different devices offer. As the union between both specified layers, it also routes messages across the layers of theprotocol stack.
An application may consist of communicating objects which cooperate to carry out the desired tasks. Tasks will typically be largely local to each device, such as the control of each household appliance. The focus of Zigbee is to distribute work among many different devices which reside within individual Zigbee nodes which in turn form a network.
The objects that form the network communicate using the facilities provided by APS, supervised by ZDO interfaces. Within a single device, up to 240 application objects can exist, numbered in the range 1–240. 0 is reserved for the ZDO data interface and 255 for broadcast; the 241-254 range is not currently in use but may be in the future.
Two services are available for application objects to use (in Zigbee 1.0):
Addressing is also part of the application layer. A network node consists of an IEEE 802.15.4-conformant radiotransceiverand one or more device descriptions (collections of attributes that can be polled or set or can be monitored through events). The transceiver is the basis for addressing, and devices within a node are specified by anendpoint identifierin the range 1 to 240.
For applications to communicate, the devices that support them must use a common application protocol (types of messages, formats and so on); these sets of conventions are grouped inprofiles. Furthermore, binding is decided upon by matching input and outputcluster identifiers[clarify]unique within the context of a given profile and associated to an incoming or outgoing data flow in a device. Binding tables contain source and destination pairs.
Depending on the available information, device discovery may follow different methods. When the network address is known, the IEEE address can be requested usingunicastcommunication. When it is not, petitions arebroadcast. End devices will simply respond with the requested address while a network coordinator or a router will also send the addresses of all the devices associated with it.
Thisextended discovery protocol[clarify]permits external devices to find out about devices in a network and the services that they offer, which endpoints can report when queried by the discovering device (which has previously obtained their addresses). Matching services can also be used.
The use of cluster identifiers enforces the binding of complementary entities using the binding tables, which are maintained by Zigbee coordinators, as the table must always be available within a network and coordinators are most likely to have a permanent power supply. Backups, managed by higher-level layers, may be needed by some applications. Binding requires an established communication link; after it exists, whether to add a new node to the network is decided, according to the application and security policies.
Communication can happen right after the association.Direct addressinguses both radio address and endpoint identifier, whereas indirect addressing uses every relevant field (address, endpoint, cluster, and attribute) and requires that they are sent to the network coordinator, which maintains associations and translates requests for communication. Indirect addressing is particularly useful to keep some devices very simple and minimize their need for storage. Besides these two methods,broadcastto all endpoints in a device is available, andgroup addressingis used to communicate with groups of endpoints belonging to a specified set of devices.
As one of its defining features, Zigbee provides facilities for carrying outsecure communications, protecting the establishment and transport ofcryptographic keysand encrypting data. It builds on the basic security framework defined in IEEE 802.15.4.
The basic mechanism to ensure confidentiality is the adequate protection of all keying material. Keys are the cornerstone of the security architecture; as such their protection is of paramount importance, and keys are never supposed to be transported through aninsecure channel. A momentary exception to this rule occurs during the initial phase of the addition to the network of a previously unconfigured device. Trust must be assumed in the initial installation of the keys, as well as in the processing of security information. The Zigbee network model must take particular care of security considerations, asad hoc networksmay be physically accessible to external devices. Also, the state of the working environment cannot be predicted.
Within the protocol stack, different network layers are not cryptographically separated, so access policies are needed, and conventional design assumed. The open trust model within a device allows for key sharing, which notably decreases potential cost. Nevertheless, the layer which creates a frame is responsible for its security. As malicious devices may exist, every network layer payload must be ciphered, so unauthorized traffic can be immediately cut off. The exception, again, is the transmission of the network key, which confers a unified security layer to the grid, to a new connecting device.
The Zigbee security architecture is based on CCM*, which adds encryption- and integrity-only features toCCM mode.[31]Zigbee uses 128-bit keys to implement its security mechanisms. A key can be associated either to a network, being usable by Zigbee layers and the MAC sublayer, or to a link, acquired through pre-installation, agreement or transport. Establishment of link keys is based on a master key which controls link key correspondence. Ultimately, at least, the initial master key must be obtained through a secure medium (transport or pre-installation), as the security of the whole network depends on it. Link and master keys are only visible to the application layer. Different services use differentone-wayvariations of the link key to avoid leaks and security risks.
Key distribution is one of the most important security functions of the network. A secure network will designate one special device, thetrust center, which other devices trust for the distribution of security keys. Ideally, devices will have the trust center address and initial master key preloaded; if a momentary vulnerability is allowed, it will be sent as described above. Typical applications without special security needs will use a network key provided by the trust center (through the initially insecure channel) to communicate.
Thus, the trust center maintains both the network key and provides point-to-point security. Devices will only accept communications originating from a key supplied by the trust center, except for the initial master key. The security architecture is distributed among the network layers as follows:
According to the German computer e-magazineHeise Online, Zigbee Home Automation 1.2 uses fallback keys for encryption negotiation which are known and cannot be changed. This makes the encryption highly vulnerable.[32][33]The Zigbee 3.0 standard features improved security features and mitigates the aforementioned weakness by giving device manufacturers the option of using a custom installation key that is then shipped together with the device, thereby preventing the network traffic from ever using the fallback key altogether. This ensures that all network traffic is securely encrypted even while pairing the device. In addition, all Zigbee devices need to randomize their network key, no matter which pairing method they use, thereby improving security for older devices. The Zigbee coordinator within the Zigbee network can be set to deny access to devices that do not employ this key randomization, further increasing security. In addition, the Zigbee 3.0 protocol features countermeasures against removing already paired devices from the network with the intention of listening to the key exchange when re-pairing.
Network simulators, likens-2,OMNeT++,OPNET, andNetSimcan be used to simulate IEEE 802.15.4 Zigbee networks. These simulators come with open sourceCorC++librariesfor users to modify. This way users can determine the validity of new algorithms before hardware implementation.
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TheISM radio bandsareportionsof theradio spectrumreserved internationally forindustrial, scientific, and medical(ISM) purposes, excluding applications intelecommunications.[1]Examples of applications for the use ofradio frequency(RF) energy in these bands includeRF heating,microwave ovens, and medicaldiathermymachines. The powerful emissions of these devices can createelectromagnetic interferenceand disruptradio communicationusing the samefrequency, so these devices are limited to certain bands of frequencies. In general, communications equipment operating in ISM bands must tolerate any interference generated by ISM applications, and users have no regulatory protection from ISM device operation in these bands.
Despite the intent of the original allocations, in recent years the fastest-growing use of these bands has been forshort-range, low-powerwireless communicationssystems, since these bands are often approved for such devices, which can be used without a government license, as would otherwise be required for transmitters; ISM frequencies are often chosen for this purpose as they already must tolerate interference issues.Cordless phones,Bluetoothdevices,near-field communication(NFC) devices,garage door openers,baby monitors, andwireless computer networks(Wi-Fi) may all use the ISM frequencies, although these low-power transmitters are not considered to be ISM devices.
The ISM bands are defined by theITU Radio Regulations(article 5) in footnotes 5.138, 5.150, and 5.280 of theRadio Regulations. Individual countries' use of the bands designated in these sections may differ due to variations in national radio regulations. Because communication devices using the ISM bands must tolerate any interference from ISM equipment, unlicensed operations are typically permitted to use these bands, since unlicensed operation typically needs to be tolerant of interference from other devices anyway. The ISM bands share allocations with unlicensed and licensed operations; however, due to the high likelihood of harmful interference, licensed use of the bands is typically low. In the United States, uses of the ISM bands are governed byPart 18of theFederal Communications Commission(FCC) rules, whilePart 15contains the rules for unlicensed communication devices, even those that share ISM frequencies. In Europe, theETSIdevelops standards for the use ofshort-range devices, some of which operate in ISM bands. The use of the ISM bands is regulated by the national spectrum regulation authorities that are members of the CEPT.
The allocation of radio frequencies is provided according toArticle 5of the ITU Radio Regulations (edition 2012).[2]
In order to improve harmonisation in spectrum utilisation, the majority of service allocations stipulated in this document were incorporated in national tables of frequency allocations and utilisations which are within the responsibilities of the appropriate national administrations. The allocation might be primary, secondary, exclusive, or shared. Exclusive or shared utilization is within the responsibility of administrations.
Type A(footnote 5.138) = frequency bands are designated forISM applications. The use of these frequency bands for ISM applications shall be subject to special authorization by the administration concerned, in agreement with other administrations whoseradiocommunication servicesmight be affected. In applying this provision, administrations shall have due regard to the latest relevant ITU-R Recommendations.
Type B(footnote 5.150) = frequency bands are also designated for ISM applications. Radiocommunication services operating within these bands must accept harmful interference which may be caused by these applications.
ITU RR, (Footnote 5.280) = In Germany, Austria, Bosnia and Herzegovina, Croatia, North Macedonia, Liechtenstein, Montenegro, Portugal, Serbia, Slovenia and Switzerland, the band 433.05–434.79 MHz (center frequency 433.92 MHz) is designated forISM applications. Radio communication services of these countries operating within this band must accept harmful interference which may be caused by these applications.
The ISM bands were first established at the International Telecommunications Conference of theITUinAtlantic City,1947. The American delegation specifically proposed several bands, including the now commonplace 2.4 GHz band, to accommodate the then nascent process of microwave heating;[3]however, FCC annual reports of that time suggest that much preparation was done ahead of these presentations.[4]
The report of the August 9th 1947 meeting of the Allocation of Frequencies committee[5]includes the remark:
"The delegate of the United States, referring to his request that the frequency 2450 Mc/s be allocated for I.S.M., indicated that there was in existence in the United States, and working on this frequency a diathermy machine and an electronic cooker, and that the latter might eventually be installed in transatlantic ships and airplanes. There was therefore some point in attempting to reach world agreement on this subject."
Radio frequencies in the ISM bands have been used for communication purposes, although such devices may experience interference from non-communication sources. In the United States, as early as 1958 Class DCitizens Band, a Part 95 service, was allocated to frequencies that are also allocated to ISM. [1]
In the U.S., the FCC first made unlicensedspread spectrumavailable in the ISM bands in rules adopted on May 9, 1985.[6]The FCC action was proposed by Michael Marcus of the FCC staff in 1980 and the subsequent regulatory action took five more years. It was part of a broader proposal to allow civil use of spread spectrum technology and was opposed at the time by mainstream equipment manufacturers and many radio system operators.[7]
Many other countries later developed similar regulations, enabling use of this technology.[8]
Industrial, scientific and medical (ISM) applications (of radio frequency energy)(short:ISM applications) are – according toarticle 1.15of theInternational Telecommunication Union's(ITU)ITU Radio Regulations(RR)[9]– defined as «Operation of equipment or appliances designed to generate and use locallyradio frequencyenergy for industrial, scientific, medical, domestic or similar purposes, excluding applications in the field oftelecommunications.»
The original ISM specifications envisioned that the bands would be used primarily for noncommunication purposes, such as heating. The bands are still widely used for these purposes. For many people, the most commonly encountered ISM device is the homemicrowave ovenoperating at 2.45 GHz which uses microwaves to cook food. Industrial heating is another big application area; such asinduction heating, microwave heat treating, plastic softening, andplastic weldingprocesses. In medical settings, shortwave and microwavediathermymachines use radio waves in the ISM bands to apply deep heating to the body for relaxation and healing. More recentlyhyperthermia therapyuses microwaves to heat tissue to kill cancer cells.
However, as detailed below, the increasing congestion of the radio spectrum, the increasing sophistication ofmicroelectronics, and the attraction of unlicensed use, has in recent decades led to an explosion of uses of these bands for short range communication systems forwireless devices, which are now by far the largest uses of these bands. These are sometimes called "non ISM" uses since they do not fall under the originally envisioned "industrial", "scientific", and "medical" application areas. One of the largest applications has beenwireless networking(Wi-Fi). TheIEEE 802.11wireless networking protocols, the standards on which almost all wireless systems are based, use the ISM bands. Virtually alllaptops,tablet computers,computer printersandcellphonesnow have 802.11wireless modemsusing the 2.4 and 5.7 GHz ISM bands.Bluetoothis another networking technology using the 2.4 GHz band, which can be problematic given the probability of interference.[10]Near-field communication(NFC) devices such asproximity cardsandcontactless smart cardsuse the lower-frequency 13 and 27 MHz ISM bands. Other short-range devices using the ISM bands are:wireless microphones,baby monitors,garage door openers, wirelessdoorbells,keyless entry systemsfor vehicles,radio controlchannels forUAVs(drones), wirelesssurveillancesystems,RFIDsystems for merchandise, andwild animal trackingsystems.
Someelectrodeless lampdesigns are ISM devices, which use RF emissions toexcitefluorescent tubes.Sulfur lampsare commercially availableplasma lamps, which use 2.45 GHzmagnetronsto heat sulfur into a brightly glowingplasma.
Long-distancewireless powersystems have been proposed and experimented with which would use high-power transmitters andrectennas, in lieu ofoverhead transmission linesandunderground cables, to send power to remote locations.NASAhas studied usingmicrowave power transmissionon 2.45 GHz to send energy collected bysolar power satellitesback to the ground.
Also in space applications, ahelicon double-layerion thrusteris a prototype spacecraft propulsion engine which uses a 13.56 MHz transmission to break down and heat gas into plasma.
In recent years ISM bands have also been shared with (non-ISM) license-free error-tolerant communications applications such aswireless sensor networksin the 915 MHz and 2.450 GHz bands, as well aswireless LANsandcordless phonesin the 915 MHz, 2.450 GHz, and 5.800 GHz bands. Because unlicensed devices are required to be tolerant of ISM emissions in these bands, unlicensed low-power users are generally able to operate in these bands without causing problems for ISM users. ISM equipment does not necessarily include a radio receiver in the ISM band (e.g. a microwave oven does not have a receiver).
In the United States, according to 47 CFR Part 15.5, low power communication devices must accept interference from licensed users of that frequency band, and the Part 15 device must not cause interference to licensed users. Note that the 915 MHz band should not be used in countries outsideRegion 2, except those that specifically allow it, such as Australia and Israel, especially those that use theGSM-900band for cellphones. The ISM bands are also widely used forradio-frequency identification(RFID) applications with the most commonly used band being the 13.56 MHz band used by systems compliant withISO/IEC 14443including those used bybiometric passportsandcontactless smart cards.
In Europe, the use of the ISM band is covered byShort Range Deviceregulations issued byEuropean Commission, based on technical recommendations byCEPTand standards byETSI. In most of Europe,LPD433band is allowed for license-free voice communication in addition toPMR446.
Wireless networkdevices use wavebands as follows:
Wireless LANs and cordless phones can also use bands other than those shared with ISM, but such uses require approval on a country by country basis.DECTphones use allocated spectrum outside the ISM bands that differs in Europe and North America.Ultra-widebandLANs require more spectrum than the ISM bands can provide, so the relevant standards such asIEEE 802.15.4aare designed to make use of spectrum outside the ISM bands. Despite the fact that these additional bands are outside the official ITU-R ISM bands, because they are used for the same types of low power personal communications, they are sometimes incorrectly referred to as ISM bands as well.
Several brands of radio control equipment use the2.4 GHzband range for low power remote control of toys, from gas powered cars to miniature aircraft.
Worldwide Digital Cordless Telecommunications or WDCT is a technology that uses the2.4 GHzradio spectrum.
Google'sProject Loonused ISM bands (specifically 2.4 and 5.8 GHz bands) for balloon-to-balloon and balloon-to-ground communications.
Pursuant to 47 CFR Part 97 some ISM bands are used by licensedamateur radiooperators for communication – includingamateur television.
[1]
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IEEE 802.15.4is a technical standard that defines the operation of alow-rate wireless personal area network(LR-WPAN). It specifies thephysical layerandmedia access controlfor LR-WPANs, and is maintained by theIEEE 802.15working group, which defined the standard in 2003.[1]It is the basis for theZigbee,[2]ISA100.11a,[3]WirelessHART,MiWi,6LoWPAN,Thread,SNAP, andClear Connect Type X[4]specifications, each of which further extends the standard by developing the upperlayers, which are not defined in IEEE 802.15.4. In particular,6LoWPANdefines a binding for theIPv6version of theInternet Protocol(IP) over WPANs, and is itself used by upper layers such asThread.
IEEE standard 802.15.4 is intended to offer the fundamental lower network layers of a type of wireless personal area network (WPAN), which focuses on low-cost, low-speed ubiquitous communication between devices. It can be contrasted with other approaches, such asWi-Fi, which offers more bandwidth and requires more power. The emphasis is on very low-cost communication of nearby devices with little to no underlying infrastructure, intending to exploit this to lower power consumption even more.
The basic framework conceives a 10-meter communications range withline of sightat atransfer rateof 250 kbit/s. Bandwidth tradeoffs are possible to favor more radicallyembedded deviceswith even lower power requirements for increased battery operating time, through the definition of not one, but several physical layers. Lower transfer rates of 20 and 40 kbit/s were initially defined, with the 100 kbit/s rate being added in the current revision.
Even lower rates can be used, which results in lower power consumption. As already mentioned, the main goal of IEEE 802.15.4 regarding WPANs is the emphasis on achieving low manufacturing and operating costs through the use of relatively simple transceivers, while enabling application flexibility and adaptability.
Key 802.15.4 features include:
Devices are designed to interact with each other over a conceptually simplewireless network. The definition of the network layers is based on theOSI model; although only the lower layers are defined in the standard, interaction with upper layers is intended, possibly using anIEEE 802.2logical link controlsublayer accessing the MAC through a convergence sublayer. Implementations may rely on external devices or be purely embedded, self-functioning devices.
The physical layer is the bottom layer in the OSI reference model used worldwide, and protocols layers transmit packets using it
Thephysical layer(PHY) provides the data transmission service. It also, provides an interface to thephysical layer management entity, which offers access to every physical layer management function and maintains a database of information on related personal area networks. Thus, the PHY manages the physicalradiotransceiver, performs channel selection along with energy and signal management functions. It operates on one of three possible unlicensed frequency bands:
The original 2003 versionof the standard specifies two physical layers based ondirect-sequence spread spectrum(DSSS) techniques: one working in the 868/915 MHz bands with transfer rates of 20 and 40 kbit/s, and one in the 2450 MHz band with a rate of 250 kbit/s.
The 2006 revisionimproves the maximum data rates of the 868/915 MHz bands, bringing them up to support 100 and 250 kbit/s as well. Moreover, it goes on to define four physical layers depending on themodulationmethod used. Three of them preserve the DSSS approach: in the 868/915 MHz bands, using either binary or, optionally, offsetquadrature phase-shift keying(QPSK); in the 2450 MHz band, using QPSK.
An optional alternative 868/915 MHz layer is defined using a combination of binary keying andamplitude-shift keying(thus based on parallel, not sequential, spread spectrum; PSSS). Dynamic switching between supported 868/915 MHz PHYs is possible.
Beyond these three bands, the IEEE 802.15.4c study group considered the newly opened 314–316 MHz, 430–434 MHz, and 779–787 MHz bands in China, while the IEEE 802.15 Task Group 4d defined an amendment to 802.15.4-2006 to support the new 950–956 MHz band in Japan. The first standard amendments by these groups were released in April 2009.
In August 2007,IEEE 802.15.4awas released expanding the four PHYs available in the earlier 2006 version to six, including one PHY using direct sequenceultra-wideband(UWB) and another usingchirp spread spectrum(CSS). The UWB PHY is allocated frequencies in three ranges: below 1 GHz, between 3 and 5 GHz, and between 6 and 10 GHz. The CSS PHY is allocated spectrum in the 2450 MHz ISM band.[7]
In April, 2009IEEE 802.15.4c and IEEE 802.15.4d were released expanding the available PHYs with several additional PHYs: one for 780 MHz band usingO-QPSKor MPSK,[8]another for 950 MHz usingGFSKorBPSK.[9]
IEEE 802.15.4e was chartered to define a MAC amendment to the existing standard 802.15.4-2006 which adopts a channel hopping strategy to improve support for the industrial market. Channel hopping increases robustness against external interference and persistent multi-path fading. On February 6, 2012, the IEEE Standards Association Board approved IEEE 802.15.4e which concluded all Task Group 4e efforts.
Themedium access control(MAC) enables the transmission of MAC frames through the use of the physical channel. Besides the data service, it offers a management interface and itself manages access to the physical channel and networkbeaconing. It also controls frame validation, guaranteestime slotsand handles node associations. Finally, it offers hook points for secure services.
Note that the IEEE 802.15 standard doesnotuse 802.1D or 802.1Q; i.e., it does not exchange standardEthernet frames. The physical frame-format is specified in IEEE802.15.4-2011 in section 5.2. It is tailored to the fact that most IEEE 802.15.4 PHYs only support frames of up to 127 bytes (adaptation layer protocols such as the IETF's 6LoWPAN provide fragmentation schemes to support larger network layer packets).
No higher-level layers or interoperability sublayers are defined in the standard. Other specifications, such asZigbee, SNAP, and6LoWPAN/Thread, build on this standard.RIOT,OpenWSN,TinyOS, Unison RTOS, DSPnano RTOS, nanoQplus,ContikiandZephyroperating systems also use some components of IEEE 802.15.4 hardware and software.
The standard defines two types of network node.
The first one is thefull-function device(FFD). It can serve as the coordinator of a personal area network just as it may function as a common node. It implements a general model of communication which allows it to talk to any other device: it may also relay messages, in which case it is dubbed a coordinator (PAN coordinator when it is in charge of the whole network).
On the other hand, there arereduced-function devices(RFD). These are meant to be extremely simple devices with very modest resource and communication requirements; due to this, they can only communicate with FFDs and can never act as coordinators.
Networks can be built as eitherpeer-to-peerorstarnetworks. However, every network needs at least one FFD to work as the coordinator of the network. Networks are thus formed by groups of devices separated by suitable distances. Each device has a unique 64-bit identifier, and if some conditions are met, short 16-bit identifiers can be used within a restricted environment. Namely, within each PAN domain, communications will probably use short identifiers.
Peer-to-peer (or point-to-point)networks can form arbitrary patterns of connections, and their extension is only limited by the distance between each pair of nodes. They are meant to serve as the basis forad hoc networkscapable of performing self-management and organization. Since the standard does not define a network layer,routingis not directly supported, but such an additional layer can add support formultihopcommunications. Further topological restrictions may be added; the standard mentions the cluster tree as a structure which exploits the fact that an RFD may only be associated with one FFD at a time to form a network where RFDs are exclusively leaves of a tree, and most of the nodes are FFDs. The structure can be extended as a genericmesh networkwhose nodes are cluster tree networks with a local coordinator for each cluster, in addition to the global coordinator.
A more structuredstarpattern is also supported, where the coordinator of the network will necessarily be the central node. Such a network can originate when an FFD decides to create its own PAN and declare itself its coordinator, after choosing a unique PAN identifier. After that, other devices can join the network, which is fully independent from all other star networks.
Framesare the basic unit of data transport, of which there are four fundamental types (data, acknowledgment, beacon and MAC command frames), which provide a reasonable tradeoff between simplicity and robustness. Additionally, a superframe structure, defined by the coordinator, may be used, in which case two beacons act as its limits and provide synchronization to other devices as well as configuration information. A superframe consists of sixteen equal-length slots, which can be further divided into an active part and an inactive part, during which the coordinator may enter power saving mode, not needing to control its network.
Within superframescontentionoccurs between their limits, and is resolved byCSMA/CA. Every transmission must end before the arrival of the second beacon. As mentioned before, applications with well-defined bandwidth needs can use up to seven domains of one or morecontentionlessguaranteed time slots, trailing at the end of the superframe. The first part of the superframe must be sufficient to give service to the network structure and its devices. Superframes are typically utilized within the context of low-latency devices, whose associations must be kept even if inactive for long periods of time.
Data transfers to the coordinator require a beacon synchronization phase, if applicable, followed byCSMA/CAtransmission (by means of slots if superframes are in use);acknowledgmentis optional. Data transfers from the coordinator usually follow device requests: if beacons are in use, these are used to signal requests; the coordinator acknowledges the request and then sends the data in packets which are acknowledged by the device. The same is done when superframes are not in use, only in this case there are no beacons to keep track of pending messages.
Point-to-point networks may either use unslottedCSMA/CAor synchronization mechanisms; in this case, communication between any two devices is possible, whereas in "structured" modes one of the devices must be the network coordinator.
In general, all implemented procedures follow a typical request-confirm/indication-response classification.
The physical medium is accessed through aCSMA/CAaccess method. Networks which are not using beaconing mechanisms utilize an unslotted variation which is based on the listening of the medium, leveraged by arandom exponential backoffalgorithm; acknowledgments do not adhere to this discipline. Common data transmission utilizes unallocated slots when beaconing is in use; again, confirmations do not follow the same process.
Confirmation messages may be optional under certain circumstances, in which case a success assumption is made. Whatever the case, if a device is unable to process a frame at a given time, it simply does not confirm its reception:timeout-based retransmissioncan be performed a number of times, following after that a decision of whether to abort or keep trying.
Because the predicted environment of these devices demands maximization of battery life, the protocols tend to favor the methods which lead to it, implementing periodic checks for pending messages, the frequency of which depends on application needs.
Regarding secure communications, the MAC sublayer offers facilities which can be harnessed by upper layers to achieve the desired level of security. Higher-layer processes may specify keys to performsymmetric cryptographyto protect the payload and restrict it to a group of devices or just a point-to-point link; these groups of devices can be specified inaccess control lists. Furthermore, MAC computesfreshness checksbetween successive receptions to ensure that presumably old frames, or data which is no longer considered valid, does not transcend to higher layers.
In addition to this secure mode, there is another, insecure MAC mode, which allows access control lists[2]merely as a means to decide on the acceptance of frames according to their (presumed) source.
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Stream ciphers, whereplaintextbits are combined with a cipher bit stream by an exclusive-or operation (xor), can be very secure if used properly.[citation needed]However, they are vulnerable to attacks if certain precautions are not followed:
Stream ciphersare vulnerable to attack if the same key is used twice (depth of two) or more.
Say we send messagesAandBof the same length, both encrypted using same key,K. The stream cipher produces a string of bitsC(K)the same length as the messages. The encrypted versions of the messages then are:
wherexoris performed bit by bit.
Say an adversary has interceptedE(A)andE(B). They can easily compute:
However,xoriscommutativeand has the property thatX xor X = 0(self-inverse) so:
If one message is longer than the other, our adversary just truncates the longer message to the size of the shorter and their attack will only reveal that portion of the longer message. In other words, if anyone intercepts two messages encrypted with the same key, they can recoverA xor B, which is a form ofrunning key cipher. Even if neither message is known, as long as both messages are in a natural language, such a cipher can often be broken by paper-and-pencil methods. DuringWorld War II, British cryptanalystJohn Tiltmanaccomplished this with theLorenz cipher(dubbed "Tunny"). With an averagepersonal computer, such ciphers can usually be broken in a matter of minutes. If one message is known, the solution is trivial.
Another situation where recovery is trivial is iftraffic-flow securitymeasures have each station sending a continuous stream of cipher bits, with null characters (e.g.LTRSinBaudot) being sent when there is no real traffic. This is common in military communications. In that case, and if the transmission channel is not fully loaded, there is a good likelihood that one of the ciphertext streams will be just nulls. TheNSAgoes to great lengths to prevent keys from being used twice. 1960s-era encryption systems often included apunched cardreader for loading keys. The mechanism would automatically cut the card in half when the card was removed, preventing its reuse.[1]: p. 6
One way to avoid this problem is to use aninitialization vector(IV), sent in the clear, that is combined with a secret master key to create a one-time key for the stream cipher. This is done in several common systems that use the popular stream cipherRC4, includingWired Equivalent Privacy(WEP),Wi-Fi Protected Access(WPA) andCiphersaber. One of the many problems with WEP was that its IV was too short, 24 bits. This meant that there was a high likelihood that the same IV would be used twice if more than a few thousand packets were sent with the same master key (seebirthday attack), subjecting the packets with duplicated IV to the key reuse attack. This problem was fixed in WPA by changing the "master" key frequently.
Suppose an adversary knows the exact content of all or part of one of our messages. As a part of aman in the middle attackorreplay attack, they can alter the content of the message without knowing the key,K. Say, for example, they know a portion of the message, say an electronics fund transfer, contains theASCIIstring"$1000.00". They can change that to"$9500.00"by XORing that portion of the ciphertext with the string:"$1000.00" xor "$9500.00". To see how this works, consider that the cipher text we send is justC(K) xor "$1000.00". The new message the adversary is creating is:
Recall that a stringXORedwith itself produces all zeros and that a string of zeros XORed with another string leaves that string intact. The result, C(K) xor "$9500.00", is what our ciphertext would have been if $9500 were the correct amount.
Bit-flipping attacks can be prevented by includingmessage authentication codeto increase the likelihood that tampering will be detected.
Stream ciphers combine a secret key with an agreed initialization vector (IV) to produce a pseudo-random sequence which from time-to-time is re-synchronized.[2]A "Chosen IV" attack relies on finding particular IV's which taken together probably will reveal information about the secret key. Typically multiple pairs of IV are chosen and differences in generated key-streams are then analysed statistically for a linearcorrelationand/or an algebraic Boolean relation (see alsoDifferential cryptanalysis). If choosing particular values of the initialization vector does expose a non-random pattern in the generated sequence, then this attack computes some bits and thus shortens the effective key length. A symptom of the attack would be frequent re-synchronisation. Modern stream ciphers include steps to adequately mix the secret key with an initialization vector, usually by performing many initial rounds.
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https://en.wikipedia.org/wiki/Stream_cipher_attacks
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Wireless securityis the prevention of unauthorized access or damage to computers or data usingwirelessnetworks, which includeWi-Fi networks. The term may also refer to the protection of the wireless network itself from adversaries seeking to damage theconfidentiality, integrity, or availabilityof the network. The most common type isWi-Fi security, which includesWired Equivalent Privacy(WEP) andWi-Fi Protected Access(WPA). WEP is an old IEEE 802.11 standard from 1997.[1]It is a notoriously weak security standard: the password it uses can often be cracked in a few minutes with a basic laptop computer and widely available software tools.[2]WEP was superseded in 2003 by WPA, a quick alternative at the time to improve security over WEP. The current standard is WPA2;[3]some hardware cannot support WPA2 without firmware upgrade or replacement. WPA2 uses an encryption device that encrypts the network with a 256-bit key; the longer key length improves security over WEP. Enterprises often enforce security using acertificate-based system to authenticate the connecting device, following the standard 802.11X.
In January 2018, the Wi-Fi Alliance announcedWPA3as a replacement to WPA2. Certification began in June 2018, and WPA3 support has been mandatory for devices which bear the "Wi-Fi CERTIFIED™" logo since July 2020.
Many laptop computers havewireless cardspre-installed. The ability to enter a network while mobile has great benefits. However, wireless networking is prone to some security issues.Hackershave found wireless networks relatively easy to break into, and even use wireless technology to hack into wired networks. As a result, it is very important that enterprises define effective wireless security policies that guard against unauthorized access to important resources.[4]Wireless Intrusion Prevention Systems(WIPS) orWireless Intrusion Detection Systems(WIDS) are commonly used to enforce wireless security policies.
The risks to users of wireless technology have increased as the service has become more popular. There were relatively few dangers when wireless technology was first introduced. Hackers had not yet had time to latch on to the new technology, and wireless networks were not commonly found in the work place. However, there are many security risks associated with the current wireless protocols andencryptionmethods, and in the carelessness and ignorance that exists at the user and corporate IT level.[5]Hacking methods have become much more sophisticated and innovative with wireless access. Hacking has also become much easier and more accessible with easy-to-useWindows- orLinux-based tools being made available on the web at no charge.
Some organizations that have nowireless access pointsinstalled do not feel that they need to address wireless security concerns. In-Stat MDR and META Group have estimated that 95% of all corporate laptop computers that were planned to be purchased in 2005 were equipped with wireless cards. Issues can arise in a supposedly non-wireless organization when a wireless laptop is plugged into the corporate network. A hacker could sit out in the parking lot and gather information from it through laptops and/or other devices, or even break in through this wireless card–equipped laptop and gain access to the wired network.
Anyone within the geographical network range of an open, unencrypted wireless network can "sniff", or capture and record, thetraffic, gain unauthorized access to internal network resources as well as to the internet, and then use the information and resources to perform disruptive or illegal acts. Such security breaches have become important concerns for both enterprise and home networks.
If router security is not activated or if the owner deactivates it for convenience, it creates a freehotspot. Since most 21st-century laptop PCs have wireless networking built in (see Intel "Centrino" technology), they do not need a third-party adapter such as aPCMCIA CardorUSBdongle. Built-in wireless networking might be enabled by default, without the owner realizing it, thus broadcasting the laptop's accessibility to any computer nearby.
Modern operating systems such asLinux,macOS, orMicrosoft Windowsmake it fairly easy to set up a PC as a wireless LAN "base station" usingInternet Connection Sharing, thus allowing all the PCs in the home to access the Internet through the "base" PC. However, lack of knowledge among users about the security issues inherent in setting up such systems often may allow others nearby access to the connection. Such"piggybacking"is usually achieved without the wireless network operator's knowledge; it may even bewithout the knowledge of the intruding userif their computer automatically selects a nearby unsecured wireless network to use as an access point.
Wireless security is another aspect of computer security. Organizations may be particularly vulnerable to security breaches[6]caused byrogue access points.
If an employee adds a wireless interface to an unsecured port of a system, they may create a breach innetwork securitythat would allow access to confidential materials.Countermeasureslike disabling open switchports during switch configuration and VLAN configuration to limit network access are available to protect the network and the information it contains, but such countermeasures must be applied uniformly to all network devices.
Wireless communication is useful in industrialmachine to machine(M2M) communication. Such industrial applications often have specific security requirements. Evaluation of these vulnerabilities and the resulting vulnerability catalogs in an industrial context when considering WLAN, NFC and ZigBee are available.[7]
The modes of unauthorised access to links, to functions and to data is as variable as the respective entities make use of program code. There does not exist a full scope model of such threat. To some extent the prevention relies on known modes and methods of attack and relevant methods for suppression of the applied methods. However, each new mode of operation will create new options of threatening. Hence prevention requires a steady drive for improvement. The described modes of attack are just a snapshot of typical methods and scenarios where to apply.
Violation of the security perimeter of a corporate network can come from a number of different methods and intents. One of these methods is referred to as “accidental association”. When a user turns on a computer and it latches on to a wireless access point from a neighboring company's overlapping network, the user may not even know that this has occurred. However, it is a security breach in that proprietary company information is exposed and now there could exist a link from one company to the other. This is especially true if the laptop is also hooked to a wired network.
Accidental association is a case of wireless vulnerability called as "mis-association".[8]Mis-association can be accidental, deliberate (for example, done to bypass corporate firewall) or it can result from deliberate attempts on wireless clients to lure them into connecting to attacker's APs.
“Malicious associations” are when wireless devices can be actively made by attackers to connect to a company network through their laptop instead of a company access point (AP). These types of laptops are known as “soft APs” and are created when a cyber criminal runs somesoftwarethat makes their wireless network card look like a legitimate access point. Once the thief has gained access, they can steal passwords, launch attacks on the wired network, or planttrojans. Since wireless networks operate at the Layer 2 level, Layer 3 protections such as network authentication andvirtual private networks(VPNs) offer no barrier. Wireless 802.1X authentications do help with some protection but are still vulnerable to hacking. The idea behind this type of attack may not be to break into aVPNor other security measures. Most likely the criminal is just trying to take over the client at the Layer 2 level.
Ad hocnetworks can pose a security threat. Ad hoc networks are defined as [peer to peer] networks between wireless computers that do not have an access point in between them. While these types of networks usually have little protection, encryption methods can be used to provide security.[9]
The security hole provided by Ad hoc networking is not the Ad hoc network itself but the bridge it provides into other networks, usually in the corporate environment, and the unfortunate default settings in most versions of Microsoft Windows to have this feature turned on unless explicitly disabled. Thus the user may not even know they have an unsecured Ad hoc network in operation on their computer. If they are also using a wired or wireless infrastructure network at the same time, they are providing a bridge to the secured organizational network through the unsecured Ad hoc connection. Bridging is in two forms. A direct bridge, which requires the user actually configure a bridge between the two connections and is thus unlikely to be initiated unless explicitly desired, and an indirect bridge which is the shared resources on the user computer. The indirect bridge may expose private data that is shared from the user's computer to LAN connections, such as shared folders or private Network Attached Storage, making no distinction between authenticated or private connections and unauthenticated Ad-Hoc networks. This presents no threats not already familiar to open/public or unsecured wifi access points, but firewall rules may be circumvented in the case of poorly configured operating systems or local settings.[10]
Non-traditional networks such as personal networkBluetoothdevices are not safe from hacking and should be regarded as a security risk.[11]Evenbarcode readers, handheldPDAs, and wireless printers and copiers should be secured. These non-traditional networks can be easily overlooked by IT personnel who have narrowly focused on laptops and access points.
Identity theft(orMAC spoofing) occurs when a hacker is able to listen in on network traffic and identify theMAC addressof a computer withnetwork privileges. Most wireless systems allow some kind ofMAC filteringto allow only authorized computers with specific MAC IDs to gain access and utilize the network. However, programs exist that have network “sniffing” capabilities. Combine these programs with other software that allow a computer to pretend it has any MAC address that the hacker desires,[12]and the hacker can easily get around that hurdle.
MAC filtering is effective only for small residential (SOHO) networks, since it provides protection only when the wireless device is "off the air". Any 802.11 device "on the air" freely transmits its unencrypted MAC address in its 802.11 headers, and it requires no special equipment or software to detect it. Anyone with an 802.11 receiver (laptop and wireless adapter) and a freeware wireless packet analyzer can obtain the MAC address of any transmitting 802.11 within range. In an organizational environment, where most wireless devices are "on the air" throughout the active working shift, MAC filtering provides only a false sense of security since it prevents only "casual" or unintended connections to the organizational infrastructure and does nothing to prevent a directed attack.
Aman-in-the-middleattacker entices computers to log into a computer which is set up as a soft AP (Access Point). Once this is done, the hacker connects to a real access point through another wireless card offering a steady flow of traffic through the transparent hacking computer to the real network. The hacker can then sniff the traffic.
One type of man-in-the-middle attack relies on security faults in challenge and handshake protocols to execute a “de-authentication attack”. This attack forces AP-connected computers to drop their connections and reconnect with the hacker's soft AP (disconnects the user from the modem so they have to connect again using their password which one can extract from the recording of the event).
Man-in-the-middle attacks are enhanced by software such as LANjack and AirJack which automate multiple steps of the process, meaning what once required some skill can now be done byscript kiddies.Hotspotsare particularly vulnerable to any attack since there is little to no security on these networks.
ADenial-of-service attack(DoS) occurs when an attacker continually bombards a targeted AP (Access Point) or network with bogus requests, premature successful connection messages, failure messages, and/or other commands. These cause legitimate users to not be able to get on the network and may even cause the network to crash. These attacks rely on the abuse of protocols such as theExtensible Authentication Protocol(EAP).
The DoS attack in itself does little to expose organizational data to a malicious attacker, since the interruption of the network prevents the flow of data and actually indirectly protects data by preventing it from being transmitted. The usual reason for performing a DoS attack is to observe the recovery of the wireless network, during which all of the initial handshake codes are re-transmitted by all devices, providing an opportunity for the malicious attacker to record these codes and use various cracking tools to analyze security weaknesses and exploit them to gain unauthorized access to the system. This works best on weakly encrypted systems such as WEP, where there are a number of tools available which can launch a dictionary style attack of "possibly accepted" security keys based on the "model" security key captured during the network recovery.
In a network injection attack, a hacker can make use of access points that are exposed to non-filtered network traffic, specifically broadcasting network traffic such as “Spanning Tree” (802.1D),OSPF,RIP, andHSRP. The hacker injects bogus networking re-configuration commands that affect routers, switches, and intelligent hubs. A whole network can be brought down in this manner and require rebooting or even reprogramming of all intelligent networking devices.
The Caffe Latte attack is another way to obtain aWEPkey and does not require a nearby access point for the targetnetwork.[13]The Caffe Latte attack works by tricking a client with the WEP password stored to connect to a malicious access point with the sameSSIDas the target network. After the client connects, the client generatesARPrequests, which the malicious access point uses to obtain keystream data. The malicious access point then repeatedly sends a deauthentication packet to the client, causing the client to disconnect, reconnect, and send additional ARP requests, which the malicious access point then uses to obtain additional keystream data. Once the malicious access point has collected a sufficient amount of keystream data. the WEP key can be cracked with a tool like [aircrack-ng].
The Caffe Latte attack was demonstrated against theWindowswireless stack, but other operating systems may also be vulnerable.
The attack was named the "Caffe Latte" attack by researcher Vivek Ramachandran because it could be used to obtain the WEP key from a remote traveler in less than the 6 minutes it takes to drink a cup of coffee.[14][15][16]
There are three principal ways to secure a wireless network.
There is no ready designed system to prevent from fraudulent usage of wireless communication or to protect data and functions with wirelessly communicating computers and other entities. However, there is a system of qualifying the taken measures as a whole according to a common understanding what shall be seen as state of the art. The system of qualifying is an international consensus as specified inISO/IEC 15408.
AWireless Intrusion Prevention System(WIPS) is a concept for the most robust way to counteract wireless security risks.[17]However such WIPS does not exist as a ready designed solution to implement as a software package. A WIPS is typically implemented as an overlay to an existingWireless LANinfrastructure, although it may be deployed standalone to enforce no-wireless policies within an organization. WIPS is considered so important to wireless security that in July 2009, thePayment Card Industry Security Standards Councilpublished wireless guidelines[18]forPCI DSSrecommending the use of WIPS to automate wireless scanning and protection for large organizations.
There are a range of wireless security measures, of varying effectiveness and practicality.
A simple but ineffective method to attempt to secure a wireless network is to hide theSSID(Service Set Identifier).[19]This provides very little protection against anything but the most casual intrusion efforts.
One of the simplest techniques is toonly allow accessfrom known, pre-approved MAC addresses. Most wireless access points contain some type ofMACID filtering. However, an attacker can simply sniff the MAC address of an authorized client andspoof this address.
Typical wireless access points provideIP addressesto clients viaDHCP. Requiring clients to set their own addresses makes it more difficult for a casual or unsophisticated intruder to log onto the network, but provides little protection against a sophisticated attacker.[19]
IEEE 802.1X is theIEEE Standardauthenticationmechanisms to devices wishing to attach to a Wireless LAN.
The Wired Equivalent Privacy (WEP)encryptionstandard was the original encryption standard for wireless, but since 2004 with the ratificationWPA2the IEEE has declared it "deprecated",[20]and while often supported, it is seldom or never the default on modern equipment.
Concerns were raised about its security as early as 2001,[21]dramatically demonstrated in 2005 by theFBI,[22]yet in 2007T.J. Maxxadmitted a massive security breach due in part to a reliance on WEP[23]and thePayment Card Industrytook until 2008 to prohibit its use – and even then allowed existing use to continue until June 2010.[24]
TheWi-Fi Protected Access(WPA and WPA2) security protocols were later created to address the problems with WEP. If a weak password, such as a dictionary word or short character string is used, WPA and WPA2 can be cracked. Using a long enough random password (e.g. 14 random letters) orpassphrase(e.g. 5randomly chosen words) makespre-shared keyWPA virtually uncrackable. The second generation of the WPA security protocol (WPA2) is based on the finalIEEE 802.11iamendment to the802.11standard and is eligible forFIPS 140-2compliance. With all those encryption schemes, any client in the network that knows the keys can read all the traffic.
Wi-Fi Protected Access (WPA) is a software/firmware improvement over WEP. All regular WLAN-equipment that worked with WEP are able to be simply upgraded and no new equipment needs to be bought. WPA is a trimmed-down version of the802.11isecurity standard that was developed by theIEEE 802.11to replace WEP. TheTKIPencryption algorithm was developed for WPA to provide improvements to WEP that could be fielded asfirmwareupgrades to existing 802.11 devices. The WPA profile also provides optional support for theAES-CCMPalgorithm that is the preferred algorithm in 802.11i and WPA2.
WPA Enterprise providesRADIUSbased authentication using 802.1X. WPA Personal uses a pre-shared Shared Key (PSK) to establish the security using an 8 to 63 character passphrase. The PSK may also be entered as a 64 character hexadecimal string. Weak PSK passphrases can be broken using off-line dictionary attacks by capturing the messages in the four-way exchange when the client reconnects after being deauthenticated. Wireless suites such asaircrack-ngcan crack a weak passphrase in less than a minute. Other WEP/WPA crackers are AirSnort andAuditor Security Collection.[25]Still, WPA Personal is secure when used with ‘good’ passphrases or a full 64-character hexadecimal key.
There was information, however, that Erik Tews (the man who created the fragmentation attack against WEP) was going to reveal a way of breaking the WPA TKIP implementation at Tokyo's PacSec security conference in November 2008, cracking the encryption on a packet in 12 to 15 minutes.[26]Still, the announcement of this 'crack' was somewhat overblown by the media, because as of August, 2009, the best attack on WPA (the Beck-Tews attack) is only partially successful in that it only works on short data packets, it cannot decipher the WPA key, and it requires very specific WPA implementations in order to work.[27]
In addition to WPAv1, TKIP,WIDSandEAPmay be added alongside. Also,VPN-networks (non-continuous secure network connections) may be set up under the 802.11-standard. VPN implementations includePPTP,L2TP,IPsecandSSH. However, this extra layer of security may also be cracked with tools such as Anger, Deceit andEttercapfor PPTP;[28]and ike-scan, IKEProbe,ipsectrace, and IKEcrack for IPsec-connections.
This stands for Temporal Key Integrity Protocol and the acronym is pronounced as tee-kip. This is part of the IEEE 802.11i standard. TKIP implements per-packet key mixing with a re-keying system and also provides a message integrity check. These avoid the problems of WEP.
The WPA-improvement over theIEEE802.1X standard already improved the authentication and authorization for access of wireless and wiredLANs. In addition to this, extra measures such as theExtensible Authentication Protocol(EAP) have initiated an even greater amount of security. This, as EAP uses a central authentication server. Unfortunately, during 2002 a Maryland professor discovered some shortcomings[citation needed]. Over the next few years these shortcomings were addressed with the use of TLS and other enhancements.[29]This new version of EAP is now called Extended EAP and is available in several versions; these include: EAP-MD5, PEAPv0, PEAPv1, EAP-MSCHAPv2, LEAP, EAP-FAST, EAP-TLS, EAP-TTLS, MSCHAPv2, and EAP-SIM.
EAP-versions include LEAP, PEAP and other EAP's.
LEAP
This stands for the Lightweight Extensible Authentication Protocol. This protocol is based on802.1Xand helps minimize the original security flaws by using WEP and a sophisticated key management system. This EAP-version is safer than EAP-MD5. This also uses MAC address authentication. LEAP is not secure; THC-LeapCracker can be used to breakCisco's version of LEAP and be used against computers connected to an access point in the form of adictionary attack. Anwrap and asleap finally are other crackers capable of breaking LEAP.[25]
PEAP
This stands for Protected Extensible Authentication Protocol. This protocol allows for a secure transport of data, passwords, and encryption keys without the need of a certificate server. This was developed by Cisco, Microsoft, andRSA Security.
Other EAPsThere are other types of Extensible Authentication Protocol implementations that are based on the EAP framework. The framework that was established supports existing EAP types as well as future authentication methods.[30]EAP-TLS offers very good protection because of its mutual authentication. Both the client and the network are authenticated using certificates and per-session WEP keys.[31]EAP-FAST also offers good protection. EAP-TTLS is another alternative made by Certicom and Funk Software. It is more convenient as one does not need to distribute certificates to users, yet offers slightly less protection than EAP-TLS.[32]
Solutions include a newer system forauthentication, IEEE802.1X, that promises to enhance security on both wired and wireless networks. Wireless access points that incorporate technologies like these often also haveroutersbuilt in, thus becomingwireless gateways.
One can argue that bothlayer 2andlayer 3encryption methods are not good enough for protecting valuable data like passwords and personal emails. Those technologies add encryption only to parts of the communication path, still allowing people to spy on the traffic if they have gained access to the wired network somehow. The solution may be encryption and authorization in theapplication layer, using technologies likeSSL,SSH,GnuPG,PGPand similar.
The disadvantage with the end-to-end method is, it may fail to cover all traffic. With encryption on the router level or VPN, a single switch encrypts all traffic, even UDP and DNS lookups. With end-to-end encryption on the other hand, each service to be secured must have its encryption "turned on", and often every connection must also be "turned on" separately. For sending emails, every recipient must support the encryption method, and must exchange keys correctly. For Web, not all web sites offer https, and even if they do, the browser sends out IP addresses in clear text.
The most prized resource is often access to the Internet. An office LAN owner seeking to restrict such access will face the nontrivial enforcement task of having each user authenticate themselves for the router.
The newest and most rigorous security to implement into WLAN's today is the 802.11i RSN-standard. This full-fledged 802.11i standard (which uses WPAv2) however does require the newest hardware (unlike WPAv1), thus potentially requiring the purchase of new equipment. This new hardware required may be either AES-WRAP (an early version of 802.11i) or the newer and better AES-CCMP-equipment. One should make sure one needs WRAP or CCMP-equipment, as the 2 hardware standards are not compatible.
WPA2is a WiFi Alliance branded version of the final 802.11i standard.[33]The primary enhancement over WPA is the inclusion of theAES-CCMPalgorithm as a mandatory feature. Both WPA and WPA2 support EAP authentication methods using RADIUS servers and preshared key (PSK).
The number of WPA and WPA2 networks are increasing, while the number of WEP networks are decreasing,[34]because of the security vulnerabilities in WEP.
WPA2 has been found to have at least one security vulnerability, nicknamed Hole196. The vulnerability uses the WPA2 Group Temporal Key (GTK), which is a shared key among all users of the sameBSSID, to launch attacks on other users of the sameBSSID. It is named after page 196 of the IEEE 802.11i specification, where the vulnerability is discussed. In order for this exploit to be performed, the GTK must be known by the attacker.[35]
Unlike 802.1X, 802.11i already has most other additional security-services such as TKIP. Just as with WPAv1, WPAv2 may work in cooperation withEAPand aWIDS.
This stands for WLAN Authentication and Privacy Infrastructure. This is a wireless security standard defined by theChinesegovernment.
Security tokenuse is a method of authentication relying upon only authorized users possessing the requisite token.Smart cardsare physical tokens in the cards that utilize an embedded integrated circuit chip for authentication, requiring a card reader.[36]USB Tokens are physical tokens that connect via USB port to authenticate the user.[37]
It is practical in some cases to apply specialized wall paint and window film to a room or building to significantly attenuate wireless signals, which keeps the signals from propagating outside a facility. This can significantly improve wireless security because it is difficult for hackers to receive the signals beyond the controlled area of a facility, such as from a parking lot.[38]
Most DoS attacks are easy to detect. However, a lot of them are difficult to stop even after detection. Here are three of the most common ways to stop a DoS attack.
Black holing is one possible way of stopping a DoS attack. This is a situation where we drop all IP packets from an attacker. This is not a very good long-term strategy because attackers can change their source address very quickly.
This may have negative effects if done automatically. An attacker could knowingly spoof attack packets with the IP address of a corporate partner. Automated defenses could block legitimate traffic from that partner and cause additional problems.
Validating the handshake involves creating false opens, and not setting aside resources until the sender acknowledges. Some firewalls address SYN floods by pre-validating the TCP handshake. This is done by creating false opens. Whenever a SYN segment arrives, the firewall sends back a SYN/ACK segment, without passing the SYN segment on to the target server.
Only when the firewall gets back an ACK, which would happen only in a legitimate connection, would the firewall send the original SYN segment on to the server for which it was originally intended. The firewall does not set aside resources for a connection when a SYN segment arrives, so handling a large number of false SYN segments is only a small burden.
Rate limiting can be used to reduce a certain type of traffic down to an amount the can be reasonably dealt with. Broadcasting to the internal network could still be used, but only at a limited rate for example. This is for more subtle DoS attacks. This is good if an attack is aimed at a single server because it keeps transmission lines at least partially open for other communication.
Rate limiting frustrates both the attacker, and the legitimate users. This helps but does not fully solve the problem. Once DoS traffic clogs the access line going to the internet, there is nothing a border firewall can do to help the situation. Most DoS attacks are problems of the community which can only be stopped with the help of ISP's and organizations whose computers are taken over as bots and used to attack other firms.
With increasing number of mobile devices with 802.1X interfaces, security of such mobile devices becomes a concern. While open standards such as Kismet are targeted towards securing laptops,[39]access points solutions should extend towards covering mobile devices also. Host based solutions for mobile handsets andPDA'swith 802.1X interface.
Security within mobile devices fall under three categories:
Wireless IPSsolutions now offer wireless security for mobile devices.[citation needed]
Mobile patient monitoring devices are becoming an integral part of healthcare industry and these devices will eventually become the method of choice for accessing and implementing health checks for patients located in remote areas. For these types of patient monitoring systems, security and reliability are critical, because they can influence the condition of patients, and could leave medical professionals in the dark about the condition of the patient if compromised.[40]
In order to implement 802.11i, one must first make sure both that the router/access point(s), as well as all client devices are indeed equipped to support the network encryption. If this is done, a server such asRADIUS, ADS,NDS, orLDAPneeds to be integrated. This server can be a computer on the local network, an access point / router with integrated authentication server, or a remote server. AP's/routers with integrated authentication servers are often very expensive and specifically an option for commercial usage likehot spots. Hosted 802.1X servers via the Internet require a monthly fee; running a private server is free yet has the disadvantage that one must set it up and that the server needs to be on continuously.[41]
To set up a server, server and client software must be installed. Server software required is anenterprise authentication serversuch as RADIUS, ADS, NDS, or LDAP. The required software can be picked from various suppliers as Microsoft, Cisco, Funk Software, Meetinghouse Data, and from some open-source projects. Software includes:
Client software comes built-in with Windows XP and may be integrated into other OS's using any of following software:
Remote Authentication Dial In User Service(RADIUS) is anAAA (authentication, authorization and accounting) protocolused for remote network access. RADIUS, developed in 1991, was originally proprietary but then published in 1997 under ISOC documents RFC 2138 and RFC 2139.[42][43]The idea is to have an inside server act as a gatekeeper by verifying identities through a username and password that is already pre-determined by the user. A RADIUS server can also be configured to enforce user policies and restrictions as well as record accounting information such as connection time for purposes such as billing.
Today, there is almost full wireless network coverage in many urban areas – the infrastructure for thewireless community network(which some consider to be the future of the internet[who?]) is already in place. One could roam around and always be connected to Internet if the nodes were open to the public, but due to security concerns, most nodes are encrypted and the users do not know how to disable encryption. Many people[who?]consider it proper etiquette to leave access points open to the public, allowing free access to Internet. Others[who?]think the default encryption provides substantial protection at small inconvenience, against dangers of open access that they fear may be substantial even on a home DSL router.
The density of access points can even be a problem – there are a limited number of channels available, and they partly overlap. Each channel can handle multiple networks, but places with many private wireless networks (for example, apartment complexes), the limited number of Wi-Fi radio channels might cause slowness and other problems.
According to the advocates of Open Access Points, it should not involve any significant risks to open up wireless networks for the public:
On the other hand, in some countries including Germany,[44]persons providing an open access point may be made (partially) liable for any illegal activity conducted via this access point. Also, many contracts with ISPs specify that the connection may not be shared with other persons.
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Disk encryptionis a technology which protects information by converting it into code that cannot be deciphered easily by unauthorized people or processes. Disk encryption usesdisk encryption softwareorhardwaretoencrypteverybitofdatathat goes on adiskor diskvolume. It is used to prevent unauthorized access to data storage.[1]
The expressionfull disk encryption (FDE)(orwhole disk encryption) signifies that everything on the disk is encrypted, but themaster boot record(MBR), or similar area of a bootable disk, with code that starts theoperating systemloading sequence, is not encrypted. Somehardware-based full disk encryptionsystems can truly encrypt an entireboot disk, including the MBR.
Transparent encryption, also known asreal-time encryptionandon-the-fly encryption(OTFE), is a method used by somedisk encryption software. "Transparent" refers to the fact that data is automaticallyencryptedor decrypted as it is loaded or saved.
With transparent encryption, the files are accessible immediately after thekeyis provided, and the entirevolumeis typicallymountedas if it were a physical drive, making the files just as accessible as any unencrypted ones. No data stored on an encrypted volume can be read (decrypted) without using the correctpassword/keyfile(s) or correctencryption keys. The entirefile systemwithin the volume is encrypted (including file names, folder names, file contents, and othermeta-data).[2]
To betransparentto the end-user, transparent encryption usually requires the use ofdevice driversto enable theencryptionprocess. Althoughadministratoraccess rights are normally required to install such drivers, encrypted volumes can typically be used by normal users without these rights.[3]
In general, every method in which data is seamlessly encrypted on write and decrypted on read, in such a way that the user and/orapplication softwareremains unaware of the process, can be called transparent encryption.
Disk encryption does not replace file encryption in all situations. Disk encryption is sometimes used in conjunction withfilesystem-level encryptionwith the intention of providing a more secure implementation. Since disk encryption generally uses the same key for encrypting the whole drive, all of the data can be decrypted when the system runs. However, some disk encryption solutions use multiple keys for encrypting different volumes. If an attacker gains access to the computer at run-time, the attacker has access to all files. Conventional file and folder encryption instead allows different keys for different portions of the disk. Thus an attacker cannot extract information from still-encrypted files and folders.
Unlike disk encryption, filesystem-level encryption does not typically encrypt filesystem metadata, such as the directory structure, file names, modificationtimestampsor sizes.
Trusted Platform Module(TPM) is asecure cryptoprocessorembedded in themotherboardthat can be used toauthenticatea hardware device. Since each TPM chip is unique to a particular device, it is capable of performing platformauthentication. It can be used to verify that the system seeking the access is the expected system.[4]
A limited number of disk encryption solutions have support for TPM. These implementations can wrap the decryption key using the TPM, thus tying thehard disk drive(HDD) to a particular device. If the HDD is removed from that particular device and placed in another, the decryption process will fail. Recovery is possible with the decryptionpasswordortoken. The TPM can impose a limit on decryption attempts per unit time, making brute-forcing harder. The TPM itself is intended to be impossible to duplicate, so that the brute-force limit is not trivially bypassed.[5]
Although this has the advantage that the disk cannot be removed from the device, it might create asingle point of failurein the encryption. For example, if something happens to the TPM or themotherboard, a user would not be able to access the data by connecting the hard drive to another computer, unless that user has a separate recovery key.
There are multiple tools available in the market that allow for disk encryption. However, they vary greatly in features and security. They are divided into three main categories:software-based, hardware-based within the storage device, and hardware-based elsewhere (such asCPUorhost bus adaptor).Hardware-based full disk encryptionwithin the storage device are called self-encrypting drives and have no impact on performance whatsoever. Furthermore, the media-encryption key never leaves the device itself and is therefore not available to any malware in the operating system.
TheTrusted Computing GroupOpal Storage Specificationprovides industry accepted standardization for self-encrypting drives. External hardware is considerably faster than the software-based solutions, although CPU versions may still have a performance impact[clarification needed], and the media encryption keys are not as well protected.
There are other (non-TCGA/OPAL based) self-encrypted drives (SED) that don't have the known vulnerabilities of the TCG/OPAL based drives (see section below).[6]They are Host/OS and BIOS independent and don't rely on the TPM module or the motherboard BIOS, and their Encryption Key never leaves the crypto-boundary of the drive.
All solutions for the boot drive require apre-boot authenticationcomponent which is available for all types of solutions from a number of vendors. It is important in all cases that the authentication credentials are usually a major potential weakness since thesymmetric cryptographyis usually strong.[clarification needed]
Secure and safe recovery mechanisms are essential to the large-scale deployment of any disk encryption solutions in an enterprise. The solution must provide an easy but secure way to recover passwords (most importantly data) in case the user leaves the company without notice or forgets the password.
Challenge–responsepassword recovery mechanism allows the password to be recovered in a secure manner. It is offered by a limited number of disk encryption solutions.
Some benefits of challenge–response password recovery:
An emergency recovery information (ERI) file provides an alternative for recovery if a challenge–response mechanism is unfeasible due to the cost of helpdesk operatives for small companies or implementation challenges.
Some benefits of ERI-file recovery:
Most full disk encryption schemes are vulnerable to acold boot attack, whereby encryptionkeyscan be stolen bycold-bootinga machine already running anoperating system, then dumping the contents ofmemorybefore the data disappears. The attack relies on thedata remanenceproperty ofcomputer memory, whereby databitscan take up to several minutes to degrade after power has been removed.[7]Even aTrusted Platform Module(TPM) is not effective against the attack, as the operating system needs to hold the decryption keys in memory in order to access the disk.[7]
Full disk encryption is also vulnerable when a computer is stolen when suspended. As wake-up does not involve aBIOSboot sequence, it typically does not ask for the FDE password. Hibernation, in contrast goes via a BIOS boot sequence, and is safe.
All software-based encryption systems are vulnerable to variousside channel attackssuch asacoustic cryptanalysisandhardware keyloggers. In contrast, self-encrypting drives are not vulnerable to these attacks since the hardware encryption key never leaves the disk controller.
Also, most full disk encryption schemes don't protect from data tampering (or silentdata corruption, i.e.bitrot).[8]That means they only provide privacy, but not integrity.Block cipher-based encryption modesused for full disk encryption are notauthenticated encryptionthemselves because of concerns of the storage overhead needed for authentication tags. Thus, if tampering would be done to data on the disk, the data would be decrypted to garbled random data when read and hopefully errors may be indicated depending on which data is tampered with (for the case of OS metadata – by the file system; and for the case of file data – by the corresponding program that would process the file). One of the ways to mitigate these concerns, is to use file systems with full data integrity checks viachecksums(likeBtrfsorZFS) on top of full disk encryption. However,cryptsetupstarted experimentally to supportauthenticated encryption[9]
Full disk encryption has several benefits compared to regular file or folder encryption, or encrypted vaults. The following are some benefits of disk encryption:
One issue to address in full disk encryption is that the blocks where theoperating systemis stored must be decrypted before the OS can boot, meaning that the key has to be available before there is a user interface to ask for a password. Most Full Disk Encryption solutions utilizePre-Boot Authenticationby loading a small, highly secure operating system which is strictly locked down and hashed versus system variables to check for the integrity of the Pre-Boot kernel. Some implementations such asBitLocker Drive Encryptioncan make use of hardware such as a Trusted Platform Module to ensure the integrity of the boot environment, and thereby frustrate attacks thattarget the boot loaderby replacing it with a modified version. This ensures that authentication can take place in a controlled environment without the possibility of a bootkit being used to subvert the pre-boot decryption.
With apre-boot authenticationenvironment, the key used to encrypt the data is not decrypted until an external key is input into the system.
Solutions for storing the external key include:
All these possibilities have varying degrees of security; however, most are better than an unencrypted disk.
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Authenticated Encryption(AE) is anencryptionscheme which simultaneously assures the data confidentiality (also known as privacy: the encrypted message is impossible to understand without the knowledge of a secretkey[1]) andauthenticity(in other words, it is unforgeable:[2]the encrypted message includes an authentication tag that the sender can calculate only while possessing the secret key[1]). Examples ofencryption modesthat provide AE areGCM,CCM.[1]
Many (but not all) AE schemes allow the message to contain "associated data" (AD) which is not made confidential, but its integrity is protected (i.e., it is readable, but tampering with it will be detected). A typical example is theheaderof anetwork packetthat contains its destination address. To properlyroutethe packet, all intermediate nodes in the message path need to know the destination, but for security reasons they cannot possess the secret key.[3]Schemes that allow associated data provideauthenticated encryption with associated data, orAEAD.[3]
A typicalprogramming interfacefor an AE implementation provides the following functions:
Theheaderpart is intended to provide authenticity and integrity protection for networking or storage metadata for which confidentiality is unnecessary, but authenticity is desired.
The need for authenticated encryption emerged from the observation that securely combining separateconfidentialityandauthenticationblock cipher operation modes could be error prone and difficult.[4][5]This was confirmed by a number of practical attacks introduced into production protocols and applications by incorrect implementation, or lack of authentication.[6]
Around the year 2000, a number of efforts evolved around the notion of standardizing modes that ensured correct implementation. In particular, strong interest in possibly secure modes was sparked by the publication ofCharanjit Jutla's integrity-aware CBC andintegrity-aware parallelizable, IAPM, modes[7]in 2000 (seeOCBand chronology[8]).
Six different authenticated encryption modes (namelyoffset codebook mode 2.0, OCB2.0;Key Wrap;counter with CBC-MAC, CCM;encrypt then authenticate then translate, EAX;encrypt-then-MAC, EtM; andGalois/counter mode, GCM) have been standardized in ISO/IEC 19772:2009.[9]More authenticated encryption methods were developed in response toNISTsolicitation.[10]Sponge functionscan be used in duplex mode to provide authenticated encryption.[11]
Bellare and Namprempre (2000) analyzed three compositions of encryption and MAC primitives, and demonstrated that encrypting a message and subsequently applying a MAC to the ciphertext (theEncrypt-then-MACapproach) implies security against anadaptive chosen ciphertext attack, provided that both functions meet minimum required properties. Katz and Yung investigated the notion under the name "unforgeable encryption" and proved it implies security against chosen ciphertext attacks.[12]
In 2013, theCAESAR competitionwas announced to encourage design of authenticated encryption modes.[13]
In 2015,ChaCha20-Poly1305is added as an alternative AE construction toGCMinIETFprotocols.
Authenticated encryption with associated data (AEAD) is a variant of AE that allows the message to include "associated data" (AD, additional non-confidential information, a.k.a. "additional authenticated data", AAD). A recipient can check the integrity of both the associated data and the confidential information in a message. AD is useful, for example, innetwork packetswhere theheadershould be visible forrouting, but the payload needs to be confidential, and both needintegrityandauthenticity. The notion of AEAD was formalized byRogaway(2002).[3]
AE was originally designed primarily to provide the ciphertext integrity: successful validation of an authentication tag byAliceusing her symmetric key KAindicates that the message was not tampered with by an adversaryMallorythat does not possess the KA. The AE schemes usually do not provide thekey commitment, a guarantee that the decryption would fail for any other key.[14]As of 2021, most existing AE schemes (including the very popular GCM) allow some messages to be decrypted without an error using more than just the (correct) KA; while the plaintext decrypted using a second (wrong) key KMwill be incorrect, the authentication tag would still match the new plaintext.[15]Since crafting a message with such property requires Mallory to already possess both KAand KM, the issue might appear to be one of a purely academic interest.[16]However, under special circumstances, practical attacks can be mounted against vulnerable implementations. For example, if anidentity authenticationprotocol is based on successful decryption of a message that uses a password-based key, Mallory's ability to craft a single message that would be successfully decrypted using 1000 different keys associated withweak, and thus known to her, potential passwords, can speed up her search for passwords by a factor of almost 1000. For thisdictionary attackto succeed, Mallory also needs an ability to distinguish successful decryption by Alice from an unsuccessful one, due, for example, to a poor protocol design or implementation turning Alice's side into anoracle. Naturally, this attack cannot be mounted at all when the keys are generated randomly.[17]
Key commitment was originally studied in the 2010s by Abdalla et al.[18]and Farshim et al.[19]under the name "robust encryption".[16][20]
To mitigate the attack described above without removing the "oracle", akey-committing AEADthat does not allow this type of crafted messages to exist can be used. AEGIS is an example of fast (if theAES instruction setis present), key-committing AEAD.[21]It is possible to add key-commitment to an existing AEAD scheme.[22][23]
The plaintext is first encrypted, then a MAC is produced based on the resulting ciphertext. The ciphertext and its MAC are sent together. ETM is the standard method according to ISO/IEC 19772:2009.[9]It is the only method which can reach the highest definition of security in AE, but this can only be achieved when the MAC used is "strongly unforgeable".[24]
IPSecadopted EtM in 2005.[25]In November 2014, TLS and DTLS received extensions for EtM withRFC7366. Various EtM ciphersuites exist for SSHv2 as well (e.g.,hmac-sha1-etm@openssh.com).
A MAC is produced based on the plaintext, and the plaintext is encrypted without the MAC. The plaintext's MAC and the ciphertext are sent together. Used in, e.g.,SSH.[26]Even though the E&M approach has not been proved to be strongly unforgeable in itself,[24]it is possible to apply some minor modifications toSSHto make it strongly unforgeable despite the approach.[27]
A MAC is produced based on the plaintext, then the plaintext and MAC are together encrypted to produce a ciphertext based on both. The ciphertext (containing an encrypted MAC) is sent. Until TLS 1.2, all availableSSL/TLScipher suites were MtE.[28]
MtE has not been proven to be strongly unforgeable in itself.[24]TheSSL/TLSimplementation has been proven to be strongly unforgeable byKrawczykwho showed that SSL/TLS was, in fact, secure because of the encoding used alongside the MtE mechanism.[29]However, Krawczyk's proof contains flawed assumptions about the randomness of theinitialization vector(IV). The 2011 BEAST attack exploited the non-random chained IV and broke all CBC algorithms in TLS 1.0 and under.[30]
In addition, deeper analysis of SSL/TLS modeled the protection as MAC-then-pad-then-encrypt, i.e. the plaintext is first padded to the block size of the encryption function. Padding errors often result in the detectable errors on the recipient's side, which in turn lead topadding oracle attacks, such asLucky Thirteen.
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Incryptography, aone-way compression functionis a function that transforms two fixed-length inputs into a fixed-length output.[1]The transformation is"one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to conventionaldata compressionalgorithms, which instead can be inverted exactly (lossless compression) or approximately (lossy compression) to the original data.
One-way compression functions are for instance used in theMerkle–Damgård constructioninsidecryptographic hash functions.
One-way compression functions are often built fromblock ciphers.
Some methods to turn any normal block cipher into a one-way compression function areDavies–Meyer,Matyas–Meyer–Oseas,Miyaguchi–Preneel(single-block-length compression functions) andMDC-2/Meyer–Schilling,MDC-4,Hirose(double-block-length compression functions). These methods are described in detail further down. (MDC-2is also the name of a hash function patented byIBM.)
Another method is2BOW(orNBOWin general), which is a "high-rate multi-block-length hash function based on block ciphers"[1]and typically achieves (asymptotic) rates between 1 and 2 independent of the hash size (only with small constant overhead). This method has not yet seen any serious security analysis, so should be handled with care.
A compression function mixes two fixed length inputs and produces a single fixed length output of the same size as one of the inputs. This can also be seen as that the compression function transforms one large fixed-length input into a shorter, fixed-length output.
For instance,input Amight be 128 bits,input B128 bits and they are compressed together to a single output of 128 bits. This is equivalent to having a single 256-bit input compressed to a single output of 128 bits.
Some compression functions do not compress by half, but instead by some other factor. For example,input Amight be 256 bits, andinput B128 bits, which are compressed to a single output of 128 bits. That is, a total of 384 input bits are compressed together to 128 output bits.
The mixing is done in such a way that fullavalanche effectis achieved. That is, every output bit depends on every input bit.
Aone-way functionis a function that is easy to compute but hard to invert. A one-way compression function (also called hash function) should have the following properties:
Ideally one would like the "infeasibility" in preimage-resistance and second preimage-resistance to mean a work of about2n{\displaystyle 2^{n}}wheren{\displaystyle n}is the number of bits in the hash function's output. However, particularly for second preimage-resistance this is a difficult problem.[citation needed]
A common use of one-way compression functions is in the Merkle–Damgård construction inside cryptographic hash functions. Most widely used hash functions, includingMD5,SHA-1(which is deprecated[2]) andSHA-2use this construction.
A hash function must be able to process an arbitrary-length message into a fixed-length output. This can be achieved by breaking the input up into a series of equal-sized blocks, and operating on them in sequence using a one-way compression function. The compression function can either be specially designed for hashing or be built from a block cipher. The last block processed should also belength padded, which is crucial to the security of this construction.
When length padding (also called MD-strengthening) is applied, attacks cannot find collisions faster than the birthday paradox (2n/2{\displaystyle 2^{n/2}},n{\displaystyle n}being the block size in bits) if the used functionf{\displaystyle f}is collision-resistant.[3][4]Hence, the Merkle–Damgård hash construction reduces the problem of finding a proper hash function to finding a proper compression function.
A second preimage attack (given a messagem1{\displaystyle m_{1}}an attacker finds another messagem2{\displaystyle m_{2}}to satisfyhash(m1)=hash(m2){\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}can be done according to Kelsey and Schneier[5]for a2k{\displaystyle 2^{k}}-message-block message in timek×2n/2+1+2n−k+1{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}. The complexity of this attack reaches a minimum of23n/4+2{\displaystyle 2^{3n/4+2}}for long messages whenk=2n/4{\displaystyle k=2^{n/4}}and approaches2n{\displaystyle 2^{n}}when messages are short.
One-way compression functions are often built from block ciphers.
Block ciphers take (like one-way compression functions) two fixed size inputs (thekeyand theplaintext) and return one single output (theciphertext) which is the same size as the input plaintext.
However, modern block ciphers are only partially one-way. That is, given a plaintext and a ciphertext it is infeasible to find a key that encrypts the plaintext to the ciphertext. But, given a ciphertext and a key a matching plaintext can be found simply by using the block cipher's decryption function. Thus, to turn a block cipher into a one-way compression function some extra operations have to be added.
Some methods to turn any normal block cipher into a one-way compression function are Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel (single-block-length compression functions) and MDC-2, MDC-4, Hirose (double-block-length compressions functions).
Single-block-length compression functions output the same number of bits as processed by the underlying block cipher. Consequently, double-block-length compression functions output twice the number of bits.
If a block cipher has ablock sizeof say 128 bits single-block-length methods create a hash function that has the block size of 128 bits and produces a hash of 128 bits. Double-block-length methods make hashes with double the hash size compared to the block size of the block cipher used. So a 128-bit block cipher can be turned into a 256-bit hash function.
These methods are then used inside the Merkle–Damgård construction to build the actual hash function. These methods are described in detail further down.
Using a block cipher to build the one-way compression function for a hash function is usually somewhat slower than using a specially designed one-way compression function in the hash function. This is because all known secure constructions do thekey schedulingfor each block of the message. Black, Cochran and Shrimpton have shown that it is impossible to construct a one-way compression function that makes only one call to a block cipher with a fixed key.[6]In practice reasonable speeds are achieved provided the key scheduling of the selected block cipher is not a too heavy operation.
But, in some cases it is easier because a single implementation of a block cipher can be used for both a block cipher and a hash function. It can also savecodespace in very tinyembedded systemslike for instancesmart cardsornodes in carsor other machines.
Therefore, the hash-rate or rate gives a glimpse of the efficiency of a hash function based on a certain compression function. The rate of an iterated hash function outlines the ratio between the number of block cipher operations and the output. More precisely, the rate represents the ratio between the number of processed bits of inputm{\displaystyle m}, the output bit-lengthn{\displaystyle n}of the block cipher, and the necessary block cipher operationss{\displaystyle s}to produce thesen{\displaystyle n}output bits. Generally, the usage of fewer block cipher operations results in a better overall performance of the entire hash function, but it also leads to a smaller hash-value which could be undesirable. The rate is expressed by the formula:
Rh=|mi|s⋅n{\displaystyle R_{h}={\frac {\left|m_{i}\right|}{s\cdot n}}}
The hash function can only be considered secure if at least the following conditions are met:
The constructions presented below: Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel and Hirose have been shown to be secure under theblack-boxanalysis.[7][8]The goal is to show that any attack that can be found is at most as efficient as thebirthday attackunder certain assumptions. The black-box model assumes that a block cipher is used that is randomly chosen from a set containing all appropriate block ciphers. In this model an attacker may freely encrypt and decrypt any blocks, but does not have access to an implementation of the block cipher. The encryption and decryption function are represented by oracles that receive a pair of either a plaintext and a key or a ciphertext and a key. The oracles then respond with a randomly chosen plaintext or ciphertext, if the pair was asked for the first time. They both share a table for these triplets, a pair from the query and corresponding response, and return the record, if a query was received for the second time. For the proof there is a collision finding algorithm that makes randomly chosen queries to the oracles. The algorithm returns 1, if two responses result in a collision involving the hash function that is built from a compression function applying this block cipher (0 else). The probability that the algorithm returns 1 is dependent on the number of queries which determine the security level.
The Davies–Meyer single-block-length compression function feeds each block of the message (mi{\displaystyle m_{i}}) as the key to a block cipher. It feeds the previous hash value (Hi−1{\displaystyle H_{i-1}}) as the plaintext to be encrypted. The output ciphertext is then alsoXORed(⊕) with the previous hash value (Hi−1{\displaystyle H_{i-1}}) to produce the next hash value (Hi{\displaystyle H_{i}}). In the first round when there is no previous hash value it uses a constant pre-specified initial value (H0{\displaystyle H_{0}}).
Inmathematical notationDavies–Meyer can be described as:
The scheme has the rate (k is the keysize):
If the block cipher uses for instance 256-bit keys then each message block (mi{\displaystyle m_{i}}) is a 256-bit chunk of the message. If the same block cipher uses a block size of 128 bits then the input and output hash values in each round is 128 bits.
Variations of this method replace XOR with any other group operation, such as addition on 32-bit unsigned integers.
A notable property of the Davies–Meyer construction is that even if the underlying block cipher is totally secure, it is possible to computefixed pointsfor the construction: for anym{\displaystyle m}, one can find a value ofh{\displaystyle h}such thatEm(h)⊕h=h{\displaystyle E_{m}(h)\oplus h=h}: one just has to seth=Em−1(0){\displaystyle h=E_{m}^{-1}(0)}.[9]This is a property thatrandom functionscertainly do not have. So far, no practical attack has been based on this property, but one should be aware of this "feature". The fixed-points can be used in a second preimage attack (given a messagem1{\displaystyle m_{1}}, attacker finds another messagem2{\displaystyle m_{2}}to satisfyhash(m1)=hash(m2){\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}) of Kelsey and Schneier[5]for a2k{\displaystyle 2^{k}}-message-block message in time3×2n/2+1+2n−k+1{\displaystyle 3\times 2^{n/2+1}+2^{n-k+1}}. If the construction does not allow easy creation of fixed points (like Matyas–Meyer–Oseas or Miyaguchi–Preneel) then this attack can be done ink×2n/2+1+2n−k+1{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}time. In both cases the complexity is above2n/2{\displaystyle 2^{n/2}}but below2n{\displaystyle 2^{n}}when messages are long and that when messages get shorter the complexity of the attack approaches2n{\displaystyle 2^{n}}.
The security of the Davies–Meyer construction in the Ideal Cipher Model was first proven by R. Winternitz.[10]
The Matyas–Meyer–Oseas single-block-length one-way compression function can be considered the dual (the opposite) of Davies–Meyer.
It feeds each block of the message (mi{\displaystyle m_{i}}) as the plaintext to be encrypted. The output ciphertext is then also XORed (⊕) with the same message block (mi{\displaystyle m_{i}}) to produce the next hash value (Hi{\displaystyle H_{i}}). The previous hash value (Hi−1{\displaystyle H_{i-1}}) is fed as the key to the block cipher. In the first round when there is no previous hash value it uses a constant pre-specified initial value (H0{\displaystyle H_{0}}).
If the block cipher has different block and key sizes the hash value (Hi−1{\displaystyle H_{i-1}}) will have the wrong size for use as the key. The cipher might also have other special requirements on the key. Then the hash value is first fed through the functiong{\displaystyle g}to be converted/padded to fit as key for the cipher.
In mathematical notation Matyas–Meyer–Oseas can be described as:
The scheme has the rate:
A second preimage attack (given a messagem1{\displaystyle m_{1}}an attacker finds another messagem2{\displaystyle m_{2}}to satisfyhash(m1)=hash(m2){\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}) can be done according to Kelsey and Schneier[5]for a2k{\displaystyle 2^{k}}-message-block message in timek×2n/2+1+2n−k+1{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}. The complexity is above2n/2{\displaystyle 2^{n/2}}but below2n{\displaystyle 2^{n}}when messages are long, and that when messages get shorter the complexity of the attack approaches2n{\displaystyle 2^{n}}.
The Miyaguchi–Preneel single-block-length one-way compression function is an extended variant of Matyas–Meyer–Oseas. It was independently proposed byShoji MiyaguchiandBart Preneel.
It feeds each block of the message (mi{\displaystyle m_{i}}) as the plaintext to be encrypted. The output ciphertext is then XORed (⊕) with the same message block (mi{\displaystyle m_{i}}) and then also XORed with the previous hash value (Hi−1{\displaystyle H_{i-1}}) to produce the next hash value (Hi{\displaystyle H_{i}}). The previous hash value (Hi−1{\displaystyle H_{i-1}}) is fed as the key to the block cipher. In the first round when there is no previous hash value it uses a constant pre-specified initial value (H0{\displaystyle H_{0}}).
If the block cipher has different block and key sizes the hash value (Hi−1{\displaystyle H_{i-1}}) will have the wrong size for use as the key. The cipher might also have other special requirements on the key. Then the hash value is first fed through the functiong{\displaystyle g}to be converted/padded to fit as key for the cipher.
In mathematical notation Miyaguchi–Preneel can be described as:
The scheme has the rate:
The roles ofmi{\displaystyle m_{i}}andHi−1{\displaystyle H_{i-1}}may be switched, so thatHi−1{\displaystyle H_{i-1}}is encrypted under the keymi{\displaystyle m_{i}}, thus making this method an extension of Davies–Meyer instead.
A second preimage attack (given a messagem1{\displaystyle m_{1}}an attacker finds another messagem2{\displaystyle m_{2}}to satisfyhash(m1)=hash(m2){\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}) can be done according to Kelsey and Schneier[5]for a2k{\displaystyle 2^{k}}-message-block message in timek×2n/2+1+2n−k+1{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}. The complexity is above2n/2{\displaystyle 2^{n/2}}but below2n{\displaystyle 2^{n}}when messages are long, and that when messages get shorter the complexity of the attack approaches2n{\displaystyle 2^{n}}.
The Hirose[8]double-block-length one-way compression function consists of a block cipher plus a permutationp{\displaystyle p}. It was proposed by Shoichi Hirose in 2006 and is based on a work[11]byMridul Nandi.
It uses a block cipher whose key lengthk{\displaystyle k}is larger than the block lengthn{\displaystyle n}, and produces a hash of size2n{\displaystyle 2n}. For example, any of theAES candidateswith a 192- or 256-bit key (and 128-bit block).
Each round accepts a portion of the messagemi{\displaystyle m_{i}}that isk−n{\displaystyle k-n}bits long, and uses it to update twon{\displaystyle n}-bit state valuesG{\displaystyle G}andH{\displaystyle H}.
First,mi{\displaystyle m_{i}}is concatenated withHi−1{\displaystyle H_{i-1}}to produce a keyKi{\displaystyle K_{i}}. Then the two feedback values are updated according to:
p(Gi−1){\displaystyle p(G_{i-1})}is an arbitrary fixed-point-free permutation on ann{\displaystyle n}-bit value, typically defined asp(x)=x⊕c{\displaystyle p(x)=x\oplus c}for an arbitrary non-zero constantc{\displaystyle c}(all ones may be a convenient choice).
Each encryption resembles the standard Davies–Meyer construction. The advantage of this scheme over other proposed double-block-length schemes is that both encryptions use the same key, and thus key scheduling effort may be shared.
The final output isHt||Gt{\displaystyle H_{t}||G_{t}}. The scheme has the rateRHirose=k−n2n{\textstyle R_{Hirose}={\frac {k-n}{2n}}}relative to encrypting the message with the cipher.
Hirose also provides a proof in the Ideal Cipher Model.
Thesponge constructioncan be used to build one-way compression functions.
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Agrippa (A Book of the Dead)is a work of art created by science fiction novelistWilliam Gibson, artistDennis Ashbaughand publisher Kevin Begos Jr. in 1992.[1][2][3][4]The work consists of a 300-line semi-autobiographicalelectronic poemby Gibson, embedded in anartist's bookby Ashbaugh.[5]Gibson's text focused on the ethereal, human-owed nature of memories retained over the passage oftime(the title referred to aKodakphoto album from which the text's memories are taken). Its principal notoriety arose from the fact that the poem, stored on a 3.5"floppy disk, was programmed to encrypt itself after a single use; similarly, the pages of the artist's book were treated with photosensitive chemicals, effecting the gradual fading of the words and images from the book's first exposure to light.[5]The work is recognised as an early example ofelectronic literature.
The impetus for the initiation of the project was Kevin Begos Jr., a publisher of museum-quality manuscripts motivated by disregard for thecommercialismof the art world,[6]who suggested to abstract painterDennis Ashbaughthat they "put out an art book on computer that vanishes".[7]Ashbaugh—who despite his "heavy art-world resume" was bored with theabstract impressionistpaintings he was doing—took the suggestion seriously, and developed it further.[7][8]
A few years beforehand, Ashbaugh had written afan lettertocyberpunknovelistWilliam Gibson, whose oeuvre he had admired, and the pair had struck up a telephone friendship.[7][8]Shortly after the project had germinated in the minds of Begos and Ashbaugh, they contacted and recruited Gibson.[2]The project exemplified Gibson's deep ambivalence towards technologically advanced futurity, and asThe New York Timesexpressed it, was "designed to challenge conventional notions about books and art while extracting money from collectors of both".[2]
Some people have said that they think this is a scam or pure hype … [m]aybe fun, maybe interesting, but still a scam. But Gibson thinks of it as becoming a memory, which he believes is more real than anything you can actually see.
The project manifested as a poem written by Gibson incorporated into anartist's bookcreated by Ashbaugh; as such it was as much a work of collaborativeconceptual artas poetry.[10]Gibson stated that Ashbaugh's design "eventually included a supposedlyself-devouringfloppy-disk intended to display the text only once, then eat itself."[11][12]
Ashbaugh was gleeful at the dilemma this would pose to librarians: in order to register the copyright of the book, he had to send two copies to the United StatesLibrary of Congress, who, in order to classify it had to read it, and in the process, necessarily had to destroy it.[8]The creators had initially intended to infect the disks with acomputer virus, but declined to after considering the potential damage to the computer systems of innocents.[8]
OK, sit down and pay attention. We're only going to say this once.
The work was premiered on December 9, 1992, atThe Kitchen, an art space inChelseain New York City.[14][15][16]The performance—known as "The Transmission"—consisted of the public reading of the poem by composer and musicianRobert Ashley, recorded and simultaneously transmitted to several other cities.[14][17][16]The poem was inscribed on a sculptural magnetic disk which had been vacuum-sealed until the event's commencement, and was reportedly (although not actually[18]) programmed to erase itself upon exposure to air.[14]Contrary to numerous colourful reports,[19]neither this disk nor the diskettes embedded in the artist's book were ever actuallyhackedin any strict sense.[20]
Academic researcher Matthew Kirschenbaum has reported that a pirated text of the poem was released the next day onMindVox, "an edgy New York City-based electronic bulletin board".[20]Kirschenbaum considers Mindvox, an interface between thedark weband the global Internet, to have been "an ideal initial host".[20]The text spread rapidly from that point on, first onFTPservers andanonymous mailersand later viaUSENETandlistservemail. Since Gibson did not use email at the time, fans sent copies of the pirated text to hisfax machine.[19]
The precise manner in which the text was obtained for MindVox is unclear, although the initial custodian of the text, known only as "Templar" attached to it an introductory note in which he claimed credit.[20]Begos claimed that a troupe ofNew York Universitystudents representing themselves as documentarians attended The Transmission and made avideotaperecording of the screen as it displayed the text as an accompaniment of Gibson's friend and stage magicianPenn Jillette's reading. Kirschenbaum speculates that this group included the offline persona of Templar or one of his associates. According to this account, ostensibly endorsed by Templar in a post toSlashdotin February 2000,[20]the students then transcribed the poem from the tape and within hours had uploaded it to MindVox. However, according to a dissenting account byhacktivistand MindVox co-founderPatrick K. Kroupa, subterfuge prior to The Transmission elicited a betrayal of trust which yielded the uploaders the text. Kirschenbaum declined to elaborate on the specifics of the Kroupa conjecture, which he declared himself "not at liberty to disclose".[20]
Agrippaowes its transmission and continuing availability to a complex network of individuals, communities, ideologies, markets, technologies, and motives. Only in the most heroic reading of the events … isAgrippasaved for posterity solely by virtue of the knight Templar. … Today, the 404 File Not Found messages that Web browsing readers ofAgrippainevitably encounter … are more than just false leads; they are latent affirmations of the work's original act of erasure that allow the text to stage anew all of its essential points about artifacts, memory, and technology. "Because the struggle for the textisthe text."
On December 9, 2008 (the sixteenth anniversary of the original Transmission), "The Agrippa Files", working with a scholarly team at theUniversity of Maryland, released an emulated run of the entire poem[21](derived from an original diskette loaned by a collector) and an hour's worth of "bootleg" footage shot covertly at the Americas Society (the source of the text that was posted onMindVox).[22]
Since its debut in 1992, the mystery ofAgripparemained hidden for 20 years. Although many had tried to hack the code and decrypt the program, the uncompiled source code was lost long ago.Alan Liuand his team at "The Agrippa Files"[23]created an extensive website with tools and resources to crack the Agrippa Code. They collaborated with Matthew Kirschenbaum at theMaryland Institute for Technology in the Humanitiesand the Digital Forensics Lab, and Quinn DuPont, a PhD student of cryptography from the University of Toronto, in calling for the aid of cryptographers to figure out how the program works by creating "Cracking the Agrippa Code: The Challenge",[18]which enlisted participants to solve the intentional scrambling of the poem in exchange for prizes.[24]The code was successfully cracked by Robert Xiao in late July 2012.[18]
There is no encryption algorithm present in the Agrippa binary; consequently, the visual encryption effect that displays when the poem has finished is a ruse. The visual effect is the result of running the decrypted ciphertext (in memory) through the re-purposed bit-scrambling decryption algorithm, and then abandoning the text in memory. Only the fake genetic code is written back to disk.[18]
The encryption resembles theRSAalgorithm. This algorithm encodes data in 3-byteblocks. First, each byte is permuted through an 8-positionpermutation, then the bits are split into two 12-bit integers (by taking the low 4 bits of the second byte and the 8 bits of the first byte as the first 12-bit integer, and the 8 bits of the third byte and the 4 high bits of the second integer as the second 12-bit integer). Each is individually encrypted by taking them to the 3491st power,mod4097; the bits are then reassembled into 3 bytes. The encrypted text is then stored in a string variable as part of the program. To shroud the would-be visible and noticeable text it is compressed with the simpleLzwbefore final storage. As the Macintosh Common Lisp compiler compresses the main program code into the executable, this was not that necessary.
In order to prevent a second running of the program it corrupts itself when run. The program simply overwrites itself with a 6000 byte longDNA-like code at a certain position. Archival documents suggest that the original plan was to use a series of ASCII 1's to corrupt the binary, but at some point in development a change was made to use fake genetic code, in keeping with the visual motifs in the book.[18]The genetic code has a codon entropy of 5.97 bits/codon, much higher than any natural DNA sequence known. However, the ciphertext was not overwritten.
Agrippacomes in a rough-hewn black box adorned with a blinking green light and an LCD readout that flickers with an endless stream of decoded DNA. The top opens like a laptop computer, revealing a hologram of a circuit board. Inside is a battered volume, the pages of which are antique rag-paper, bound and singed by hand.
The book was published in 1992 in twolimited editions—Deluxe and Small—by Kevin Begos Jr. Publishing, New York City.[1]The deluxe edition came in a 16 by 21½-inch (41 cm × 55 cm) metal mesh case sheathed inKevlar(a polymer used to makebulletproof vests) and designed to look like a buried relic.[2]Inside is a book of 93 ragged andcharredpages sewn by hand and bound in stained and singed linen by Karl Foulkes;[26]the book gives the impression of having survived a fire;[1][2]it was described by Peter Schwenger as "ablack boxrecovered from some unspecified disaster."[7]The edition includes pages ofDNA sequencesset in double columns of 42 lines each like theGutenberg Bible, andcopperplateaquatintetchingsby Ashbaugh editioned by Peter Pettingill on Fabriano Tiepolo paper.[27][28]The monochromatic etchings depict stylisedchromosomes, a hallmark of Ashbaugh's work, accompanied by imagery of apistol, camera or in some instances simple line drawings—all allusions to Gibson's contribution.[29]
The deluxe edition was set inMonotypeGill SansatGolgonooza Letter Foundry, and printed on Rives heavyweight text by Begos and the Sun Hill Press.[28]The final 60 pages of the book were then fused together, with ahollowed-out sectioncut into the centre, containing the self-erasing diskette on which the text of Gibson's poem was encrypted.[2]The encryption was the work of a pseudonymouscomputer programmer, "BRASH", assisted byElectronic Frontier FoundationfoundersJohn Perry BarlowandJohn Gilmore.[26]The deluxe edition was originally priced atUS$1500 (later $2000), and each copy is unique to some degree because of handmade or hand-finished elements.[26]
The small edition was sold for $450;[30]like the deluxe edition, it was set in MonotypeGill Sans, but in single columns.[28]It was printed on Mohawk Superfine text by the Sun Hill Press,[29]with the reproduction of the etchings printed on aCanonlaser printer. The edition was then Smythe sewn at Spectrum Bindery and enclosed in asolander box.[28]A bronze-boxed collectors' copy was also released, and retailed at $7,500.[30]
Fewer than 95 deluxe editions ofAgrippaare extant, although the exact number is unknown and is the source of considerable mystery.[26][31]TheVictoria and Albert Museumpossesses a deluxe edition, numbered 4 of 10.[26]A publicly accessible copy of the deluxe edition is available at the Rare Books Division of theNew York Public Libraryand a small copy resides atWestern Michigan UniversityinKalamazoo, Michigan, while the Frances Mulhall Achilles Library at theWhitney Museum of American Artin New York City hosts a promotional prospectus.[26]TheVictoria and Albert Museum's copy was first exhibited in a display entitledThe Book and Beyond, held in the Museum's 20th Century Gallery from April to October 1995.[32]The same copy was subsequently also included in a V&A exhibition entitledDigital Pioneers, from 2009 to 2010. Both V&A shows were curated by Douglas Dodds. Another copy of the book was exhibited in the 2003–2004 exhibitionNinety from the Ninetiesat the New York Public Library. Gibson at one point claimed never to have seen a copy of the printed book, spurring speculation that no copies had actually been made. Many copies have since been documented, and Gibson's signature was noted on copies held by the New York Public Library and the V&A.[29]In 2011, theBodleian Library's Special Collections Department at the University of Oxford acquired Kevin Begos' copy of Agrippa, as well as the archive of Begos' papers related to the work.[33][34]
The construction of the book and the subject matter of the poem within it share a metaphorical connection in the decay of memory.[35][36]In this light, critic Peter Schwenger asserts thatAgrippacan be understood as organized by two ideas: the death of Gibson's father, and the disappearance or absence of the book itself.[37]In this sense, it instantiates the ephemeral nature of all text.[38]
The poem is a detailed description of several objects, including a photo album and the camera that took the pictures in it, and is essentially about the nostalgia that the speaker, presumably Gibson himself, feels towards the details of his family's history: the painstaking descriptions of the houses they lived in, the cars they drove, and even their pets.
It starts around 1919 and moves up to today, or possibly beyond. If it works, it makes the reader uncomfortably aware of how much we tend to accept the contemporary media version of the past. You can see it in Westerns, the way the 'mise-en-scene' and the collars on cowboys change through time. It's never really the past; it's always a version of your own time.
In its original form, the text of the poem was supposed to fade from the page and, in Gibson's own words, "eat itself" off of the diskette enclosed with the book. The reader would, then, be left with only the memory of the text, much like the speaker is left with only the memory of his home town and his family after moving to Canada fromSouth Carolina, in the course of the poem (as Gibson himself did during theVietnam War).[39]
The poem contains amotifof "the mechanism", described as "Forever / Dividing that from this",[40]and which can take the form of thecameraor of the ancientgunthat misfires in the speaker's hands.[41][42]Technology, "the mechanism", is the agent of memory,[41]which transforms subjective experience into allegedly objective records (photography). It is also the agent of life and death, one moment dispensing lethal bullets, but also likened to the life-giving qualities of sex. Shooting the gun is "[l]ike the first time you put your mouth / on a woman".[43]
The poem is, then, not merely about memory, but how memories are formed from subjective experience, and how those memories compare to mechanically reproduced recordings. In the poem, "the mechanism" is strongly associated withrecording, which can replacesubjective experience.
Insomuch as memories constitute ouridentities, "the mechanism" thus represents the destruction of theselfvia recordings. Hence both cameras, as devices of recording, and guns, as instruments of destruction, are part of the same mechanism—dividingthat(memory,identity,life) fromthis(recordings,anonymity,death).
Agrippawas extremely influential—as asigilfor the artistic community to appreciate the potential of electronic media—for the extent to which it entered public consciousness.[36]It caused a fierce controversy in the art world, among museums and among libraries.[44]It challenged established notions of permanence of art and literature, and, as Ashbaugh intended,[8]raised significant problems for archivists seeking to preserve it for the benefit of future generations.[44]Agrippawas also used as the key of abook cipherin theCicada 3301mystery.[45]
Agrippawas particularly well received by critics,[46]withdigital mediatheoristPeter Lunenfelddescribing it in 2001 as "one of the most evocative hypertexts published in the 1990s".[1]Professor ofEnglish literatureJohn Johnson has claimed that the importance ofAgrippastems not only from its "foregrounding of mediality in an assemblage of texts", but also from the fact that "media in this work are explicitly as passageways to the realm of the dead".[47]English Professor Raymond Malewitz argues that "the poem's stanzas form a metaphorical DNA fingerprint that reveals Gibson's life to be, paradoxically, a novel repetition of his father's and grandfather's lives."[48]The Cambridge History of Twentieth-Century English Literature, which described the poem as "a mournful text", praisedAgrippa's inventive use of digital format.[42]However, academic Joseph Tabbi remarked in a 2008 paper thatAgrippawas among those works that are "canonized before they have beenread, resisted, and reconsidered among fellow authors within an institutional environment that persists in time and finds outlets in many media".[10]
In a lecture at the exhibition ofAgrippaat theCenter for Book Artsin New York City, semiotician Marshall Blonsky ofNew York Universitydrew an allusion between the project and the work of two French literary figures—philosopherMaurice Blanchot(author of "The Absence of the Book"), and poetStéphane Mallarmé, a 19th-century forerunner ofsemioticsanddeconstruction.[2]In response to Blonsky's analysis that "[t]he collaborators inAgrippaare responding to a historical condition of language, a modern skepticism about it", Gibson disparagingly commented "Honest to God, these academics who think it's all some sort of big-time French philosophy—that's a scam. Those guys worshipJerry Lewis, they get our pop culture all wrong."[2]
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Acryptosystemis considered to haveinformation-theoretic security(also calledunconditional security[1]) if the system is secure againstadversarieswith unlimited computing resources and time. In contrast, a system which depends on the computational cost ofcryptanalysisto be secure (and thus can be broken by an attack with unlimited computation) is calledcomputationally secureor conditionally secure.[2]
An encryption protocol with information-theoretic security is impossible to break even with infinite computational power. Protocols proven to be information-theoretically secure are resistant to future developments in computing. The concept of information-theoretically secure communication was introduced in 1949 by American mathematicianClaude Shannon, one of the founders of classicalinformation theory, who used it to prove theone-time padsystem was secure.[3]Information-theoretically secure cryptosystems have been used for the most sensitive governmental communications, such asdiplomatic cablesand high-level military communications.[citation needed]
There are a variety of cryptographic tasks for which information-theoretic security is a meaningful and useful requirement. A few of these are:
Algorithms which are computationally or conditionally secure (i.e., they are not information-theoretically secure) are dependent on resource limits. For example,RSArelies on the assertion that factoring large numbers is hard.
A weaker notion of security, defined byAaron D. Wyner, established a now-flourishing area of research that is known as physical layer encryption.[4]It exploits the physicalwirelesschannel for its security by communications, signal processing, and coding techniques. The security isprovable,unbreakable, and quantifiable (in bits/second/hertz).
Wyner's initial physical layer encryption work in the 1970s posed the Alice–Bob–Eve problem in which Alice wants to send a message to Bob without Eve decoding it. If the channel from Alice to Bob is statistically better than the channel from Alice to Eve, it had been shown that secure communication is possible.[5]That is intuitive, but Wyner measured the secrecy in information theoretic terms defining secrecy capacity, which essentially is the rate at which Alice can transmit secret information to Bob. Shortly afterward,Imre Csiszárand Körner showed that secret communication was possible even if Eve had a statistically better channel to Alice than Bob did.[6]The basic idea of the information theoretic approach to securely transmit confidential messages (without using an encryption key) to a legitimate receiver is to use the inherent randomness of the physical medium (including noises and channel fluctuations due to fading) and exploit the difference between the channel to a legitimate receiver and the channel to an eavesdropper to benefit the legitimate receiver.[7]More recent theoretical results are concerned with determining the secrecy capacity and optimal power allocation in broadcast fading channels.[8][9]There are caveats, as many capacities are not computable unless the assumption is made that Alice knows the channel to Eve. If that were known, Alice could simply place a null in Eve's direction. Secrecy capacity forMIMOand multiplecolludingeavesdroppers is more recent and ongoing work,[10][11]and such results still make the non-useful assumption about eavesdropper channel state information knowledge.
Still other work is less theoretical by attempting to compare implementable schemes. One physical layer encryption scheme is to broadcast artificial noise in all directions except that of Bob's channel, which basically jams Eve. One paper by Negi and Goel details its implementation, and Khisti and Wornell computed the secrecy capacity when only statistics about Eve's channel are known.[12][13]
Parallel to that work in the information theory community is work in the antenna community, which has been termed near-field direct antenna modulation or directional modulation.[14]It has been shown that by using aparasitic array, the transmitted modulation in different directions could be controlled independently.[15]Secrecy could be realized by making the modulations in undesired directions difficult to decode. Directional modulation data transmission was experimentally demonstrated using aphased array.[16]Others have demonstrated directional modulation withswitched arraysandphase-conjugating lenses.[17][18][19]
That type of directional modulation is really a subset of Negi and Goel's additive artificial noise encryption scheme. Another scheme usingpattern-reconfigurabletransmit antennas for Alice called reconfigurablemultiplicative noise(RMN) complements additive artificial noise.[20]The two work well together in channel simulations in which nothing is assumed known to Alice or Bob about the eavesdroppers.
The different works mentioned in the previous part employ, in one way or another, the randomness present in the wireless channel to transmit information-theoretically secure messages.
Conversely, we could analyze how much secrecy one can extract from the randomness itself in the form of asecret key.
That is the goal ofsecret key agreement.
In this line of work, started by Maurer[21]and Ahlswede and Csiszár,[22]the basic system model removes any restriction on the communication schemes and assumes that the legitimate users can communicate over a two-way, public, noiseless, and authenticated channel at no cost. This model has been subsequently extended to account for multiple users[23]and a noisy channel[24]among others.
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Anumbers stationis ashortwaveradio stationcharacterized by broadcasts of formatted numbers, which are believed to be addressed tointelligence officersoperating in foreign countries.[1]Most identified stations usespeech synthesisto vocalize numbers, although digital modes such asphase-shift keyingandfrequency-shift keying, as well asMorse codetransmissions, are not uncommon. Most stations have set time schedules or schedule patterns; however, some appear to have no discernible pattern and broadcast at random times. Stations may have set frequencies in thehigh-frequencyband.[2]
Numbers stations have been reported since at least the start ofWorld War Iand continue in use today. Amongst amateur radio enthusiasts, there is an interest in monitoring and classifying numbers stations, with many being given nicknames to represent their quirks or origins.
According to the notes ofThe Conet Project,[3][4]which has compiled recordings of these transmissions, number stations have been reported sinceWorld War Iwith the numbers transmitted in Morse code. It is reported thatArchduke Anton of Austriain his youth during World War I used to listen in to their transmissions, writing them down and passing them on to the Austrian military intelligence.[5]
Numbers stations were most abundant during theCold Warera. According to an internal Cold War-era report of the Polish Ministry of the Interior, numbers stations DCF37 (3.370 MHz) and DFD21 (4.010 MHz) were transmitted fromWest Germanybeginning in the early 1950s.[6]
Many stations from this era continue to broadcast and some long-time stations may have been taken over by different operators.[7][8]TheCzech Ministry of the Interiorand theSwedish Security Servicehave both acknowledged the use of numbers stations byCzechoslovakiafor espionage,[9][10][11]with declassified documents proving the same. FewQSLresponses have been received from numbers stations[12]byshortwave listeners[13]who sent reception reports to stations that identified themselves or to entities the listeners believed responsible for the broadcasts, which is the expected behaviour of a non-clandestine station.[14][15]
One well-known numbers station was the E03 "Lincolnshire Poacher",[16]which is thought to have been run by the BritishSecret Intelligence Service.[17]It was first broadcast fromBletchley Parkin the mid-1970s but later was broadcast fromRAF AkrotiriinCyprus. It ceased broadcasting in 2008.[18]
In 2001, the United States tried theCuban Fiveon the charge of spying for Cuba. The group had received and decoded messages that had been broadcast from the "Atención" number station in Cuba.[19]
The "Atención" station of Cuba became the world's first numbers station to be officially and publicly accused of transmitting to spies. It was the centerpiece of a United States federal court espionage trial, following the arrest of theWasp Networkof Cuban spies in 1998. The U.S. prosecutors claimed the accused were writing down number codes received from Atención, using Sony hand-held shortwave receivers, and typing the numbers intolaptopcomputers to decode spying instructions. The FBI testified that they had entered a spy's apartment in 1995, and copied the computer decryption program for the Atención numbers code. They used it to decode Atención spy messages, which the prosecutors unveiled in court.[19]
The United States government's evidence included the following three examples of decoded Atención messages.[19]
The moderator of an e-mail list for global numbers station hobbyists claimed that "Someone on the Spooks list had already cracked the code for a repeated transmission [from Havana to Miami] if it was received garbled." Such code-breaking may be possible if aone-time paddecoding key is used more than once.[19]If used properly, however, the codecannot be broken.
In 2001,Ana Belén Montes, a senior USDefense Intelligence Agencyanalyst, was arrested and charged with espionage. The federal prosecutors alleged that Montes was able to communicate with the CubanIntelligence Directoratethrough encoded messages, with instructions being received through "encrypted shortwave transmissions from Cuba".
In 2006,Carlos Alvarezand his wife,Elsa, were arrested and charged with espionage. The U.S. District Court for the Southern District of Florida[20][which?]stated that "defendants would receive assignments via shortwave radio transmissions".[citation needed]
In June 2009, the United States similarly chargedWalter Kendall Myerswith conspiracy to spy for Cuba, and receiving and decoding messages broadcast from a numbers station operated by the Cuban Intelligence Directorate to further that conspiracy.[21][22]As discovered by the FBI up to 2010, one way that Russian agents of theIllegals Programwere receiving instructions was via coded messages on shortwave radio.[18]It has been reported that the United States has used number stations to communicate encoded information to persons in other countries.[19]There are also claims thatState Department-operated stations, such as KKN50 and KKN44, used to broadcast similar "numbers" messages or related traffic, although these radio stations have been off the air for many years.[23][24]
North Korearevived number broadcasts in July 2016 after a hiatus of sixteen years, a move which some analysts speculated waspsychological war;[25]sixteen such broadcasts occurred in 2017, including unusually timed transmissions in April.[26]
It has long been speculated, and was argued in one court case, that these stations operate as a simple and fool-proof method for government agencies to communicate with spies working undercover.[27]According to this hypothesis, the messages must have been encrypted with aone-time padto avoid any risk of decryption by the enemy. Writing in 2008, Wallace &Meltondescribed how numbers stations could be used in this way for espionage:[28]
Evidence to support this theory includes the fact that numbers stations have changed details of their broadcasts or produced special, nonscheduled broadcasts coincident with extraordinary political events, such as theattempted coup of August 1991in theSoviet Union.[29]
A 1998 article inThe Daily Telegraphquoted a spokesperson for theDepartment of Trade and Industry(the government department that, at that time, regulated radio broadcasting in the United Kingdom) as saying
Generally, numbers stations follow a basic format, although there are many differences in details between stations. Transmissions usually begin on the hour or half-hour.[citation needed]
The prelude, introduction, or call-up of a transmission (from which stations' informal nicknames are often derived) includes some kind of identifier,[31]for the station itself, the intended recipient, or both. This can take the form of numeric orradio-alphabet"code names" (e.g. "Charlie India Oscar", "250 250 250", "Six-Niner-Zero-Oblique-Five-Four"), characteristic phrases (e.g. "¡Atención!", "Achtung!", "Ready? Ready?", "1234567890"), and sometimes musical or electronic sounds (e.g. "The Lincolnshire Poacher", "Magnetic Fields"). Sometimes, as in the case of radio-alphabet stations, the prelude can also signify the nature or priority of the message to follow (e.g., it may indicate that no message follows). Often the prelude repeats for a period before the body of the message begins.[citation needed]
After the prelude, there is usually an announcement of the number of number-groups in the message,[31]the page to be used from the one-time pad, or other pertinent information. The groups are then recited. Groups are usually either four or five digits or radio-alphabet letters. The groups are typically repeated, either by reading each group twice or by repeating the entire message as a whole.[citation needed]
Some stations send more than one message during a transmission. In this case, some or all of the above process is repeated, with different contents.[citation needed]
Finally, after all the messages have been sent, the station will sign off in some characteristic fashion. Usually, it will simply be some form of the word "end" in whatever language the station uses (e.g., "End of message; End of transmission", "Ende", "Fini", "Final", "конец"). Some stations, especially those thought to originate from the former Soviet Union, end with a series of zeros, e.g., "00000" "000 000"; others end with music or other sounds.[31]
Because of the secretive nature of the messages, thecryptographic functionemployed by particular stations is not publicly known, except in one (or possibly two)[a]) cases. It is assumed that most stations use a one-time pad that would make the contents of these number groups indistinguishable from randomly generated numbers or digits. In one confirmed case, West Germany did use a one-time pad for numbers transmissions.[32]
High-frequencyradio signals transmitted at relatively low power can travel around the world under idealpropagationconditions – which are affected by localRF noiselevels, weather, season, andsunspots– and can then be best received with a properly tuned antenna (of adequate, possibly conspicuous size) and a good receiver.[19]
Although few numbers stations have been tracked down by location, the technology used to transmit the numbers has historically been clear—stock shortwavetransmittersusing powers from 10kW to 100kW.[citation needed]
Amplitude modulated(AM) transmitters with optionally–variable frequency, usingclass-Cpower output stages withplate modulation, are the workhorses of international shortwave broadcasting, including numbers stations.[citation needed]
Application ofspectrum analysisto numbers station signals has revealed the presence of data bursts,radioteletype-modulatedsubcarriers,phase-shifted carriers, and other unusual transmitter modulations likepolytones.[33](RTTY-modulated subcarriers were also present on some U.S. commercial radio transmissions during the Cold War.[34])
The frequently reported use of high-tech modulations likedata bursts, in combination or in sequence with spoken numbers, suggests varying transmissions for differing intelligence operations.[35]
Those receiving the signals often have to work only with available hand-held receivers, sometimes under difficult local conditions, and in all reception conditions (such as sunspot cycles and seasonal static).[19]However, in the field low-tech spoken number transmissions continue to have advantages even in the 21st century. High-tech data-receiving equipment can be difficult to obtain and even a non-standard civilian shortwave radio can be difficult to obtain in a totalitarian state.[36]Being caught with just a shortwave radio has a degree ofplausible deniability, for example, that no spying is being conducted.[citation needed]
The North Korean foreign language serviceVoice of Koreabegan to broadcast on the E03Lincolnshire Poacher's former frequency, 11545 kHz, in 2006, possibly to deliberately interfere with its propagation.[citation needed]However, Lincolnshire Poacher broadcasts on three different frequencies, and the remaining two, have not been interfered with. The apparent target zone for the Lincolnshire Poacher signals originating in Cyprus was the Middle East, not the Far East, which is covered by its sister station, E03aCherry Ripe.[37][38]
On 27 September 2006, amateur radio transmissions in the 30 m band were affected by an S06 "Russian Man"[39]numbers station at 17:40 UTC.[38]
In October 1990, it was reported that a numbers station had been interfering with communications on 6577 kHz, a frequency used by air traffic in the Caribbean. The interference was such that on at least one monitored transmission, it blocked the channel entirely and forced the air traffic controller to switch the pilot to an alternative frequency.[38]
ABBCfrequency, 7325 kHz, has also been used. This prompted a letter to the BBC from a listener inAndorra. She wrote to theWorld ServiceWaveguideprogramme in 1983 complaining that her listening had been spoiled by a female voice reading out numbers in English and asked the announcer what this interference was. The BBC presenter laughed at the suggestion of spy activity. He had consulted the experts atBush House(BBC World Service headquarters), who declared that the voice was reading out nothing more sinister than snowfall figures for the ski slopes near the listener's home. After more research into this case, shortwave enthusiasts are fairly certain that this was a numbers station being broadcast on a random frequency.[40]
The Cuban numbers station "HM01" has been known to interfere with shortwave broadcaster Voice of Welt on 11530 kHz.[41]
Numbers station transmissions have often been the target of intentional jamming attempts. Despite this targeting, many numbers stations continue to broadcast unhindered. Historical examples of jamming include the E10 (a station thought to originate from Israel'sMossadintelligence agency) being jammed by the "Chinese Music Station" (thought to originate from thePeople's Republic of Chinaand usually used to jam "Sound of Hope" radio broadcasts which are anti-CCP in nature).[42]
Monitoring and chronicling transmissions from numbers stations has been a hobby for shortwave andham radioenthusiasts from as early as the 1970s.[43]Numbers stations are often given nicknames by enthusiasts, often reflecting some distinctive element of the station such as theinterval signal. For example, the "Lincolnshire Poacher" station played the first two bars of the folk song "The Lincolnshire Poacher" before each string of numbers.[44]Sometimes these traits have helped to uncover the broadcast location of a station. The "Atención" station was thought to be fromCuba, because a supposed error allowedRadio Havana Cubato be carried on the frequency.[45][full citation needed]
Although many numbers stations have nicknames which usually describe some aspect of the station itself, these nicknames have sometimes led to confusion among listeners, particularly when discussing stations with similar traits. M. Gauffman of the ENIGMA numbers stations monitoring group originally assigned a code to each known station.[46]
Portions of the originalENIGMA groupmoved on to other interests in 2000 and the classification of numbers stations was continued by the follow-on group ENIGMA 2000.[47]The document containing the description of each station and its code designation was called the "ENIGMA Control List" until 2016, after which it was incorporated into the "ENIGMA 2000 Active Station List"; the latest edition of the list was published in September 2017.[48]This classification scheme takes the form of a letter followed by a number (or, in the case of some "X" stations, more numbers).[49]The letter indicates the language used by the station in question:
There are also a few other stations[31]with a specific classification:
Some stations have also been stripped of their designation when they were discovered not to be a numbers station. This was the case for E22, which was discovered in 2005 to be test transmissions forAll India Radio.[50]
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Asession keyis a single-usesymmetric keyused forencryptingallmessagesin onecommunication session. A closely related term iscontent encryption key(CEK),traffic encryption key(TEK), ormulticastkeywhich refers to any key used for encrypting messages, contrary to other uses like encrypting other keys (key encryption key(KEK) orkey encryption has been made public key).
Session keys can introduce complications into a system, yet they solve some real problems. There are two primary reasons to use session keys:
Like allcryptographic keys, session keys must be chosen so that they cannot be predicted by an attacker, usually requiring them to be chosen randomly. Failure to choose session keys (or any key) properly is a major (and too common in actual practice) design flaw in any crypto system.[citation needed]
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Steganography(/ˌstɛɡəˈnɒɡrəfi/ⓘSTEG-ə-NOG-rə-fee) is the practice of representing information within another message or physical object, in such a manner that the presence of the concealed information would not be evident to an unsuspecting person's examination. In computing/electronic contexts, acomputer file, message, image, or video is concealed within another file, message, image, or video. Generally, the hidden messages appear to be (or to be part of) something else: images, articles, shopping lists, or some other cover text. For example, the hidden message may be ininvisible inkbetween the visible lines of a private letter. Some implementations of steganography that lack a formalshared secretare forms ofsecurity through obscurity, while key-dependent steganographic schemes try to adhere toKerckhoffs's principle.[1]
The wordsteganographycomes fromGreeksteganographia, which combines the wordssteganós(στεγανός), meaning "covered or concealed", and-graphia(γραφή) meaning "writing".[2]The first recorded use of the term was in 1499 byJohannes Trithemiusin hisSteganographia, a treatise oncryptographyand steganography, disguised as a book on magic.
The advantage of steganography over cryptography alone is that the intended secret message does not attract attention to itself as an object of scrutiny. Plainly visibleencryptedmessages, no matter how unbreakable they are, arouse interest and may in themselves be incriminating in countries in which encryption is illegal.[3]Whereas cryptography is the practice of protecting the contents of a message alone, steganography is concerned with concealing both the fact that a secret message is being sent and its contents.
Steganography includes the concealment of information within computer files. In digital steganography, electronic communications may include steganographic coding inside a transport layer, such as a document file, image file, program, or protocol. Media files are ideal for steganographic transmission because of their large size. For example, a sender might start with an innocuous image file and adjust the color of every hundredthpixelto correspond to a letter in the alphabet. The change is so subtle that someone who is not looking for it is unlikely to notice the change.
The first recorded uses of steganography can be traced back to 440 BC inGreece, whenHerodotusmentions two examples in hisHistories.[4]Histiaeussent a message to his vassal,Aristagoras, by shaving the head of his most trusted servant, "marking" the message onto his scalp, then sending him on his way once his hair had regrown, with the instruction, "When thou art come to Miletus, bid Aristagoras shave thy head, and look thereon." Additionally,Demaratussent a warning about a forthcoming attack to Greece by writing it directly on the wooden backing of awax tabletbefore applying its beeswax surface. Wax tablets were in common use then as reusable writing surfaces, sometimes used forshorthand.
In his workPolygraphiae,Johannes Trithemiusdeveloped hisAve Mariacipherthat can hide information in a Latin praise of God.[5][better source needed]"Auctor sapientissimus conseruans angelica deferat nobis charitas potentissimi creatoris", for example, contains the concealed wordVICIPEDIA.[citation needed]
Numerous techniques throughout history have been developed to embed a message within another medium.
Placing the message in a physical item has been widely used for centuries.[6]Some notable examples includeinvisible inkon paper, writing a message inMorse codeonyarnworn by a courier,[6]microdots, or using amusic cipherto hide messages asmusical notesinsheet music.[7]
In communities with social or government taboos or censorship, people use cultural steganography—hiding messages in idiom, pop culture references, and other messages they share publicly and assume are monitored. This relies on social context to make the underlying messages visible only to certain readers.[8][9]Examples include:
Since the dawn of computers, techniques have been developed to embed messages in digital cover mediums. The message to conceal is often encrypted, then used to overwrite part of a much larger block of encrypted data or a block of random data (an unbreakable cipher like theone-time padgenerates ciphertexts that look perfectly random without the private key).
Examples of this include changing pixels in image or sound files,[10]properties of digital text such as spacing and font choice,chaffing and winnowing,mimic functions, modifying the echo of a sound file (echo steganography).[citation needed], and including data in ignored sections of a file.[11]
Since the era of evolving network applications, steganography research has shifted from image steganography to steganography in streaming media such asVoice over Internet Protocol(VoIP).
In 2003, Giannoula et al. developed a data hiding technique leading to compressed forms of source video signals on a frame-by-frame basis.[12]
In 2005, Dittmann et al. studied steganography and watermarking of multimedia contents such as VoIP.[13]
In 2008, Yongfeng Huang and Shanyu Tang presented a novel approach to information hiding in low bit-rate VoIP speech stream, and their published work on steganography is the first-ever effort to improve the codebook partition by using Graph theory along with Quantization Index Modulation in low bit-rate streaming media.[14]
In 2011 and 2012, Yongfeng Huang and Shanyu Tang devised new steganographic algorithms that use codec parameters as cover object to realise real-time covert VoIP steganography. Their findings were published inIEEE Transactions on Information Forensics and Security.[15][16][17]
In 2024, Cheddad & Cheddad proposed a new framework[18]for reconstructing lost or corrupted audio signals using a combination of machine learning techniques and latent information. The main idea of their paper is to enhance audio signal reconstruction by fusing steganography, halftoning (dithering), and state-of-the-art shallow and deep learning methods (e.g., RF, LSTM). This combination of steganography, halftoning, and machine learning for audio signal reconstruction may inspire further research in optimizing this approach or applying it to other domains, such as image reconstruction (i.e., inpainting).
Adaptive steganography is a technique for concealing information within digital media by tailoring the embedding process to the specific features of the cover medium. An example of this approach is demonstrated in the work.[19]Their method develops a skin tone detection algorithm, capable of identifying facial features, which is then applied to adaptive steganography. By incorporating face rotation into their approach, the technique aims to enhance its adaptivity to conceal information in a manner that is both less detectable and more robust across various facial orientations within images. This strategy can potentially improve the efficacy of information hiding in both static images and video content.
Academic work since 2012 demonstrated the feasibility of steganography forcyber-physical systems(CPS)/theInternet of Things(IoT). Some techniques of CPS/IoT steganography overlap with network steganography, i.e. hiding data in communication protocols used in CPS/the IoT. However, specific techniques hide data in CPS components. For instance, data can be stored in unused registers of IoT/CPS components and in the states of IoT/CPS actuators.[20][21]
Digital steganography output may be in the form of printed documents. A message, theplaintext, may be first encrypted by traditional means, producing aciphertext. Then, an innocuouscover textis modified in some way so as to contain the ciphertext, resulting in thestegotext. For example, the letter size, spacing,typeface, or other characteristics of a cover text can be manipulated to carry the hidden message. Only a recipient who knows the technique used can recover the message and then decrypt it.Francis BacondevelopedBacon's cipheras such a technique.
The ciphertext produced by most digital steganography methods, however, is not printable. Traditional digital methods rely on perturbing noise in the channel file to hide the message, and as such, the channel file must be transmitted to the recipient with no additional noise from the transmission. Printing introduces much noise in the ciphertext, generally rendering the message unrecoverable. There are techniques that address this limitation, one notable example being ASCII Art Steganography.[22]
Although not classic steganography, some types of modern color laser printers integrate the model, serial number, and timestamps on each printout for traceability reasons using a dot-matrix code made of small, yellow dots not recognizable to the naked eye — seeprinter steganographyfor details.
In 2015, a taxonomy of 109 network hiding methods was presented by Steffen Wendzel, Sebastian Zander et al. that summarized core concepts used in network steganography research.[23]The taxonomy was developed further in recent years by several publications and authors and adjusted to new domains, such as CPS steganography.[24][25][26]
In 1977, Kent concisely described the potential for covert channel signaling in general network communication protocols, even if the traffic is encrypted (in a footnote) in "Encryption-Based Protection for Interactive User/Computer Communication," Proceedings of the Fifth Data Communications Symposium, September 1977.
In 1987, Girling first studied covert channels on a local area network (LAN), identified and realised three obvious covert channels (two storage channels and one timing channel), and his research paper entitled “Covert channels in LAN’s” published inIEEE Transactions on Software Engineering, vol. SE-13 of 2, in February 1987.[27]
In 1989, Wolf implemented covert channels in LAN protocols, e.g. using the reserved fields, pad fields, and undefined fields in the TCP/IP protocol.[28]
In 1997, Rowland used the IP identification field, the TCP initial sequence number and acknowledge sequence number fields in TCP/IP headers to build covert channels.[29]
In 2002, Kamran Ahsan made an excellent summary of research on network steganography.[30]
In 2005, Steven J. Murdoch and Stephen Lewis contributed a chapter entitled "Embedding Covert Channels into TCP/IP" in the "Information Hiding" book published by Springer.[31]
All information hiding techniques that may be used to exchange steganograms in telecommunication networks can be classified under the general term of network steganography. This nomenclature was originally introduced by Krzysztof Szczypiorski in 2003.[32]Contrary to typical steganographic methods that use digital media (images, audio and video files) to hide data, network steganography uses communication protocols' control elements and their intrinsic functionality. As a result, such methods can be harder to detect and eliminate.[33]
Typical network steganography methods involve modification of the properties of a single network protocol. Such modification can be applied to theprotocol data unit(PDU),[34][35][36]to the time relations between the exchanged PDUs,[37]or both (hybrid methods).[38]
Moreover, it is feasible to utilize the relation between two or more different network protocols to enable secret communication. These applications fall under the term inter-protocol steganography.[39]Alternatively, multiple network protocols can be used simultaneously to transfer hidden information and so-called control protocols can be embedded into steganographic communications to extend their capabilities, e.g. to allow dynamic overlay routing or the switching of utilized hiding methods and network protocols.[40][41]
Network steganography covers a broad spectrum of techniques, which include, among others:
Discussions of steganography generally use terminology analogous to and consistent with conventional radio and communications technology. However, some terms appear specifically in software and are easily confused. These are the most relevant ones to digital steganographic systems:
Thepayloadis the data covertly communicated. Thecarrieris the signal, stream, or data file that hides the payload, which differs from thechannel, which typically means the type of input, such as a JPEG image. The resulting signal, stream, or data file with the encoded payload is sometimes called thepackage,stego file, orcovert message. The proportion of bytes, samples, or other signal elements modified to encode the payload is called theencoding densityand is typically expressed as a number between 0 and 1.
In a set of files, the files that are considered likely to contain a payload aresuspects. Asuspectidentified through some type of statistical analysis can be referred to as acandidate.
Detecting physical steganography requires a careful physical examination, including the use of magnification, developer chemicals, andultraviolet light. It is a time-consuming process with obvious resource implications, even in countries that employ many people to spy on other citizens. However, it is feasible to screen mail of certain suspected individuals or institutions, such as prisons or prisoner-of-war (POW) camps.
DuringWorld War II, prisoner of war camps gave prisoners specially-treatedpaperthat would revealinvisible ink. An article in the 24 June 1948 issue ofPaper Trade Journalby the Technical Director of theUnited States Government Printing Officehad Morris S. Kantrowitz describe in general terms the development of this paper. Three prototype papers (Sensicoat,Anilith, andCoatalith) were used to manufacture postcards and stationery provided to German prisoners of war in the US and Canada. If POWs tried to write a hidden message, the special paper rendered it visible. The US granted at least twopatentsrelated to the technology, one to Kantrowitz,U.S. patent 2,515,232, "Water-Detecting paper and Water-Detecting Coating Composition Therefor," patented 18 July 1950, and an earlier one, "Moisture-Sensitive Paper and the Manufacture Thereof,"U.S. patent 2,445,586, patented 20 July 1948. A similar strategy issues prisoners with writing paper ruled with a water-soluble ink that runs in contact with water-based invisible ink.
In computing, steganographically encoded package detection is calledsteganalysis. The simplest method to detect modified files, however, is to compare them to known originals. For example, to detect information being moved through the graphics on a website, an analyst can maintain known clean copies of the materials and then compare them against the current contents of the site. The differences, if the carrier is the same, comprise the payload. In general, using extremely high compression rates makes steganography difficult but not impossible. Compression errors provide a hiding place for data, but high compression reduces the amount of data available to hold the payload, raising the encoding density, which facilitates easier detection (in extreme cases, even by casual observation).
There are a variety of basic tests that can be done to identify whether or not a secret message exists. This process is not concerned with the extraction of the message, which is a different process and a separate step. The most basic approaches ofsteganalysisare visual or aural attacks, structural attacks, and statistical attacks. These approaches attempt to detect the steganographic algorithms that were used.[44]These algorithms range from unsophisticated to very sophisticated, with early algorithms being much easier to detect due to statistical anomalies that were present. The size of the message that is being hidden is a factor in how difficult it is to detect. The overall size of the cover object also plays a factor as well. If the cover object is small and the message is large, this can distort the statistics and make it easier to detect. A larger cover object with a small message decreases the statistics and gives it a better chance of going unnoticed.
Steganalysis that targets a particular algorithm has much better success as it is able to key in on the anomalies that are left behind. This is because the analysis can perform a targeted search to discover known tendencies since it is aware of the behaviors that it commonly exhibits. When analyzing an image the least significant bits of many images are actually not random. The camera sensor, especially lower-end sensors are not the best quality and can introduce some random bits. This can also be affected by the file compression done on the image. Secret messages can be introduced into the least significant bits in an image and then hidden. A steganography tool can be used to camouflage the secret message in the least significant bits but it can introduce a random area that is too perfect. This area of perfect randomization stands out and can be detected by comparing the least significant bits to the next-to-least significant bits on an image that hasn't been compressed.[44]
Generally, though, there are many techniques known to be able to hide messages in data using steganographic techniques. None are, by definition, obvious when users employ standard applications, but some can be detected by specialist tools. Others, however, are resistant to detection—or rather it is not possible to reliably distinguish data containing a hidden message from data containing just noise—even when the most sophisticated analysis is performed. Steganography is being used to conceal and deliver more effective cyber attacks, referred to asStegware. The term Stegware was first introduced in 2017[45]to describe any malicious operation involving steganography as a vehicle to conceal an attack. Detection of steganography is challenging, and because of that, not an adequate defence. Therefore, the only way of defeating the threat is to transform data in a way that destroys any hidden messages,[46]a process calledContent Threat Removal.
Some modern computer printers use steganography, includingHewlett-PackardandXeroxbrand color laser printers. The printers add tiny yellow dots to each page. The barely-visible dots contain encoded printer serial numbers and date and time stamps.[47]
The larger the cover message (in binary data, the number ofbits) relative to the hidden message, the easier it is to hide the hidden message (as an analogy, the larger the "haystack", the easier it is to hide a "needle"). Sodigital pictures, which contain much data, are sometimes used to hide messages on theInternetand on other digital communication media. It is not clear how common this practice actually is.
For example, a 24-bitbitmapuses 8 bits to represent each of the three color values (red, green, and blue) of eachpixel. The blue alone has 28different levels of blue intensity. The difference between 111111112and 111111102in the value for blue intensity is likely to be undetectable by the human eye. Therefore, theleast significant bitcan be used more or less undetectably for something else other than color information. If that is repeated for the green and the red elements of each pixel as well, it is possible to encode one letter ofASCIItext for every threepixels.
Stated somewhat more formally, the objective for making steganographic encoding difficult to detect is to ensure that the changes to the carrier (the original signal) because of the injection of the payload (the signal to covertly embed) are visually (and ideally, statistically) negligible. The changes are indistinguishable from thenoise floorof the carrier. All media can be a carrier, but media with a large amount of redundant or compressible information is better suited.
From aninformation theoreticalpoint of view, that means that thechannelmust have morecapacitythan the "surface"signalrequires. There must beredundancy. For a digital image, it may benoisefrom the imaging element; fordigital audio, it may be noise from recording techniques oramplificationequipment. In general, electronics that digitize ananalog signalsuffer from several noise sources, such asthermal noise,flicker noise, andshot noise. The noise provides enough variation in the captured digital information that it can be exploited as a noise cover for hidden data. In addition,lossy compressionschemes (such asJPEG) always introduce some error to the decompressed data, and it is possible to exploit that for steganographic use, as well.
Although steganography and digital watermarking seem similar, they are not. In steganography, the hidden message should remain intact until it reaches its destination. Steganography can be used fordigital watermarkingin which a message (being simply an identifier) is hidden in an image so that its source can be tracked or verified (for example,Coded Anti-Piracy) or even just to identify an image (as in theEURion constellation). In such a case, the technique of hiding the message (here, the watermark) must be robust to prevent tampering. However, digital watermarking sometimes requires a brittle watermark, which can be modified easily, to check whether the image has been tampered with. That is the key difference between steganography and digital watermarking.
In 2010, theFederal Bureau of Investigationalleged that theRussian foreign intelligence serviceuses customized steganography software for embedding encrypted text messages inside image files for certain communications with "illegal agents" (agents without diplomatic cover) stationed abroad.[48]
On 23 April 2019 the U.S. Department of Justice unsealed an indictment charging Xiaoqing Zheng, a Chinese businessman and former Principal Engineer at General Electric, with 14 counts of conspiring to steal intellectual property and trade secrets from General Electric. Zheng had allegedly used steganography to exfiltrate 20,000 documents from General Electric to Tianyi Aviation Technology Co. in Nanjing, China, a company the FBI accused him of starting with backing from the Chinese government.[49]
There are distributed steganography methods,[50]including methodologies that distribute the payload through multiple carrier files in diverse locations to make detection more difficult. For example,U.S. patent 8,527,779by cryptographer William Easttom (Chuck Easttom).
The puzzles that are presented byCicada 3301incorporate steganography with cryptography and other solving techniques since 2012.[51]Puzzles involving steganography have also been featured in otheralternative reality games.
The communications[52][53]ofThe May Day mysteryincorporate steganography and other solving techniques since 1981.[54]
It is possible to steganographically hide computer malware into digital images, videos, audio and various other files in order to evade detection byantivirus software. This type of malware is called stegomalware. It can be activated by external code, which can be malicious or even non-malicious if some vulnerability in the software reading the file is exploited.[55]
Stegomalware can be removed from certain files without knowing whether they contain stegomalware or not. This is done throughcontent disarm and reconstruction(CDR) software, and it involves reprocessing the entire file or removing parts from it.[56][57]Actually detecting stegomalware in a file can be difficult and may involve testing the file behaviour invirtualenvironments ordeep learninganalysis of the file.[55]
Stegoanalytical algorithms can be cataloged in different ways, highlighting: according to the available information and according to the purpose sought.
There is the possibility of cataloging these algorithms based on the information held by the stegoanalyst in terms of clear and encrypted messages. It is a technique similar to cryptography, however, they have several differences:
The principal purpose of steganography is to transfer information unnoticed, however, it is possible for an attacker to have two different pretensions:
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Tradecraft, within theintelligence community, refers to the techniques, methods, and technologies used in modernespionage(spying) and generally as part of the activity ofintelligence assessment. This includes general topics or techniques (dead drops, for example), or the specific techniques of a nation or organization (the particular form ofencryption(encoding) used by theNational Security Agency, for example).
In the books of suchspy novelistsasIan Fleming,John le CarréandTom Clancy, characters frequently engage in tradecraft, e.g. making or retrieving items from "dead drops", "dry cleaning", and wiring, using, or sweeping for intelligence gathering devices, such as cameras or microphones hidden in the subjects' quarters, vehicles, clothing, or accessories.
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Incryptography,unicity distanceis the length of an originalciphertextneeded to break the cipher by reducing the number of possiblespurious keysto zero in abrute force attack. That is, after trying every possiblekey, there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy.[1]
Claude Shannondefined the unicity distance in his 1949 paper "Communication Theory of Secrecy Systems".[2]
Consider an attack on the ciphertext string "WNAIW" encrypted using aVigenère cipherwith a five letter key. Conceivably, this string could be deciphered into any other string—RIVER and WATER are both possibilities for certain keys. This is a general rule ofcryptanalysis: with no additional information it is impossible to decode this message.
Of course, even in this case, only a certain number of five letter keys will result in English words. Trying all possible keys we will not only get RIVER and WATER, but SXOOS and KHDOP as well. The number of "working" keys will likely be very much smaller than the set of all possible keys. The problem is knowing which of these "working" keys is the right one; the rest are spurious.
In general, given particular assumptions about the size of the key and the number of possible messages, there is an average ciphertext length where there is only one key (on average) that will generate a readable message. In the example above we see onlyupper caseEnglish characters, so if we assume that theplaintexthas this form, then there are 26 possible letters for each position in the string. Likewise if we assume five-character upper case keys, there are K=265possible keys, of which the majority will not "work".
A tremendous number of possible messages, N, can be generated using even this limited set of characters: N = 26L, where L is the length of the message. However, only a smaller set of them is readableplaintextdue to the rules of the language, perhaps M of them, where M is likely to be very much smaller than N. Moreover, M has a one-to-one relationship with the number of keys that work, so given K possible keys, only K × (M/N) of them will "work". One of these is the correct key, the rest are spurious.
Since M/N gets arbitrarily small as the length L of the message increases, there is eventually some L that is large enough to make the number of spurious keys equal to zero. Roughly speaking, this is the L that makes KM/N=1. This L is the unicity distance.
The unicity distance can equivalently be defined as the minimum amount of ciphertext required to permit a computationally unlimited adversary to recover the unique encryption key.[1]
The expected unicity distance can then be shown to be:[1]
whereUis the unicity distance,H(k) is the entropy of the key space (e.g. 128 for 2128equiprobable keys, rather less if the key is a memorized pass-phrase).Dis defined as the plaintext redundancy in bits per character.
Now an alphabet of 32 characters can carry 5 bits of information per character (as 32 = 25). In general the number of bits of information per character islog2(N), whereNis the number of characters in the alphabet andlog2is thebinary logarithm. So for English each character can conveylog2(26) = 4.7bits of information.
However the average amount of actual information carried per character in meaningful English text is only about 1.5 bits per character. So the plain text redundancy isD= 4.7 − 1.5 = 3.2.[1]
Basically the bigger the unicity distance the better. For a one time pad of unlimited size, given the unbounded entropy of the key space, we haveU=∞{\displaystyle U=\infty }, which is consistent with theone-time padbeing unbreakable.
For a simplesubstitution cipher, the number of possible keys is26! = 4.0329 × 1026= 288.4, the number of ways in which the alphabet can be permuted. Assuming all keys are equally likely,H(k) = log2(26!) = 88.4bits. For English textD= 3.2, thusU= 88.4/3.2 = 28.
So given 28 characters of ciphertext it should be theoretically possible to work out an English plaintext and hence the key.
Unicity distance is a useful theoretical measure, but it does not say much about the security of a block cipher when attacked by an adversary with real-world (limited) resources. Consider a block cipher with a unicity distance of three ciphertext blocks. Although there is clearly enough information for a computationally unbounded adversary to find the right key (simple exhaustive search), this may be computationally infeasible in practice.
The unicity distance can be increased by reducing the plaintext redundancy. One way to do this is to deploydata compressiontechniques prior to encryption, for example by removing redundant vowels while retaining readability. This is a good idea anyway, as it reduces the amount of data to be encrypted.
Ciphertexts greater than the unicity distance can be assumed to have only one meaningful decryption. Ciphertexts shorter than the unicity distance may have multiple plausible decryptions. Unicity distance is not a measure of how much ciphertext is required for cryptanalysis,[why?]but how much ciphertext is required for there to be only one reasonable solution for cryptanalysis.
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Theno-hiding theorem[1]states that if information is lost from a system viadecoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and the environment. This is a fundamental consequence of thelinearityandunitarityofquantum mechanics. Thus, information is never lost. This has implications in theblack hole information paradoxand in fact any process that tends to lose information completely. The no-hiding theorem is robust to imperfection in the physical process that seemingly destroys the original information.
This was proved bySamuel L. BraunsteinandArun K. Patiin 2007. In 2011, the no-hiding theorem was experimentally tested[2]usingnuclear magnetic resonancedevices where a singlequbitundergoes completerandomization; i.e., a pure state transforms to a random mixed state. Subsequently, the lost information has been recovered from theancillaqubits using suitable local unitary transformation only in the environmentHilbert spacein accordance with the no-hiding theorem. This experiment for the first time demonstrated the conservation ofquantum information.[3]
Let|ψ⟩{\displaystyle |\psi \rangle }be an arbitraryquantum statein someHilbert spaceand let there be a physical process that transforms|ψ⟩⟨ψ|→ρ{\displaystyle |\psi \rangle \langle \psi |\rightarrow \rho }withρ=∑kpk|k⟩⟨k|{\textstyle \rho =\sum _{k}p_{k}|k\rangle \langle k|}.Ifρ{\displaystyle \rho }is independent of the input state|ψ⟩{\displaystyle |\psi \rangle }, then in the enlarged Hilbert space the mapping is of the form|ψ⟩⊗|A⟩→∑kpk|k⟩⊗|Ak(ψ)⟩=∑kpk|k⟩⊗(|qk⟩⊗|ψ⟩⊕0),{\displaystyle |\psi \rangle \otimes |A\rangle \rightarrow \sum _{k}{\sqrt {p_{k}}}|k\rangle \otimes |A_{k}(\psi )\rangle =\sum _{k}{\sqrt {p_{k}}}|k\rangle \otimes (|q_{k}\rangle \otimes |\psi \rangle \oplus 0),}where|A⟩{\displaystyle |A\rangle }is the initial state of the environment,|Ak(ψ)⟩{\displaystyle |A_{k}(\psi )\rangle }'s are theorthonormal basisof the environment Hilbert space and⊕0{\displaystyle \oplus 0}denotes the fact that one may augment the unused dimension of the environment Hilbert space by zero vectors.
The proof of the no-hiding theorem is based on the linearity and the unitarity of quantum mechanics. The original information which is missing from the final state simply remains in the subspace of the environmental Hilbert space. Also, note that the original information is not in the correlation between the system and the environment. This is the essence of the no-hiding theorem. One can in principle, recover the lost information from the environment by local unitary transformations acting only on the environment Hilbert space. The no-hiding theorem provides new insights to the nature of quantum information. For example, if classical information is lost from one system it may either move to another system or can be hidden in the correlation between a pair of bit strings. However, quantum information cannot be completely hidden in correlations between a pair of subsystems. Quantum mechanics allows only one way to completely hide an arbitrary quantum state from one of its subsystems. If it is lost from one subsystem, then it moves to other subsystems.
In physics, conservation laws play important roles. For example, the law of conservation of energy states that the energy of a closed system must remain constant. It can neither increase nor decrease without coming in contact with an external system. If we consider the whole universe as a closed system, the total amount of energy always remains the same. However, the form of energy keeps changing. One may wonder if there is any such law for the conservation of information. In the classical world, information can be copied and deleted perfectly. In the quantum world, however, the conservation of quantum information should mean that information cannot be created nor destroyed. This concept stems from two fundamental theorems of quantum mechanics: theno-cloning theoremand theno-deleting theorem. But the no-hiding theorem is a more general proof of conservation of quantum information which originates from the proof of conservation of wave function in quantum theory.
It may be noted that the conservation of entropy holds for a quantum system undergoing unitary time evolution and that if entropy represents information in quantum theory, then it is believed then that information should somehow be conserved. For example, one can prove that pure states remain pure states and probabilistic combinations of pure states (called as mixed states) remain mixed states under unitary evolution. However, it was never proved that if the probability amplitude disappears from one system, it will reappear in another system. Now, using the no-hiding theorem one can make a precise statement. One may say that as energy keeps changing its form, the wave function keep moving from one Hilbert space to another Hilbert space. Since the wave function contains all the relevant information about a physical system, the conservation of wave function is tantamount to conservation of quantum information.
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https://en.wikipedia.org/wiki/No-hiding_theorem
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Incryptography, anoblivious transfer(OT) protocol is a type of protocol in which a sender transfers one of potentially many pieces of information to a receiver, but remainsobliviousas to what piece (if any) has been transferred.
The first form of oblivious transfer was introduced in 1981 byMichael O. Rabin.[1]In this form, the sender sends a message to the receiver withprobability1/2, while the sender remains oblivious as to whether or not the receiver received the message. Rabin's oblivious transfer scheme is based on theRSAcryptosystem. A more useful form of oblivious transfer called1–2 oblivious transferor "1 out of 2 oblivious transfer", was developed later byShimon Even,Oded Goldreich, andAbraham Lempel,[2]in order to build protocols forsecure multiparty computation. It is generalized to "1 out ofnoblivious transfer" where the user gets exactly one database element without the server getting to know which element was queried, and without the user knowing anything about the other elements that were not retrieved. The latter notion of oblivious transfer is a strengthening ofprivate information retrieval, in which the database is not kept private.
Claude Crépeaushowed that Rabin's oblivious transfer is equivalent to 1–2 oblivious transfer.[3]
Further work has revealed oblivious transfer to be a fundamental and important problem in cryptography. It is considered one of the critical problems in the field, because of the importance of the applications that can be built based on it. In particular, it iscompleteforsecure multiparty computation: that is, given an implementation of oblivious transfer it is possible to securely evaluate any polynomial time computable function without any additional primitive.[4]
In Rabin's oblivious transfer protocol, the sender generates an RSA public modulusN=pqwherepandqare largeprime numbers, and an exponenterelatively primetoλ(N)= (p− 1)(q− 1). The sender encrypts the messagemasmemodN.
If the receiver findsyis neitherxnor −xmoduloN, the receiver will be able tofactorNand therefore decryptmeto recoverm(seeRabin encryptionfor more details). However, ifyisxor −xmodN, the receiver will have no information aboutmbeyond the encryption of it. Since everyquadratic residuemoduloNhas four square roots, the probability that the receiver learnsmis 1/2.
In a 1–2 oblivious transfer protocol, Alice the sender has two messagesm0andm1, and wants to ensure that the receiver only learns one. Bob, the receiver, has a bitband wishes to receivembwithout Alice learningb.
The protocol of Even, Goldreich, and Lempel (which the authors attribute partially toSilvio Micali) is general, but can be instantiated using RSA encryption as follows.
A 1-out-of-noblivious transfer protocol can be defined as a natural generalization of a 1-out-of-2 oblivious transfer protocol. Specifically, a sender hasnmessages, and the receiver has an indexi, and the receiver wishes to receive thei-th among the sender's messages, without the sender learningi, while the sender wants to ensure that the receiver receive only one of thenmessages.
1-out-of-noblivious transfer is incomparable toprivate information retrieval(PIR).
On the one hand, 1-out-of-noblivious transfer imposes an additional privacy requirement for the database: namely, that the receiver learn at most one of the database entries. On the other hand, PIR requires communicationsublinearinn, whereas 1-out-of-noblivious transfer has no such requirement. However, assuming single server PIR is a sufficient assumption in order to construct 1-out-of-2 Oblivious Transfer.[5]
1-out-of-noblivious transfer protocol withsublinearcommunication was first constructed (as a generalization of single-server PIR) byEyal KushilevitzandRafail Ostrovsky.[6]More efficient constructions were proposed byMoni NaorandBenny Pinkas,[7]William Aiello,Yuval IshaiandOmer Reingold,[8]Sven LaurandHelger Lipmaa.[9]In 2017,Kolesnikov et al.,[10]proposed an efficient 1-n oblivious transfer protocol which requires roughly 4x the cost of 1-2 oblivious transfer in amortized setting.
Brassard,CrépeauandRobertfurther generalized this notion tok-noblivious transfer,[11]wherein the receiver obtains a set ofkmessages from thenmessage collection. The set ofkmessages may be received simultaneously ("non-adaptively"), or they may be requested consecutively, with each request based on previous messages received.[12]
k-nOblivious transfer is a special case of generalized oblivious transfer, which was presented by Ishai and Kushilevitz.[13]In that setting, the sender has a setUofnmessages, and the transfer constraints are specified by a collectionAof permissible subsets ofU.
The receiver may obtain any subset of the messages inUthat appears in the collectionA. The sender should remain oblivious of the selection made by the receiver, while the receiver cannot learn the value of the messages outside the subset of messages that he chose to obtain. The collectionAis monotone decreasing, in the sense that it is closed under containment (i.e., if a given subsetBis in the collectionA, so are all of the subsets ofB).
The solution proposed by Ishai and Kushilevitz uses the parallel invocations of 1-2 oblivious transfer while making use of a special model of private protocols. Later on, other solutions that are based on secret sharing were published – one by Bhavani Shankar, Kannan Srinathan, andC. Pandu Rangan,[14]and another by Tamir Tassa.[15]
In the early seventiesStephen Wiesnerintroduced a primitive calledmultiplexingin his seminal paper "Conjugate Coding",
which was the starting point ofquantum cryptography.[16]Unfortunately it took more than ten years to be published. Even though
this primitive was equivalent to what was later called1–2 oblivious transfer, Wiesner did not see its application to cryptography.
Protocols for oblivious transfer can be implemented withquantum systems. In contrast to other tasks inquantum cryptography, likequantum key distribution, it has been shown that quantum oblivious transfer cannot be implemented with unconditional security, i.e. the security of quantum oblivious transfer protocols cannot be guaranteed only from the laws ofquantum physics.[17]
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https://en.wikipedia.org/wiki/Oblivious_transfer
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Incryptography, anaccumulatoris aone waymembershiphash function. It allows users to certify that potential candidates are a member of a certainsetwithout revealing the individual members of the set. This concept was formally introduced by Josh Benaloh and Michael de Mare in 1993.[1][2]
There are several formal definitions which have been proposed in the literature. This section lists them by proposer, in roughly chronological order.[2]
Benaloh and de Mare define a one-way hash function as a family of functionshℓ:Xℓ×Yℓ→Zℓ{\displaystyle h_{\ell }:X_{\ell }\times Y_{\ell }\to Z_{\ell }}which satisfy the following three properties:[1][2]
(With the first two properties, one recovers the normal definition of a cryptographic hash function.)
From such a function, one defines the "accumulated hash" of a set{y1,…,ym}{\displaystyle \{y_{1},\dots ,y_{m}\}}and starting valuex{\displaystyle x}w.r.t. a valuez{\displaystyle z}to beh(h(⋯h(h(x,y1),y2),…,ym−1),ym){\displaystyle h(h(\cdots h(h(x,y_{1}),y_{2}),\dots ,y_{m-1}),y_{m})}. The result, does not depend on the order of elementsy1,y2,...,yn{\displaystyle y_{1},y_{2},...,y_{n}}becauseh{\displaystyle h}is quasi-commutative.[1][2]
Ify1,y2,...,yn{\displaystyle y_{1},y_{2},...,y_{n}}belong to some users of a cryptosystem, then everyone can compute the accumulated valuez.{\displaystyle z.}Also, the user ofyi{\displaystyle y_{i}}can compute the partial accumulated valuezi{\displaystyle z_{i}}of(y1,...,yi−1,yi+1,...,yn){\displaystyle (y_{1},...,y_{i-1},y_{i+1},...,y_{n})}. Then,h(zi,yi)=z.{\displaystyle h(z_{i},y_{i})=z.}So thei−{\displaystyle i-}user can provide the pair(zi,yi){\displaystyle (z_{i},y_{i})}to any other part, in order to authenticateyi{\displaystyle y_{i}}.
The basic functionality of a quasi-commutative hash function is not immediate from the definition. To fix this, Barić and Pfitzmann defined a slightly more general definition, which is the notion of anaccumulator schemeas consisting of the following components:[2][3]
It is relatively easy to see that one can define an accumulator scheme from any quasi-commutative hash function, using the technique shown above.[2]
One observes that, for many applications, the set of accumulated values will change many times. Naïvely, one could completely redo the accumulator calculation every time; however, this may be inefficient, especially if our set is very large and the change is very small. To formalize this intuition, Camenish and Lysyanskaya defined adynamic accumulator schemeto consist of the 4 components of an ordinary accumulator scheme, plus three more:[2][4]
Fazio and Nicolosi note that since Add, Del, and Upd can be simulated by rerunning Eval and Wit, this definition does not add any fundamentally new functionality.[2]
One example ismultiplicationover largeprime numbers. This is a cryptographic accumulator, since it takes superpolynomial time tofactora composite number (at least according to conjecture), but it takes only a small amount of time (polynomial in size) to divide a prime into an integer to check if it is one of the factors and/or to factor it out. New members may be added or subtracted to the set of factors by multiplying or factoring out the number respectively. In this system, two accumulators that have accumulated a single shared prime can have it trivially discovered by calculating their GCD, even without prior knowledge of the prime (which would otherwise require prime factorization of the accumulator to discover).[citation needed]
More practical accumulators use aquasi-commutativehash function, so that the size of the accumulator does not grow with the number of members. For example, Benaloh and de Mare propose a cryptographic accumulator inspired byRSA: the quasi-commutative functionh(x,y):=xy(modn){\displaystyle h(x,y):=x^{y}{\pmod {n}}}for some composite numbern{\displaystyle n}. They recommend to choosen{\displaystyle n}to be arigidinteger (i.e. the product of twosafe primes).[1]Barić and Pfitzmann proposed a variant wherey{\displaystyle y}was restricted to be prime and at mostn/4{\displaystyle n/4}(this constant is very close toϕ(n){\displaystyle \phi (n)}, but does not leak information about the prime factorization ofn{\displaystyle n}).[2][3]
David Naccacheobserved in 1993 thaten,c(x,y):=xycy−1(modn){\displaystyle e_{n,c}(x,y):=x^{y}c^{y-1}{\pmod {n}}}is quasi-commutative for all constantsc,n{\displaystyle c,n}, generalizing the previous RSA-inspired cryptographic accumulator. Naccache also noted that theDickson polynomialsare quasi-commutative in the degree, but it is unknown whether this family of functions is one-way.[1]
In 1996, Nyberg constructed an accumulator which is provably information-theoretically secure in therandom oracle model. Choosing some upper limitN=2d{\displaystyle N=2^{d}}for the number of items that can be securely accumulated andλ{\displaystyle \lambda }the security parameter, define the constantℓ:≈elog2(e)λNlog2(N){\displaystyle \ell :\approx {\frac {e}{\log _{2}(e)}}\lambda N\log _{2}(N)}to be an integer multiple ofd{\displaystyle d}(so that one can writeℓ=rd{\displaystyle \ell =rd}) and letH:{0,1}∗→{0,1}ℓ{\displaystyle H:\{0,1\}^{*}\to \{0,1\}^{\ell }}be somecryptographically secure hash function. Choose a keyk{\displaystyle k}as a randomr{\displaystyle r}-bit bitstring. Then, to accumulate using Nyberg's scheme, use the quasi-commutative hash functionh(x,y):=x⊙αr(H(y)){\displaystyle h(x,y):=x\odot \alpha _{r}(H(y))}, where⊙{\displaystyle \odot }is thebitwise andoperation andαr:{0,1}ℓ→{0,1}r{\displaystyle \alpha _{r}:\{0,1\}^{\ell }\to \{0,1\}^{r}}is the function that interprets its input as a sequence ofd{\displaystyle d}-bit bitstrings of lengthr{\displaystyle r}, replaces every all-zero bitstring with a single 0 and every other bitstring with a 1, and outputs the result.[2][5]
Haber and Stornetta showed in 1990 that accumulators can be used totimestampdocuments through cryptographic chaining. (This concept anticipates the modern notion of a cryptographicblockchain.)[1][2][6]Benaloh and de Mare proposed an alternative scheme in 1991 based on discretizing time into rounds.[1][7]
Benaloh and de Mare showed that accumulators can be used so that a large group of people can recognize each other at a later time (which Fazio and Nicolosi call an "ID Escrow" situation). Each person selects ay{\displaystyle y}representing their identity, and the group collectively selects a public accumulatorh{\displaystyle h}and a secretx{\displaystyle x}. Then, the group publishes or saves the hash function and the accumulated hash of all the group's identities w.r.t the secretx{\displaystyle x}and public accumulator; simultaneously, each member of the group keeps both its identity valuey{\displaystyle y}and the accumulated hash of all the group's identitiesexcept that of the member. (If the large group of people do not trust each other, or if the accumulator has a cryptographic trapdoor as in the case of the RSA-inspired accumulator, then they can compute the accumulated hashes bysecure multiparty computation.) To verify that a claimed member did indeed belong to the group later, they present their identity and personal accumulated hash (or azero-knowledge proofthereof); by accumulating the identity of the claimed member and checking it against the accumulated hash of the entire group, anyone can verify a member of the group.[1][2]With a dynamic accumulator scheme, it is additionally easy to add or remove members afterward.[2][4]
Cryptographic accumulators can also be used to construct other cryptographically securedata structures:
The concept has received renewed interest due to theZerocoinadd on tobitcoin, which employs cryptographic accumulators to eliminate trackable linkage in the bitcoin blockchain, which would make transactions anonymous and more private.[10][11][12]More concretely, tomint(create) a Zerocoin, one publishes a coin and acryptographic commitmentto a serial number with a secret random value (which all users will accept as long as it is correctly formatted); tospend(reclaim) a Zerocoin, one publishes the Zerocoin's serial number along with anon-interactive zero-knowledge proofthat they know of some published commitment that relates to the claimed serial number, then claims the coin (which all users will accept as long as the NIZKP is valid and the serial number has not appeared before).[10][11]Since the initial proposal of Zerocoin, it has been succeeded by theZerocashprotocol and is currently being developed intoZcash, a digital currency based on Bitcoin's codebase.[13][14]
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https://en.wikipedia.org/wiki/Accumulator_(cryptography)
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Inpublic-key cryptography, akey signing partyis an event at which people present their publickeysto others in person, who, if they are confident the key actually belongs to the person who claims it,digitally signthecertificatecontaining thatpublic keyand the person's name, etc.[1]Key signing parties are common within thePGPandGNU Privacy Guardcommunity, as the PGP public key infrastructure does not depend on a central key certifying authority and instead uses a distributedweb of trustapproach. Key signing parties are a way to strengthen theweb of trust. Participants at a key signing party are expected to present adequateidentity documents.[2]
Although PGP keys are generally used withpersonal computersforInternet-related applications, key signing parties themselves generally do not involve computers, since that would give adversaries increased opportunities for subterfuge. Rather, participants write down a string of letters and numbers, called apublic key fingerprint, which represents their key. The fingerprint is created by acryptographic hash function, which condenses the public key down to a string which is shorter and more manageable. Participants exchange these fingerprints as they verify each other's identification. Then, after the party, they obtain the public keys corresponding to the fingerprints they received anddigitally signthem.[3]
This cryptography-related article is astub. You can help Wikipedia byexpanding it.
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https://en.wikipedia.org/wiki/Key_signing_party
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Incryptography, aweb of trustis a concept used inPGP,GnuPG, and otherOpenPGP-compatible systems to establish theauthenticityof the binding between apublic keyand its owner. Its decentralizedtrust modelis an alternative to the centralized trust model of apublic key infrastructure(PKI), which relies exclusively on acertificate authority(or a hierarchy of such).[1]As with computer networks, there are many independent webs of trust, and any user (through theirpublic key certificate) can be a part of, and a link between, multiple webs.
The web of trust concept was first put forth by PGP creatorPhil Zimmermannin 1992 in the manual for PGP version 2.0:
As time goes on, you will accumulate keys from other people that you may want to designate as trusted introducers. Everyone else will each choose their own trusted introducers. And everyone will gradually accumulate and distribute with their key a collection of certifying signatures from other people, with the expectation that anyone receiving it will trust at least one or two of the signatures. This will cause the emergence of a decentralized fault-tolerant web of confidence for all public keys.
Note the use of the wordemergencein this context. The web of trust makes use of the concept of emergence.
All OpenPGP-compliant implementations include a certificatevettingscheme to assist with this; its operation has been termed a web of trust. OpenPGP certificates (which include one or more public keys along with owner information) can be digitally signed by other users who, by that act, endorse the association of that public key with the person or entity listed in the certificate. This is commonly done atkey signing parties.[2]
OpenPGP-compliant implementations also include a vote counting scheme which can be used to determine which public key – owner association a user will trust while using PGP. For instance, if three partially trusted endorsers have vouched for a certificate (and so its included public key – ownerbinding), or if one fully trusted endorser has done so, the association between owner and public key in that certificate will be trusted to be correct. The parameters are user-adjustable (e.g., no partials at all, or perhaps six partials) and can be completely bypassed if desired.
The scheme is flexible, unlike most public key infrastructure designs, and leaves trust decisions in the hands of individual users. It is not perfect and requires both caution and intelligent supervision by users. Essentially all PKI designs are less flexible and require users to follow the trust endorsement of the PKI generated, certificate authority (CA)-signed, certificates.
There are two keys pertaining to a person: a public key which is shared openly and a private key that is withheld by the owner. The owner's private key will decrypt any information encrypted with its public key. In the web of trust, each user has a key ring with other people's public keys.
Senders encrypt their information with the recipient's public key, and only the recipient's private key will decrypt it. Each sender then digitally signs the encrypted information with their private key. When the recipient verifies the received encrypted information against the sender's public key, they can confirm that it is from the sender. Doing this will ensure that the encrypted information came from the specific user and has not been tampered with, and only the intended recipient can decrypt the information (because only they know their private key).
Unlike WOT, a typicalX.509PKI enables each certificate to be signed by a single party: acertificate authority(CA). The CA's certificate may itself be signed by a different CA, all the way up to a 'self-signed'root certificate. Root certificates must be available to those who use a lower-level CA certificate and so are typically distributed widely. They are for instance, distributed with such applications as browsers and email clients. In this waySSL/TLS-protected Web pages, email messages, etc. can be authenticated without requiring users to manually install root certificates. Applications commonly include over one hundred root certificates from dozens of PKIs, thus by default bestowing trust throughout the hierarchy of certificates which lead back to them.
WOT favors the decentralization of trust anchors to prevent a single point of failure from compromising the CA hierarchy.[3]
The OpenPGP web of trust is essentially unaffected by such things as company failures, and has continued to function with little change. However, a related problem does occur: users, whether individuals or organizations, who lose track of a private key can no longer decrypt messages sent to them produced using the matching public key found in an OpenPGP certificate. Early PGP certificates did not include expiry dates, and those certificates had unlimited lives. Users had to prepare a signed cancellation certificate against the time when the matching private key was lost or compromised. One very prominent cryptographer is still getting messages encrypted using a public key for which he long ago lost track of the private key.[4]They can't do much with those messages except discard them after notifying the sender that they were unreadable and requesting resending with a public key for which they still have the matching private key. Later PGP, and all OpenPGP compliant certificates include expiry dates which automatically preclude such troubles (eventually) when used sensibly. This problem can also be easily avoided by the use of "designated revokers", which were introduced in the early 1990s. A key owner may designate a third party that has permission to revoke the key owner's key (in case the key owner loses his own private key and thus loses the ability to revoke his own public key).
A non-technical, social difficulty with a Web of Trust like the one built into PGP/OpenPGP type systems is that every web of trust without a central controller (e.g., aCA) depends on other users for trust. Those with new certificates (i.e., produced in the process of generating a new key pair) will not likely be readily trusted by other users' systems, that is by those they have not personally met, until they find enough endorsements for the new certificate. This is because many other Web of Trust users will have their certificate vetting set to require one or more fully trusted endorsers of an otherwise unknown certificate (or perhaps several partial endorsers) before using the public key in that certificate to prepare messages, believe signatures, etc.
Despite the wide use of OpenPGP compliant systems and easy availability of on-line multiplekey servers, it is possible in practice to be unable to readily find someone (or several people) to endorse a new certificate (e.g., by comparing physical identification to key owner information and then digitally signing the new certificate). Users in remote areas or undeveloped ones, for instance, may find other users scarce. And, if the other's certificate is also new (and with no or few endorsements from others), then its signature on any new certificate can offer only marginal benefit toward becoming trusted by still other parties' systems and so able to securely exchange messages with them.Key signing partiesare a relatively popular mechanism to resolve this problem of finding other users who can install one's certificate in existing webs of trust by endorsing it. Websites also exist to facilitate the location of other OpenPGP users to arrange keysignings. TheGossamer Spider Web of Trustalso makes key verification easier by linking OpenPGP users via a hierarchical style web of trust where end users can benefit by coincidental or determined trust of someone who is endorsed as an introducer, or by explicitly trusting GSWoT's top-level key minimally as a level 2 introducer (the top-level key endorses level 1 introducers).
The possibility of finding chains of certificates is often justified by the "small world phenomenon": given two individuals, it is often possible to find a short chain of people between them such that each person in the chain knows the preceding and following links. However, such a chain is not necessarily useful: the person encrypting an email or verifying a signature not only has to find a chain of signatures from their private key to their correspondent's, but also to trust each person of the chain to be honest and competent about signing keys (that is, they have to judge whether these people are likely to honestly follow the guidelines about verifying the identity of people before signing keys). This is a much stronger constraint.
Another obstacle is the requirement to physically meet with someone (for example, at akey signing party) to verify their identity and ownership of a public key and email address, which may involve travel expenses and scheduling constraints affecting both sides. A software user may need to verify hundreds of software components produced by thousands of developers located around the world. As the general population of software users cannot meet in person with all software developers to establish direct trust, they must instead rely on the comparatively slower propagation of indirect trust.[citation needed]
Obtaining the PGP/GPG key of an author (or developer, publisher, etc.) from a public key server also presents risks, since the key server is a third-partymiddle-man, itself vulnerable to abuse or attacks. To avoid this risk, an author can instead choose to publish their public key on their own key server (i.e., a web server accessible through a domain name owned by them, and securely located in their private office or home) and require the use of HKPS-encrypted connections for the transmission of their public key. For details, seeWOT Assisting Solutionsbelow.
Thestrong setrefers to the largest collection ofstrongly connectedPGPkeys.[5]This forms the basis for the global web of trust. Any two keys in the strong set have a path between them; while islands of sets of keys that only sign each other in a disconnected group can and do exist, only one member of that group needs to exchange signatures with the strong set for that group to also become a part of the strong set.[6]
Henk P. Penning charted the growth in the size of the strong set from approximately 18,000 in early 2003 to approximately 62,000 at the beginning of 2018; however, it then decreased and by May of 2019 it was at approximately 57,500.[7]In a paper published in September 2022, Gunnar Wolf and Jorge Luis Ortega-Arjona mentioned the size of the strong set as being 60,000.[8]
In statistical analysis of thePGP/GnuPG/OpenPGPWeb of trust themean shortest distance (MSD)is one measurement of how "trusted" a given PGP key is within the strongly connected set of PGP keys that make up the Web of trust.
MSD has become a common metric for analysis of sets of PGP keys. Very often you will see the MSD being calculated for a given subset of keys and compared with theglobal MSDwhich generally refers to the keys ranking within one of the larger key analyses of the global Web of trust.
Physically meeting with original developer or author, is always the best way to obtain and distribute and verify and trust PGP/GPG Keys with highest trust level, and will remain as the best level of best trustworthy way. Publishing of GPG/PGP full Key or full Key fingerprint on/with widely known (physical/paper-material based) book, by the original author/developer, is the 2nd best form of sharing trustworthy key with and for users. Before meeting a developer or author, users should research on their own on the developer or author in book library and via internet, and aware of developer's or author's photo, work, pub-key fingerprint, email-address, etc.
However, it is not practical for millions of users who want to communicate or message securely to physically meet with each recipient users, and it is also not practical for millions of software users who need to physically meet with hundreds of software developers or authors, whose software or file signingPGP/GPGpublic Key they want to verify and trust and ultimately use in their computers. Therefore, one or moretrusted third-party authority(TTPA) type of entity or group need to be available for users and be usable by users, and such entity/group need to be capable of providing trusted-verificationor trust-delegationservices for millions of users around the world, at any time.
Practically, to verify any downloaded or received content or data or email or file'sauthenticity, a user need to verify their downloaded main content or main data/email or main file's PGP/GPGsignaturecode/file (ASC, SIG). So users would need to use original developer's or original author's trustworthy and verified public-key, or users would need to use trustworthy file-signing public-key trusted-by the original owner of that public-key. And to really trust a specific PGP/GPG key, users would need to physically meet with every specific original author or developer, or users would need to physically meet with the original-releaser of file-signing pub-key, or, users would need to find another alternative trustworthy user, who is in trusted-chain of WOT (aka, another user or another developer or another author, who is trusted by that very specific original author or developer), and then physically meet with that person, to verify their real ID with his/her PGP/GPG key (and also provide your own ID and key to the other user, so that both side can sign/certify and trust each other's PGP/GPG key). Whether a software is popular or not, software users are usually located around the world in different locations. It is physically not possible for an original author or developer or file-releaser to provide public-key or trust or ID verification services to millions of users. Neither is it practical for millions of software users to physically meet with each and every software or every software-library or every piece of code's developer or author or releaser, which they will (use or) need to use in their computers. Even with multiple trusted people/person (by original-author) in trusted-chain from WOT, its still not physically or practically possible for every developer or author to meet with every other users, and it is also not possible for every users to meet with hundreds of developers whose software they will be using or working on. When this decentralized hierarchy based WoT chain model will become popular and used by most nearby users, only then physical meeting and pub-key certify and sign procedure of WoT will be easier.
A fewsolutionsare: original author/developer need to first set a trust-level to sign/certify their own file-signing key. Then updated public-keys and updated file-signing public-keys must also have to be published and distributed (or made accessible) to users, via online secure and encrypted mediums, so that any user from any location in world, can get the correct and trusted and unmodified public-key. To make sure that each users are getting the correct and trusted public-keys and signed-code/file, original dev/author or original-releaser must publish their updated public-keys on their ownkey serverand force HKPS encrypted connection usage, or publish their updated and full public-keys (and signed-code/file) on their ownHTTPSencrypted webpage, under their own web server, from their own primary domain website, (not-from any sub-domains which are located in external-servers, not-from any mirror, not-from any external/shared forum/wiki etc website servers, not-from any public or external/shared cloud or hosting service servers), and must have to be located and kept securely inside their own premises: own-home, own-home-office, or own-office. In that way, those small pieces of original keys/code, will travel intact through internet and will remain unmodified during transit (because of encrypted connection) and will reach destination without being eavesdropped or modified, into user's side, and can be treated as trustworthy public-keys because of single or multi channel TTPA based verification. When a public-key is obtained (from original developer's own web-server) via more than oneTTPA(trusted third party authority) based secured, verified and encrypted connection, then it is more trustworthy.
When original public-keys/signed-codes are shown in original dev's or author's own web server or key server, over encrypted connection or encrypted webpage, then any other files, data or content can be transferred over any type of non-encrypted connection, like: HTTP/FTP etc from any sub-domain server or from any mirror or from any shared cloud/hosting servers, because, non-encrypted connection based downloaded items/data/files can be authenticated later, by using the original public-keys/signed-codes, which were obtained from the original author's/developer's own server over secured, encrypted, and trusted (aka, verified) connection/channels.
Using encrypted connection to transfer keys or signed/signature code/files, allow software users to delegate their trust with aPKITTPA(trusted third party authority), like publicCA(Certificate Authority), to help in providing trusted connection in between the original developer/author's web server, and millions of worldwide users' computers, at any time.
When the original author/developer's domain-name and name-server is signed byDNSSEC, and when usedSSL/TLSpublic certificate is declared/shown in TLSA/DANEDNSSec DNS resource-record, (and when SSL/TLS Certs in the trust chain are pinned and used viaHPKPtechnique by web servers), then a web-server's webpage or data can also be verified via another PKITTPA: DNSSEC and DNS namespace maintainerICANN, other than a public CA. DNSSEC is another form of PGP/GPG WOT but for name-servers; it creates a trusted-chain for name-servers first (instead of people/person), and then people/person's PGP/GPG Keys and fingerprints can also be added into a server's DNSSEC DNS records. So any users who want to communicate securely (or any software users), can effectively get/receive their data/key/code/webpage etc. verified (aka, authenticated) via two (aka, dual/double) trusted PKI TTPAs/Channels at the same time: ICANN (DNSSEC) andCA(SSL/TLS Certificate). So PGP/GPG key/signed-code data (or file) can be trusted, when such solutions and techniques are used: HKPS, HKPS+DNSSEC+DANE, HTTPS, HTTPS+HPKP or HTTPS+HPKP+DNSSEC+DANE.
If a vast number of user's group create their own newDLVbased DNSSECregistry, and if users use that new DLV (along with ICANN-DNSSEC) root-key in their own local DNSSEC-based DNS Resolver/Server, and if domain-owners also use it for additional signing of their own domain-names, then there can be a new third TTPA. In such case, any PGP/GPG Key/signed-code data or a webpage or web data can be three/triple-channel verified.ISC's DLV itself can be used as a third TTPA as its still used widely and active, so availability of another new DLV will become fourth TTPA.
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https://en.wikipedia.org/wiki/Web_of_trust
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Zerocoinis aprivacy protocolproposed in 2013 byJohns Hopkins UniversityprofessorMatthew D. Greenand his graduate students, Ian Miers and Christina Garman. It was designed as an extension to theBitcoin protocolthat would improveBitcointransactions'anonymityby having coin-mixing capabilities natively built into the protocol.[citation needed]Zerocoin is not currently compatible with Bitcoin.
Due to the public nature of theblockchain, users may have theirprivacycompromised while interacting with the network. To address this problem,third-partycoin mixing servicecan be used to obscure the trail of cryptocurrency transactions. In May 2013,Matthew D. Greenand his graduate students (Ian Miers and Christina Garman) proposed the Zerocoin protocol where cryptocurrency transactions can be anonymized without going through a trusted third-party, by which a coin is destroyed then minted again to erase its history.[1]
While a coin is spent, there is no information available which reveal exactly which coin is being spent.[2]Initially, the Zerocoin protocol was planned to be integrated into theBitcoin network.[3]However, the proposal was not accepted by the Bitcoin community. Thus, the Zerocoin developers decided to launch the protocol into an independent cryptocurrency.[4]The project to create a standalone cryptocurrency implementing the Zerocoin protocol was named "Moneta".[5]In September 2016, Zcoin (XZC), the first cryptocurrency to implement the zerocoin protocol, was launched by Poramin Insom and team.[6]In January 2018, an academic paper partially funded by Zcoin was published on replacingProof-of-work systemwith memory intensiveMerkle treeproof algorithm in ensuring more equitable mining among ordinary users.[7]In April 2018, a cryptographic flaw was found in the Zerocoin protocol which allows an attacker to destroy the coins owned by honest users, create coins out of thin air, and steal users' coins.[8]The Zcoin cryptocurrency team while acknowledging the flaw, stated the high difficulty in performing such attacks and the low probability of giving economic benefit to the attacker.[9]In December 2018, Zcoin released an academic paper proposing the Lelantus protocol that removes the need for a trusted setup and hides the origin and the amount of coins in a transaction when using the Zerocoin protocol.[10][11]
Transactions which use the Zerocoin feature are drawn from anescrowpool, where each coin's transaction history is erased when it emerges.[12]Transactions are verified byzero-knowledge proofs, a mathematical way to prove a statement is true without revealing any other details about the question.[13]
On 16 November 2013, Matthew D. Green announced the Zerocash protocol, which provides additional anonymity by shielding the amount transacted.[14]Zerocash reduces transaction sizes by 98%, however was significantly more computationally expensive, taking up to 3.2 GB of memory to generate.[15][16]More recent developments into the protocol have reduced this to 40 MB.
Zerocash utilizes succinct non-interactive zero-knowledge arguments of knowledge (also known aszk-SNARKs), a special kind ofzero-knowledgemethod for proving the integrity of computations.[17]Such proofs are less than 300 bytes long and can be verified in only a few milliseconds, and contain the additional advantage of hiding the amount transacted as well. However, unlike Zerocoin, Zerocash requires an initial set up by a trusted entity.[18]
Developed byMatthew D. Green, the assistant professor behind the Zerocoin protocol,Zcashwas the first Zerocash based cryptocurrency which began development in 2013.[19]
In the late 2014, Poramin Insom, a student in Masters in Security Informatics from Johns Hopkins University wrote a paper on implementing the zerocoin protocol into a cryptocurrency with Matthew Green as faculty member.[20][21]Roger Ver[6]and Tim Lee were Zcoin's initial investors.[22]Poramin also set up an exchanged named "Satang" that can convert Thai Baht to Zcoin directly.[21]
On 20 February 2017, a malicious coding attack on Zerocoin protocol created 370,000 fake tokens which perpetrators sold for over 400 Bitcoins ($440,000). Zcoin team announced that a single-symbol error in a piece of code "allowed an attacker to create Zerocoin spend transactions without a corresponding mint".[23]UnlikeEthereumduring theDAO event, developers have opted not to destroy any coins or attempt to reverse what happened with the newly generated ones.[24]
In September 2018, Zcoin introduced the Dandelion protocol that hides the origin IP address of a sender without using aThe Onion Router(Tor) orVirtual Private Network(VPN).[25][26]In November 2018, Zcoin conducted the world's first large-scale party elections inThailand Democrat PartyusingInterPlanetary File System(IPFS).[27]In December 2018, Zcoin implementedMerkle treeproof, a mining algorithm that deters the usage ofApplication-specific integrated circuit(ASIC) in mining coins by being more memory intensive for the miners. This allows ordinary users to usecentral processing unit(CPU) andgraphics cardfor mining, so as to enableegalitarianismin coin mining.[28]On 30 July 2019, Zcoin formally departed from Zerocoin protocol by adopting a new protocol called "Sigma" that prevents counterfeit privacy coins from inflating coin supply. This is achieved by removing a feature called "trusted setup" from the Zerocoin protocol.[29]
One criticism of zerocoin is the added computation time required by the process, which would need to have been performed primarily by bitcoin miners. If the proofs were posted to the blockchain, this would also dramatically increase the size of the blockchain. Nevertheless, as stated by the original author, the proofs could be stored outside the blockchain.[30]
Since a zerocoin will have the same denomination as the bitcoin used to mint the zerocoin, anonymity would be compromised if no other zerocoins (or few zerocoins) with the same denomination are currently minted but unspent. A potential solution to this problem would be to only allow zerocoins of specific set denominations, however, this would increase the needed computation time since multiple zerocoins could be needed for one transaction.[citation needed]
Depending on the specific implementation, Zerocoin requires two very largeprime numbersto generate a parameter which cannot be easily factored. As such, these values must either be generated by trusted parties, or rely on RSA unfactorable objects to avoid the requirement of a trusted party.[1]Such a setup, however, is not possible with theZerocashprotocol.
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https://en.wikipedia.org/wiki/Zerocoin
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Ananagramis a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once.[1]For example, the wordanagramitself can be rearranged into the phrase "nag a ram"; which is anEaster eggsuggestion inGoogleafter searching for the word "anagram".[2]
The original word or phrase is known as thesubjectof the anagram. Any word or phrase that exactly reproduces the letters in another order is an anagram. Someone who creates anagrams may be called an "anagrammatist",[3]and the goal of a serious or skilled anagrammatist is to produce anagrams that reflect or comment on their subject.
Anagrams may be created as a commentary on the subject. They may be a parody, a criticism or satire. For example:
An anagram may also be a synonym of the original word or phrase. For example:
An anagram that has a meaning opposed to that of the original word or phrase is called an "antigram".[4]For example:
They can sometimes change from a proper noun or personal name into an appropriate sentence:
They can changepart of speech, such as the adjective "silent" to the verb "listen".
"Anagrams" itself can be anagrammatized as"Ars magna"(Latin, 'the great art').[5]
Anagrams can be traced back to the time of the ancient Greeks, and were used to find the hidden and mystical meaning in names.[6]They were popular throughout Europe during theMiddle Ages, for example with the poet and composerGuillaume de Machaut.[7]They are said to date back at least to the Greek poetLycophron, in the third century BCE; but this relies on an account of Lycophron given byJohn Tzetzesin the 12th century.[8]
In theTalmudicandMidrashicliterature, anagrams were used tointerprettheHebrew Bible, notably byEleazar of Modi'im. Later,Kabbaliststook this up with enthusiasm, calling anagramstemurah.[9]
Anagrams inLatinwere considered witty over many centuries.Est vir qui adest, explained below, was cited as the example inSamuel Johnson'sA Dictionary of the English Language. They became hugely popular in theearly modern period, especially in Germany.[10]
Any historical material on anagrams must always be interpreted in terms of the assumptions and spellings that were current for the language in question. In particular, spelling in English only slowly became fixed. There were attempts to regulate anagram formation, an important one in English being that ofGeorge Puttenham'sOf the Anagram or Posy TransposedinThe Art of English Poesie(1589).
As a literary game when Latin was the common property of the literate, Latin anagrams were prominent.[11]Two examples are the change ofAve Maria, gratia plena, Dominus tecum(Latin: Hail Mary, full of grace, the Lord [is] with you) intoVirgo serena, pia, munda et immaculata(Latin: Serenevirgin, pious, clean andspotless), and the anagrammatic answer toPilate's question,Quid est veritas?(Latin: What is truth?), namely,Est vir qui adest(Latin: It is the man who is here). The origins of these are not documented.
Latin continued to influence letter values (such as I = J, U = V and W = VV). There was an ongoing tradition of allowing anagrams to be "perfect" if the letters were all used once, but allowing for these interchanges. This can be seen in a popular Latin anagram against theJesuits:Societas Jesuturned intoVitiosa seces(Latin: Cut off the wicked things). Puttenham, in the time ofElizabeth I, wished to start fromElissabet Anglorum Regina(Latin: Elizabeth Queen of the English), to obtainMulta regnabis ense gloria(Latin: By thy sword shalt thou reign in great renown); he explains carefully that H is "a note ofaspirationonly and no letter", and that Z inGreekor Hebrew is a mere SS. The rules were not completely fixed in the 17th century.William Camdenin hisRemainscommented, singling out some letters—Æ, K, W, and Z—not found in the classicalRoman alphabet:[12]
The precise in this practice strictly observing all the parts of the definition, are only bold with H either in omitting or retaining it, for that it cannot challenge the right of a letter. But the Licentiats somewhat licentiously, lest they should prejudice poetical liberty, will pardon themselves for doubling or rejecting a letter, if the sence fall aptly, and "think it no injury to use E for Æ; V for W; S for Z, and C for K, and contrariwise.
When it comes to the 17th century and anagrams in English or other languages, there is a great deal of documented evidence of learned interest. The lawyerThomas Egertonwas praised through the anagramgestat honorem('he carries honor'); the physicianGeorge Enttook the anagrammatic mottogenio surget('he rises through spirit/genius'), which requires his first name asGeorgius.[13]James I'scourtiers discovered in "James Stuart" "a just master", and converted "Charles James Stuart" into "ClaimsArthur'sseat" (even at that point in time, the letters I and J were more-or-less interchangeable). Walter Quin, tutor to the future Charles I, worked hard on multilingual anagrams on the name of father James.[14]A notorious murder scandal, the Overbury case, threw up two imperfect anagrams that were aided by typically loose spelling and were recorded bySimonds D'Ewes: "Francis Howard" (forFrances Carr, Countess of Somerset, her maiden name spelled in a variant) became "Car findes a whore", with the letters E hardly counted, and the victimThomas Overbury, as "Thomas Overburie", was written as "O! O! a busie murther" (an old form of "murder"), with a V counted as U.[15][16]
William Drummond of Hawthornden, in an essayOn the Character of a Perfect Anagram, tried to lay down rules for permissible substitutions (such as S standing for Z) and letter omissions.[17]William Camden[18]provided a definition of "Anagrammatisme" as "a dissolution of a name truly written into his letters, as his elements, and a new connection of it by artificial transposition, without addition, subtraction or change of any letter, into different words, making some perfect sense appliable (i.e., applicable) to the person named."DrydeninMacFlecknoedisdainfully called the pastime the "torturing of one poor word ten thousand ways".[19]
"Eleanor Audeley", wife ofSir John Davies, is said to have been brought before theHigh Commission[clarification needed]in 1634 for extravagances, stimulated by the discovery that her name could be transposed to "Reveale, O Daniel", and to have been laughed out of court by another anagram submitted bySir John Lambe, thedean of the Arches, "Dame Eleanor Davies", "Never soe mad a ladie".[20][21]
An example from France was a flattering anagram forCardinal Richelieu, comparing him toHerculesor at least one of his hands (Hercules being a kingly symbol), whereArmand de RichelieubecameArdue main d'Hercule("difficult hand of Hercules").[22]
Examples from the 19th century are the transposition of "Horatio Nelson" intoHonor est a Nilo(Latin: Honor is from theNile); and of "Florence Nightingale" into "Flit on, cheering angel".[23]The Victorian love of anagramming as recreation is alluded to by the mathematicianAugustus De Morgan[24]using his own name as an example; "Great Gun, do us a sum!" is attributed to his sonWilliam De Morgan, but a family friendJohn Thomas Graveswas prolific, and a manuscript with over 2,800 has been preserved.[25][26][27]
With the advent ofsurrealismas a poetic movement, anagrams regained the artistic respect they had had in theBaroque period. The German poetUnica Zürn, who made extensive use of anagram techniques, came to regard obsession with anagrams as a "dangerous fever", because it created isolation of the author.[28]The surrealist leaderAndré Bretoncoined the anagramAvida DollarsforSalvador Dalí, to tarnish his reputation by the implication of commercialism.
While anagramming is certainly a recreation first, there are ways in which anagrams are put to use, and these can be more serious, or at least not quite frivolous and formless. For example, psychologists use anagram-oriented tests, often called "anagram solution tasks", to assess theimplicit memoryof young adults and adults alike.[29]
Natural philosophers (astronomers and others) of the 17th century transposed their discoveries into Latin anagrams, to establish their priority. In this way they laid claim to new discoveries before their results were ready for publication.
GalileousedsmaismrmilmepoetaleumibunenugttauirasforAltissimum planetam tergeminum observavi(Latin: I have observed the most distant planet to have a triple form) for discovering therings of Saturnin 1610.[30][31]Galileo announced his discovery thatVenushadphaseslike the Moon in the formHaec immatura a me iam frustra leguntur oy(Latin: These immature ones have already been read in vain by me -oy), that is, when rearranged,Cynthiae figuras aemulatur Mater Amorum(Latin: The Mother of Loves [= Venus] imitates the figures ofCynthia[= the moon]). In both cases,Johannes Keplerhad solved the anagrams incorrectly, assuming they were talking about theMoons of Mars(Salve, umbistineum geminatum Martia proles) and ared spot on Jupiter(Macula rufa in Jove est gyratur mathem), respectively.[32]By coincidence, he turned out to be right about the actual objects existing.
In 1656,Christiaan Huygens, using a better telescope than those available to Galileo, figured that Galileo's earlier observations of Saturn actually meant it had a ring (Galileo's tools were only sufficient to see it as bumps) and, like Galileo, had published an anagram,aaaaaaacccccdeeeeeghiiiiiiillllmmnnnnnnnnnooooppqrrstttttuuuuu. Upon confirming his observations, three years later he revealed it to meanAnnulo cingitur, tenui, plano, nusquam coherente, ad eclipticam inclinato(Latin: It [Saturn] is surrounded by a thin, flat, ring, nowhere touching, inclined to the ecliptic).[33]
WhenRobert HookediscoveredHooke's lawin 1660, he first published it in anagram form,ceiiinosssttuv, forut tensio, sic vis(Latin: as the extension, so the force).[34]
Anagrams are connected to pseudonyms, by the fact that they may conceal or reveal, or operate somewhere in between like a mask that can establish identity. For example,Jim Morrisonused an anagram of his name inthe Doorssong "L.A. Woman", calling himself "Mr. Mojo Risin'".[35]The use of anagrams and fabricated personal names may be to circumvent restrictions on the use of real names, as happened in the 18th century whenEdward Cavewanted to get around restrictions imposed on the reporting of theHouse of Commons.[36]In a genre such asfarceorparody, anagrams as names may be used for pointed and satiric effect.
Pseudonyms adopted by authors are sometimes transposed forms of their names; thus "Calvinus" becomes "Alcuinus" (here V = U) or "François Rabelais" = "Alcofribas Nasier". The name "Voltaire" of François Marie Arouet fits this pattern, and is allowed to be an anagram of "Arouet, l[e] j[eune]" (U = V, J = I) that is, "Arouet the younger". Other examples include:
Several of these are "imperfect anagrams", letters having been left out in some cases for the sake of easy pronunciation.
Anagrams used for titles afford scope for some types of wit. Examples:
In Hebrew, the name "Gernot Zippe" (גרנוט ציפה), the inventor of theZippe-type centrifuge, is an anagram of the word "centrifuge" (צנטריפוגה).
The sentence "Name is Anu Garg", referring to anagrammer and founder of wordsmith.orgAnu Garg, can be rearranged to spell "Anagram genius".[39]
Anagrams are in themselves a recreational activity, but they also make up part of many other games, puzzles and game shows. TheJumbleis a puzzle found in many newspapers in the United States requiring the unscrambling of letters to find the solution.Cryptic crosswordpuzzles frequently use anagrammatic clues, usually indicating that they are anagrams by the inclusion of a descriptive term like "confused" or "in disarray". An example would beBusinessman burst into tears (9 letters). The solution,stationer, is an anagram ofinto tears, the letters of which haveburstout of their original arrangement to form the name of a type ofbusinessman.
Numerous other games and contests involve some element of anagram formation as a basic skill. Some examples:
Multiple anagramming is a technique used to solve some kinds of cryptograms, such as apermutation cipher, atransposition cipher, and theJefferson disk.[40]Solutions may be computationally found using aJumble algorithm.
Sometimes, it is possible to "see" anagrams in words, unaided by tools, though the more letters involved the more difficult this becomes. The difficulty is that for a word ofndifferent letters, there aren!(factorialofn) differentpermutationsand son! − 1different anagrams of the word.Anagram dictionariescan also be used. Computer programs, known as "anagram search", "anagram servers", and "anagram solvers", among other names, offer a much faster route to creating anagrams, and a large number of these programs are available on the Internet.[41][42]Some programs use theAnatreealgorithm to compute anagrams efficiently.
Theprogramorservercarries out an exhaustive search of a database of words, to produce a list containing every possible combination of words or phrases from the input word or phrase using ajumble algorithm. Some programs (such asLexpert) restrict to one-word answers. Many anagram servers (for example,The Words Oracle) can control the search results, by excluding or including certain words, limiting the number or length of words in each anagram, or limiting the number of results. Anagram solvers are often banned from online anagram games. The disadvantage of computer anagram solvers, especially when applied to multi-word anagrams, is their poor understanding of the meaning of the words they are manipulating. They usually cannot filter out meaningful or appropriate anagrams from large numbers of nonsensical word combinations. Some servers attempt to improve on this using statistical techniques that try to combine only words that appear together often. This approach provides only limited success since it fails to recognize ironic and humorous combinations.
Some anagrammatists indicate the method they used. Anagrams constructed without the aid of a computer are noted as having been done "manually" or "by hand"; those made by utilizing a computer may be noted "by machine" or "by computer", or may indicate the name of the computer program (usingAnagram Genius).
There are also a few "natural" instances: English words unconsciously created by switching letters around. The Frenchchaise longue("long chair") became the American "chaise lounge" bymetathesis(transposition of letters and/or sounds). It has also been speculated that the English "curd" comes from the Latincrudus("raw"). Similarly, the ancient English word for bird was "brid".
The French kingLouis XIIIhad a man namedThomas Billonappointed as his Royal Anagrammatist with an annual salary of 1,200livres.[43]Among contemporary anagrammers,Anu Garg, created an Internet Anagram Server in 1994 together with the satirical anagram-based newspaperThe Anagram Times. Mike Keith has anagrammed the complete text ofMoby Dick.[44]He, along with Richard Brodie, has publishedThe Anagrammed Biblethat includes anagrammed version of many books of the Bible.[45]Popular television personalityDick Cavettis known for his anagrams of famous celebrities such as Alec Guinness and Spiro Agnew.[46]
Thy genius calls thee not to purchase fameIn keen iambics, but mild anagram:Leave writing plays, and choose for thy commandSome peaceful province in acrostic land.There thou may'st wings display and altars raise,And torture one poor word ten thousand ways.
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https://en.wikipedia.org/wiki/Anagram#Establishment_of_priority
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Arithmetic dynamics[1]is a field that amalgamates two areas of mathematics,dynamical systemsandnumber theory. Part of the inspiration comes fromcomplex dynamics, the study of theiterationof self-maps of thecomplex planeor other complexalgebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties ofinteger,rational,p-adic, or algebraic points under repeated application of apolynomialorrational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.
Global arithmetic dynamicsis the study of analogues of classicaldiophantine geometryin the setting of discrete dynamical systems, whilelocal arithmetic dynamics, also calledp-adic or nonarchimedean dynamics, is an analogue of complex dynamics in which one replaces the complex numbersCby ap-adic field such asQporCpand studies chaotic behavior and theFatouandJulia sets.
The following table describes a rough correspondence between Diophantine equations, especiallyabelian varieties, and dynamical systems:
LetSbe a set and letF:S→Sbe a map fromSto itself. The iterate ofFwith itselfntimes is denoted
A pointP∈SisperiodicifF(n)(P) =Pfor somen≥ 1.
The point ispreperiodicifF(k)(P)is periodic for somek≥ 1.
The (forward)orbit ofPis the set
ThusPis preperiodic if and only if its orbitOF(P)is finite.
LetF(x)be a rational function of degree at least two with coefficients inQ. A theorem ofDouglas Northcott[2]says thatFhas only finitely manyQ-rational preperiodic points, i.e.,Fhas only finitely many preperiodic points inP1(Q). Theuniform boundedness conjecture for preperiodic points[3]of Patrick Morton andJoseph Silvermansays that the number of preperiodic points ofFinP1(Q)is bounded by a constant that depends only on the degree ofF.
More generally, letF:PN→PNbe a morphism of degree at least two defined over a number fieldK. Northcott's theorem says thatFhas only finitely many preperiodic points inPN(K), and the general Uniform Boundedness Conjecture says that the number of preperiodic points inPN(K)may be bounded solely in terms ofN, the degree ofF, and the degree ofKoverQ.
The Uniform Boundedness Conjecture is not known even for quadratic polynomialsFc(x) =x2+cover the rational numbersQ. It is known in this case thatFc(x)cannot have periodic points of period four,[4]five,[5]or six,[6]although the result for period six is contingent on the validity of theconjecture of Birch and Swinnerton-Dyer.Bjorn Poonenhas conjectured thatFc(x)cannot have rational periodic points of any period strictly larger than three.[7]
The orbit of a rational map may contain infinitely many integers. For example, ifF(x)is a polynomial with integer coefficients and ifais an integer, then it is clear that the entire orbitOF(a)consists of integers. Similarly, ifF(x)is a rational map and some iterateF(n)(x)is a polynomial with integer coefficients, then everyn-th entry in the orbit is an integer. An example of this phenomenon is the mapF(x) =x−d, whose second iterate is a polynomial. It turns out that this is the only way that an orbit can contain infinitely many integers.
There are general conjectures due toShouwu Zhang[10]and others concerning subvarieties that contain infinitely many periodic points or that intersect an orbit in infinitely many points. These are dynamical analogues of, respectively, theManin–Mumford conjecture, proven byMichel Raynaud, and theMordell–Lang conjecture, proven byGerd Faltings. The following conjectures illustrate the general theory in the case that the subvariety is a curve.
The field ofp-adic (or nonarchimedean) dynamicsis the study of classical dynamical questions over a fieldKthat is complete with respect to a nonarchimedean absolute value. Examples of such fields are the field ofp-adic rationalsQpand the completion of its algebraic closureCp. The metric onKand the standard definition of equicontinuity leads to the usual definition of theFatouandJulia setsof a rational mapF(x) ∈K(x). There are many similarities between the complex and the nonarchimedean theories, but also many differences. A striking difference is that in the nonarchimedean setting, the Fatou set is always nonempty, but the Julia set may be empty. This is the reverse of what is true over the complex numbers. Nonarchimedean dynamics has been extended toBerkovich space,[11]which is a compact connected space that contains the totally disconnected non-locally compact fieldCp.
There are natural generalizations of arithmetic dynamics in whichQandQpare replaced by number fields and theirp-adic completions. Another natural generalization is to replace self-maps ofP1orPNwith self-maps (morphisms)V→Vof other affine orprojective varieties.
There are many other problems of a number theoretic nature that appear in the setting of dynamical systems, including:
TheArithmetic Dynamics Reference Listgives an extensive list of articles and books covering a wide range of arithmetical dynamical topics.
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In algebra, anelliptic algebrais a certainregular algebraof aGelfand–Kirillov dimensionthree (quantum polynomial ringin three variables) that corresponds to a cubic divisor in the projective spaceP2. If the cubic divisor happens to be anelliptic curve, then the algebra is called aSklyanin algebra. The notion is studied in the context ofnoncommutative projective geometry.
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Inmathematics, anelliptic surfaceis a surface that has an ellipticfibration, in other words aproper morphismwith connectedfibersto analgebraic curvesuch that almost all fibers aresmoothcurves ofgenus1. (Over an algebraically closed field such as thecomplex numbers, these fibers areelliptic curves, perhaps without a chosen origin.) This is equivalent to thegeneric fiberbeing a smooth curve of genus one. This follows fromproper base change.
The surface and the base curve are assumed to be non-singular (complex manifoldsorregular schemes, depending on the context). The fibers that are not elliptic curves are called thesingular fibersand were classified byKunihiko Kodaira. Both elliptic and singular fibers are important instring theory, especially inF-theory.
Elliptic surfaces form a large class of surfaces that contains many of the interesting examples of surfaces, and are relatively well understood in the theories of complex manifolds andsmooth4-manifolds. They are similar to (have analogies with, that is), elliptic curves overnumber fields.
Most of the fibers of an elliptic fibration are (non-singular) elliptic curves. The remaining fibers are called singular fibers: there are a finite number of them, and each one consists of a union of rational curves, possibly with singularities or non-zero multiplicities (so the fibers may be non-reduced schemes). Kodaira and Néron independently classified the possible fibers, andTate's algorithmcan be used to find the type of the fibers of an elliptic curve over a number field.
The following table lists the possible fibers of aminimalelliptic fibration. ("Minimal" means roughly one that cannot be factored through a "smaller" one; precisely, the singular fibers should contain no smooth rational curves with self-intersection number −1.) It gives:
This table can be found as follows. Geometric arguments show that the intersection matrix of the components of the fiber must be negative semidefinite, connected, symmetric, and have no diagonal entries equal to −1 (by minimality). Such a matrix must be 0 or a multiple of the Cartan matrix of an affine Dynkin diagram of typeADE.
The intersection matrix determines the fiber type with three exceptions:
Themonodromyaround each singular fiber is a well-definedconjugacy classin the group SL(2,Z) of 2 × 2 integer matrices withdeterminant1. The monodromy describes the way the firsthomologygroup of a smooth fiber (which is isomorphic toZ2) changes as we go around a singular fiber. Representatives for these conjugacy classes associated to singular fibers are given by:[1]
For singular fibers of type II, III, IV, I0*, IV*, III*, or II*, the monodromy has finite order in SL(2,Z). This reflects the fact that an elliptic fibration haspotential good reductionat such a fiber. That is, after a ramified finite covering of the base curve, the singular fiber can be replaced by a smooth elliptic curve. Which smooth curve appears is described by thej-invariantin the table. Over the complex numbers, the curve withj-invariant 0 is the unique elliptic curve with automorphism group of order 6, and the curve withj-invariant 1728 is the unique elliptic curve with automorphism group of order 4. (All other elliptic curves have automorphism group of order 2.)
For an elliptic fibration with asection, called aJacobian elliptic fibration, the smooth locus of each fiber has a group structure. For singular fibers, this group structure on the smooth locus is described in the table, assuming for convenience that the base field is the complex numbers. (For a singular fiber with intersection matrix given by an affine Dynkin diagramΓ~{\displaystyle {\tilde {\Gamma }}}, the group of components of the smooth locus is isomorphic to the center of the simply connected simple Lie group with Dynkin diagramΓ{\displaystyle \Gamma }, as listedhere.) Knowing the group structure of the singular fibers is useful for computing theMordell-Weil groupof an elliptic fibration (the group of sections), in particular its torsion subgroup.
To understand how elliptic surfaces fit into theclassification of surfaces, it is important to compute thecanonical bundleof a minimal elliptic surfacef:X→S. Over the complex numbers, Kodaira proved the followingcanonical bundle formula:[2]
Here the multiple fibers off(if any) are written asf∗(pi)=miDi{\displaystyle f^{*}(p_{i})=m_{i}D_{i}}, for an integermiat least 2 and a divisorDiwhose coefficients have greatest common divisor equal to 1, andLis some line bundle on the smooth curveS. IfSis projective (or equivalently, compact), then thedegreeofLis determined by theholomorphic Euler characteristicsofXandS: deg(L) = χ(X,OX) − 2χ(S,OS). The canonical bundle formula implies thatKXisQ-linearly equivalent to the pullback of someQ-divisor onS; it is essential here that the elliptic surfaceX→Sis minimal.
Building on work ofKenji Ueno, Takao Fujita (1986) gave a useful variant of the canonical bundle formula, showing howKXdepends on the variation of the smooth fibers.[3]Namely, there is aQ-linear equivalence
where thediscriminant divisorBSis an explicit effectiveQ-divisor onSassociated to the singular fibers off, and themoduli divisorMSis(1/12)j∗O(1){\displaystyle (1/12)j^{*}O(1)}, wherej:S→P1is the function giving thej-invariantof the smooth fibers. (ThusMSis aQ-linear equivalence class ofQ-divisors, using the identification between thedivisor class groupCl(S) and thePicard groupPic(S).) In particular, forSprojective, the moduli divisorMShas nonnegative degree, and it has degree zero if and only if the elliptic surface is isotrivial, meaning that all the smooth fibers are isomorphic.
The discriminant divisor in Fujita's formula is defined by
wherec(p) is thelog canonical thresholdlct(X,f∗(p)){\displaystyle {\text{lct}}(X,f^{*}(p))}. This is an explicit rational number between 0 and 1, depending on the type of singular fiber. Explicitly, the lct is 1 for a smooth fiber or typeIν{\displaystyle I_{\nu }}, and it is 1/mfor a multiple fibermIν{\displaystyle {}_{m}I_{\nu }}, 1/2 forIν∗{\displaystyle I_{\nu }^{*}}, 5/6 for II, 3/4 for III, 2/3 for IV, 1/3 for IV*, 1/4 for III*, and 1/6 for II*.
The canonical bundle formula (in Fujita's form) has been generalized byYujiro Kawamataand others to families ofCalabi–Yau varietiesof any dimension.[4]
Alogarithmic transformation(of ordermwith centerp) of an elliptic surface or fibration turns a fiber of multiplicity 1 over a pointpof the base space into a fiber of multiplicitym. It can be reversed, so fibers of high multiplicity can all be turned into fibers of multiplicity 1, and this can be used to eliminate all multiple fibers.
Logarithmic transformations can be quite violent: they can change the Kodaira dimension, and can turn algebraic surfaces into non-algebraic surfaces.
Example:LetLbe the latticeZ+iZofC, and letEbe the elliptic curveC/L. Then the projection map fromE×CtoCis an elliptic fibration. We will show how to replace the fiber over 0 with a fiber of multiplicity 2.
There is an automorphism ofE×Cof order 2 that maps (c,s) to (c+1/2,−s). We letXbe the quotient ofE×Cby this group action. We makeXinto a fiber space overCby mapping (c,s) tos2. We construct an isomorphism fromXminus the fiber over 0 toE×Cminus the fiber over 0 by mapping (c,s) to (c-log(s)/2πi,s2). (The two fibers over 0 are non-isomorphic elliptic curves, so the fibrationXis certainly not isomorphic to the fibrationE×Cover all ofC.)
Then the fibrationXhas a fiber of multiplicity 2 over 0, and otherwise looks likeE×C. We say thatXis obtained by applying a logarithmic transformation of order 2 toE×Cwith center 0.
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The following tables provide acomparison ofcomputer algebra systems(CAS).[1][2][3]A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.[4][5]A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorithms, efficient data structures and a fast kernel.[6]
These computer algebra systems are sometimes combined with "front end" programs that provide a better user interface, such as the general-purposeGNU TeXmacs.
Below is a summary of significantly developedsymbolicfunctionality in each of the systems.
Those which do not "edit equations" may have aGUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people who do not have a computer algebra system installed.
The software can run under their respectiveoperating systemsnatively withoutemulation. Some systems must be compiled first using an appropriate compiler for the source language and target platform. For some platforms, only older releases of the software may be available.
Somegraphing calculatorshave CAS features.
2.01.7000 (ClassPad II, fx-CG500)
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In mathematics, particularly inalgebraic geometry, anisogenyis amorphismofalgebraic groups(also known as group varieties) that issurjectiveand has a finitekernel.
If thegroupsareabelian varieties, then any morphismf:A→Bof the underlying algebraic varieties which is surjective with finitefibresis automatically an isogeny, provided thatf(1A) = 1B. Such an isogenyfthen provides agroup homomorphismbetween the groups ofk-valued points ofAandB, for anyfieldkover whichfis defined.
The terms "isogeny" and "isogenous" come from the Greek word ισογενη-ς, meaning "equal in kind or nature". The term "isogeny" was introduced byWeil; before this, the term "isomorphism" was somewhat confusingly used for what is now called an isogeny.
Letf:A→Bbe isogeny between two algebraic groups.
This mapping induces a pullback mappingf*:K(B)→K(A)between theirrational function fields. Since the mapping is nontrivial, it is a field embedding andimf∗{\displaystyle \operatorname {im} f^{*}}is a subfield ofK(A). Thedegreeof the extensionK(A)/imf∗{\displaystyle K(A)/\operatorname {im} f^{*}}is called degree of isogeny:
Properties of degree:
Forabelian varieties, such aselliptic curves, this notion can also be formulated as follows:
LetE1andE2be abelian varieties of the same dimension over a fieldk. AnisogenybetweenE1andE2is a dense morphismf:E1→E2of varieties that preserves basepoints (i.e.fmaps the identity point onE1to that onE2).
This is equivalent to the above notion, as every dense morphism between two abelian varieties of the same dimension is automatically surjective with finite fibres, and if it preserves identities then it is a homomorphism of groups.
Two abelian varietiesE1andE2are calledisogenousif there is an isogenyE1→E2. This can be shown to be an equivalence relation; in the case of elliptic curves, symmetry is due to the existence of thedual isogeny. As above, every isogeny induces homomorphisms of the groups of the k-valued points of the abelian varieties.
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In the study of the arithmetic ofelliptic curves, thej-lineover aringRis the coarsemoduli schemeattached to the moduli problem sending a ringR{\displaystyle R}to the set of isomorphism classes of elliptic curves overR{\displaystyle R}. Since elliptic curves over the complex numbers are isomorphic (over an algebraic closure) if and only if theirj{\displaystyle j}-invariants agree, the affine spaceAj1{\displaystyle \mathbb {A} _{j}^{1}}parameterizingj-invariantsof elliptic curves yields acoarse moduli space. However, this fails to be afine moduli spacedue to the presence of elliptic curves with automorphisms, necessitating the construction of theModuli stack of elliptic curves.
This is related to thecongruence subgroupΓ(1){\displaystyle \Gamma (1)}in the following way:[1]
Here thej-invariant is normalized such thatj=0{\displaystyle j=0}hascomplex multiplicationbyZ[ζ3]{\displaystyle \mathbb {Z} [\zeta _{3}]}, andj=1728{\displaystyle j=1728}has complex multiplication byZ[i]{\displaystyle \mathbb {Z} [i]}.
Thej-line can be seen as giving a coordinatization of theclassical modular curveof level 1,X0(1){\displaystyle X_{0}(1)}, which is isomorphic to thecomplexprojective lineP/C1{\displaystyle \mathbb {P} _{/\mathbb {C} }^{1}}.[2]
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Inalgebraic geometry, alevel structureon aspaceXis an extra structure attached toXthat shrinks or eliminates theautomorphism groupofX, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased asrigidifyingthe geometry ofX.[1][2]
In applications, a level structure is used in the construction ofmoduli spaces; a moduli space is often constructed as a quotient. The presence of automorphisms poses a difficulty to forming aquotient; thus introducing level structures helps overcome this difficulty.
There is no single definition of a level structure; rather, depending on the spaceX, one introduces the notion of a level structure. The classic one is that on anelliptic curve(see#Example: an abelian scheme). There is a level structure attached to aformal groupcalled aDrinfeld level structure, introduced in (Drinfeld 1974).[3]
Classically, level structures on elliptic curvesE=C/Λ{\displaystyle E=\mathbb {C} /\Lambda }are given by a lattice containing the defining lattice of the variety. From the moduli theory of elliptic curves, all such lattices can be described as the latticeZ⊕Z⋅τ{\displaystyle \mathbb {Z} \oplus \mathbb {Z} \cdot \tau }forτ∈h{\displaystyle \tau \in {\mathfrak {h}}}in the upper-half plane. Then, the lattice generated by1/n,τ/n{\displaystyle 1/n,\tau /n}gives a lattice which contains alln{\displaystyle n}-torsion points on the elliptic curve denotedE[n]{\displaystyle E[n]}. In fact, given such a lattice is invariant under theΓ(n)⊂SL2(Z){\displaystyle \Gamma (n)\subset {\text{SL}}_{2}(\mathbb {Z} )}action onh{\displaystyle {\mathfrak {h}}}, where
Γ(n)=ker(SL2(Z)→SL2(Z/n))={M∈SL2(Z):M≡(1001)(mod n)}{\displaystyle {\begin{aligned}\Gamma (n)&={\text{ker}}({\text{SL}}_{2}(\mathbb {Z} )\to {\text{SL}}_{2}(\mathbb {Z} /n))\\&=\left\{M\in {\text{SL}}_{2}(\mathbb {Z} ):M\equiv {\begin{pmatrix}1&0\\0&1\end{pmatrix}}{\text{ (mod n)}}\right\}\end{aligned}}}
hence it gives a point inΓ(n)∖h{\displaystyle \Gamma (n)\backslash {\mathfrak {h}}}[4]called the moduli space of level N structures of elliptic curvesY(n){\displaystyle Y(n)}, which is amodular curve. In fact, this moduli space contains slightly more information: theWeil pairing
en(1n,τn)=e2πi/n{\displaystyle e_{n}\left({\frac {1}{n}},{\frac {\tau }{n}}\right)=e^{2\pi i/n}}
gives a point in then{\displaystyle n}-th roots of unity, hence inZ/n{\displaystyle \mathbb {Z} /n}.
LetX→S{\displaystyle X\to S}be anabelian schemewhose geometric fibers have dimensiong.
Letnbe a positive integer that is prime to the residue field of eachsinS. Forn≥ 2, aleveln-structureis a set of sectionsσ1,…,σ2g{\displaystyle \sigma _{1},\dots ,\sigma _{2g}}such that[5]
See also:modular curve#Examples,moduli stack of elliptic curves.
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Innumber theory, themodularity theoremstates thatelliptic curvesover the field ofrational numbersare related tomodular formsin a particular way.Andrew WilesandRichard Taylorproved the modularity theorem forsemistable elliptic curves, which was enough to implyFermat's Last Theorem. Later, a series of papers by Wiles's former studentsBrian Conrad,Fred Diamondand Richard Taylor, culminating in a joint paper withChristophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001. Before that, the statement was known as theTaniyama–Shimura conjecture,Taniyama–Shimura–Weil conjecture, or themodularity conjecture for elliptic curves.
Thetheoremstates that anyelliptic curveoverQ{\displaystyle \mathbb {Q} }can be obtained via arational mapwithintegercoefficientsfrom theclassical modular curveX0(N)for some integerN; this is a curve with integer coefficients with an explicit definition. This mapping is called a modular parametrization of levelN. IfNis the smallest integer for which such a parametrization can be found (which by the modularity theorem itself is now known to be a number called theconductor), then the parametrization may be defined in terms of a mapping generated by a particular kind of modular form of weight two and levelN, a normalizednewformwith integerq-expansion, followed if need be by anisogeny.
The modularity theorem implies a closely related analytic statement:
To each elliptic curveEoverQ{\displaystyle \mathbb {Q} }we may attach a correspondingL-series. TheL-series is aDirichlet series, commonly written
Thegenerating functionof the coefficientsanis then
If we make the substitution
we see that we have written theFourier expansionof a functionf(E,τ)of the complex variableτ, so the coefficients of theq-series are also thought of as the Fourier coefficients off. The function obtained in this way is, remarkably, acusp formof weight two and levelNand is also an eigenform (an eigenvector of allHecke operators); this is theHasse–Weil conjecture, which follows from the modularity theorem.
Some modular forms of weight two, in turn, correspond toholomorphic differentialsfor an elliptic curve. The Jacobian of the modular curve can (up to isogeny) be written as a product of irreducibleAbelian varieties, corresponding to Hecke eigenforms of weight 2. The 1-dimensional factors are elliptic curves (there can also be higher-dimensional factors, so not all Hecke eigenforms correspond to rational elliptic curves). The curve obtained by finding the corresponding cusp form, and then constructing a curve from it, isisogenousto the original curve (but not, in general, isomorphic to it).
Yutaka Taniyama[1]stated a preliminary (slightly incorrect) version of the conjecture at the 1955 international symposium onalgebraic number theoryinTokyoandNikkōas the twelfth of hisset of 36 unsolved problems.Goro Shimuraand Taniyama worked on improving its rigor until 1957.André Weil[2]rediscovered the conjecture, and showed in 1967 that it would follow from the (conjectured) functional equations for some twistedL-series of the elliptic curve; this was the first serious evidence that the conjecture might be true. Weil also showed that the conductor of the elliptic curve should be the level of the corresponding modular form. The Taniyama–Shimura–Weil conjecture became a part of theLanglands program.[3][4]
The conjecture attracted considerable interest whenGerhard Frey[5]suggested in 1986 that it impliesFermat's Last Theorem. He did this by attempting to show that any counterexample to Fermat's Last Theorem would imply the existence of at least one non-modular elliptic curve. This argument was completed in 1987 when Jean-Pierre Serre[6]identified a missing link (now known as theepsilon conjectureor Ribet's theorem) in Frey's original work, followed two years later by Ken Ribet's completion of a proof of the epsilon conjecture.[7]
Even after gaining serious attention, the Taniyama–Shimura–Weil conjecture was seen by contemporary mathematicians as extraordinarily difficult to prove or perhaps even inaccessible to prove.[8]For example, Wiles's Ph.D. supervisorJohn Coatesstates that it seemed "impossible to actually prove", and Ken Ribet considered himself "one of the vast majority of people who believed [it] was completely inaccessible".
In 1995, Andrew Wiles, with some help fromRichard Taylor, proved the Taniyama–Shimura–Weil conjecture for allsemistable elliptic curves. Wiles used this to prove Fermat's Last Theorem,[9]and the full Taniyama–Shimura–Weil conjecture was finally proved by Diamond,[10]Conrad, Diamond & Taylor; and Breuil, Conrad, Diamond & Taylor; building on Wiles's work, they incrementally chipped away at the remaining cases until the full result was proved in 1999.[11][12]Once fully proven, the conjecture became known as the modularity theorem.
Several theorems in number theory similar to Fermat's Last Theorem follow from the modularity theorem. For example: no cube can be written as a sum of twocoprimenth powers,n≥ 3.[a]
The modularity theorem is a special case of more general conjectures due toRobert Langlands. TheLanglands programseeks to attach anautomorphic formorautomorphic representation(a suitable generalization of a modular form) to more general objects ofarithmetic algebraic geometry, such as to every elliptic curve over anumber field. Most cases of these extended conjectures have not yet been proved.
In 2013, Freitas, Le Hung, and Siksek proved that elliptic curves defined over realquadratic fieldsare modular.[13]
For example,[14][15][16]the elliptic curvey2−y=x3−x, with discriminant (and conductor) 37, is associated to the form
For prime numberslnot equal to 37, one can verify the property about the coefficients. Thus, forl= 3, there are 6 solutions of the equation modulo 3:(0, 0),(0, 1),(1, 0),(1, 1),(2, 0),(2, 1); thusa(3) = 3 − 6 = −3.
The conjecture, going back to the 1950s, was completely proven by 1999 using the ideas ofAndrew Wiles, who proved it in 1994 for a large family of elliptic curves.[17]
There are several formulations of the conjecture. Showing that they are equivalent was a main challenge of number theory in the second half of the 20th century. The modularity of an elliptic curveEof conductorNcan be expressed also by saying that there is a non-constantrational mapdefined overℚ, from the modular curveX0(N)toE. In particular, the points ofEcan be parametrized bymodular functions.
For example, a modular parametrization of the curvey2−y=x3−xis given by[18]
where, as above,q=e2πiz. The functionsx(z)andy(z)are modular of weight 0 and level 37; in other words they aremeromorphic, defined on theupper half-planeIm(z) > 0and satisfy
and likewise fory(z), for all integersa,b,c,dwithad−bc= 1and37 |c.
Another formulation depends on the comparison ofGalois representationsattached on the one hand to elliptic curves, and on the other hand to modular forms. The latter formulation has been used in the proof of the conjecture. Dealing with the level of the forms (and the connection to the conductor of the curve) is particularly delicate.
The most spectacular application of the conjecture is the proof ofFermat's Last Theorem(FLT). Suppose that for a primep≥ 5, the Fermat equation
has a solution with non-zero integers, hence a counter-example to FLT. Then asYves Hellegouarch[fr]was the first to notice,[19]the elliptic curve
of discriminant
cannot be modular.[7]Thus, the proof of the Taniyama–Shimura–Weil conjecture for this family of elliptic curves (called Hellegouarch–Frey curves) implies FLT. The proof of the link between these two statements, based on an idea ofGerhard Frey(1985), is difficult and technical. It was established byKenneth Ribetin 1987.[20]
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Inmathematics, themoduli stack of elliptic curves, denoted asM1,1{\displaystyle {\mathcal {M}}_{1,1}}orMell{\displaystyle {\mathcal {M}}_{\mathrm {ell} }}, is analgebraic stackoverSpec(Z){\displaystyle {\text{Spec}}(\mathbb {Z} )}classifyingelliptic curves. Note that it is a special case of themoduli stack of algebraic curvesMg,n{\displaystyle {\mathcal {M}}_{g,n}}. In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a schemeS{\displaystyle S}to it correspond to elliptic curves overS{\displaystyle S}. The construction of this space spans over a century because of the various generalizations of elliptic curves as the field has developed. All of these generalizations are contained inM1,1{\displaystyle {\mathcal {M}}_{1,1}}.
The moduli stack of elliptic curves is a smooth separatedDeligne–Mumford stackof finite type overSpec(Z){\displaystyle {\text{Spec}}(\mathbb {Z} )}, but is not a scheme as elliptic curves have non-trivial automorphisms.
There is a proper morphism ofM1,1{\displaystyle {\mathcal {M}}_{1,1}}to the affine line, the coarse moduli space of elliptic curves, given by thej-invariantof an elliptic curve.
It is a classical observation that every elliptic curve overC{\displaystyle \mathbb {C} }is classified by itsperiods. Given a basis for its integral homologyα,β∈H1(E,Z){\displaystyle \alpha ,\beta \in H_{1}(E,\mathbb {Z} )}and a global holomorphic differential formω∈Γ(E,ΩE1){\displaystyle \omega \in \Gamma (E,\Omega _{E}^{1})}(which exists since it is smooth and the dimension of the space of such differentials is equal to thegenus, 1), the integrals[∫αω∫βω]=[ω1ω2]{\displaystyle {\begin{bmatrix}\int _{\alpha }\omega &\int _{\beta }\omega \end{bmatrix}}={\begin{bmatrix}\omega _{1}&\omega _{2}\end{bmatrix}}}give the generators for aZ{\displaystyle \mathbb {Z} }-lattice of rank 2 inside ofC{\displaystyle \mathbb {C} }[1]pg 158. Conversely, given an integral latticeΛ{\displaystyle \Lambda }of rank2{\displaystyle 2}inside ofC{\displaystyle \mathbb {C} }, there is an embedding of the complex torusEΛ=C/Λ{\displaystyle E_{\Lambda }=\mathbb {C} /\Lambda }intoP2{\displaystyle \mathbb {P} ^{2}}from theWeierstrass P function[1]pg 165. This isomorphic correspondenceϕ:C/Λ→E(C){\displaystyle \phi :\mathbb {C} /\Lambda \to E(\mathbb {C} )}is given byz↦[℘(z,Λ),℘′(z,Λ),1]∈P2(C){\displaystyle z\mapsto [\wp (z,\Lambda ),\wp '(z,\Lambda ),1]\in \mathbb {P} ^{2}(\mathbb {C} )}and holds up tohomothetyof the latticeΛ{\displaystyle \Lambda }, which is the equivalence relationzΛ∼Λforz∈C∖{0}{\displaystyle z\Lambda \sim \Lambda ~{\text{for}}~z\in \mathbb {C} \setminus \{0\}}It is standard to then write the lattice in the formZ⊕Z⋅τ{\displaystyle \mathbb {Z} \oplus \mathbb {Z} \cdot \tau }forτ∈h{\displaystyle \tau \in {\mathfrak {h}}}, an element of theupper half-plane, since the latticeΛ{\displaystyle \Lambda }could be multiplied byω1−1{\displaystyle \omega _{1}^{-1}}, andτ,−τ{\displaystyle \tau ,-\tau }both generate the same sublattice. Then, the upper half-plane gives a parameter space of all elliptic curves overC{\displaystyle \mathbb {C} }. There is an additional equivalence of curves given by the action of theSL2(Z)={(abcd)∈Mat2,2(Z):ad−bc=1}{\displaystyle {\text{SL}}_{2}(\mathbb {Z} )=\left\{{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in {\text{Mat}}_{2,2}(\mathbb {Z} ):ad-bc=1\right\}}where an elliptic curve defined by the latticeZ⊕Z⋅τ{\displaystyle \mathbb {Z} \oplus \mathbb {Z} \cdot \tau }is isomorphic to curves defined by the latticeZ⊕Z⋅τ′{\displaystyle \mathbb {Z} \oplus \mathbb {Z} \cdot \tau '}given by themodular action(abcd)⋅τ=aτ+bcτ+d=τ′{\displaystyle {\begin{aligned}{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\cdot \tau &={\frac {a\tau +b}{c\tau +d}}\\&=\tau '\end{aligned}}}Then, the moduli stack of elliptic curves overC{\displaystyle \mathbb {C} }is given by the stack quotientM1,1≅[SL2(Z)∖h]{\displaystyle {\mathcal {M}}_{1,1}\cong [{\text{SL}}_{2}(\mathbb {Z} )\backslash {\mathfrak {h}}]}Note some authors construct this moduli space by instead using the action of theModular groupPSL2(Z)=SL2(Z)/{±I}{\displaystyle {\text{PSL}}_{2}(\mathbb {Z} )={\text{SL}}_{2}(\mathbb {Z} )/\{\pm I\}}. In this case, the points inM1,1{\displaystyle {\mathcal {M}}_{1,1}}having only trivial stabilizers are dense.
{\displaystyle \qquad }
Generically, the points inM1,1{\displaystyle {\mathcal {M}}_{1,1}}are isomorphic to the classifying stackB(Z/2){\displaystyle B(\mathbb {Z} /2)}since every elliptic curve corresponds to a double cover ofP1{\displaystyle \mathbb {P} ^{1}}, so theZ/2{\displaystyle \mathbb {Z} /2}-action on the point corresponds to the involution of these two branches of the covering. There are a few special points[2]pg 10-11corresponding to elliptic curves withj{\displaystyle j}-invariantequal to1728{\displaystyle 1728}and0{\displaystyle 0}where the automorphism groups are of order 4, 6, respectively[3]pg 170. One point in theFundamental domainwith stabilizer of order4{\displaystyle 4}corresponds toτ=i{\displaystyle \tau =i}, and the points corresponding to the stabilizer of order6{\displaystyle 6}correspond toτ=e2πi/3,eπi/3{\displaystyle \tau =e^{2\pi i/3},e^{\pi i/3}}[4]pg 78.
Given a plane curve by itsWeierstrass equationy2=x3+ax+b{\displaystyle y^{2}=x^{3}+ax+b}and a solution(t,s){\displaystyle (t,s)}, generically forj-invariantj≠0,1728{\displaystyle j\neq 0,1728}, there is theZ/2{\displaystyle \mathbb {Z} /2}-involution sending(t,s)↦(t,−s){\displaystyle (t,s)\mapsto (t,-s)}. In the special case of a curve withcomplex multiplicationy2=x3+ax{\displaystyle y^{2}=x^{3}+ax}there theZ/4{\displaystyle \mathbb {Z} /4}-involution sending(t,s)↦(−t,−1⋅s){\displaystyle (t,s)\mapsto (-t,{\sqrt {-1}}\cdot s)}. The other special case is whena=0{\displaystyle a=0}, so a curve of the formy2=x3+b{\displaystyle y^{2}=x^{3}+b}there is theZ/6{\displaystyle \mathbb {Z} /6}-involution sending(t,s)↦(ζ3t,−s){\displaystyle (t,s)\mapsto (\zeta _{3}t,-s)}whereζ3{\displaystyle \zeta _{3}}is the thirdroot of unitye2πi/3{\displaystyle e^{2\pi i/3}}.
There is a subset of the upper-half plane called theFundamental domainwhich contains every isomorphism class of elliptic curves. It is the subsetD={z∈h:|z|≥1andRe(z)≤1/2}{\displaystyle D=\{z\in {\mathfrak {h}}:|z|\geq 1{\text{ and }}{\text{Re}}(z)\leq 1/2\}}It is useful to consider this space because it helps visualize the stackM1,1{\displaystyle {\mathcal {M}}_{1,1}}. From the quotient maph→SL2(Z)∖h{\displaystyle {\mathfrak {h}}\to {\text{SL}}_{2}(\mathbb {Z} )\backslash {\mathfrak {h}}}the image ofD{\displaystyle D}is surjective and its interior is injective[4]pg 78. Also, the points on the boundary can be identified with their mirror image under the involution sendingRe(z)↦−Re(z){\displaystyle {\text{Re}}(z)\mapsto -{\text{Re}}(z)}, soM1,1{\displaystyle {\mathcal {M}}_{1,1}}can be visualized as the projective curveP1{\displaystyle \mathbb {P} ^{1}}with a point removed at infinity[5]pg 52.
There are line bundlesL⊗k{\displaystyle {\mathcal {L}}^{\otimes k}}over the moduli stackM1,1{\displaystyle {\mathcal {M}}_{1,1}}whose sections correspond tomodular functionsf{\displaystyle f}on the upper-half planeh{\displaystyle {\mathfrak {h}}}. OnC×h{\displaystyle \mathbb {C} \times {\mathfrak {h}}}there areSL2(Z){\displaystyle {\text{SL}}_{2}(\mathbb {Z} )}-actions compatible with the action onh{\displaystyle {\mathfrak {h}}}given bySL2(Z)×C×h→C×h{\displaystyle {\text{SL}}_{2}(\mathbb {Z} )\times {\displaystyle \mathbb {C} \times {\mathfrak {h}}}\to {\displaystyle \mathbb {C} \times {\mathfrak {h}}}}The degreek{\displaystyle k}action is given by(abcd):(z,τ)↦((cτ+d)kz,aτ+bcτ+d){\displaystyle {\begin{pmatrix}a&b\\c&d\end{pmatrix}}:(z,\tau )\mapsto \left((c\tau +d)^{k}z,{\frac {a\tau +b}{c\tau +d}}\right)}hence the trivial line bundleC×h→h{\displaystyle \mathbb {C} \times {\mathfrak {h}}\to {\mathfrak {h}}}with the degreek{\displaystyle k}action descends to a unique line bundle denotedL⊗k{\displaystyle {\mathcal {L}}^{\otimes k}}. Notice the action on the factorC{\displaystyle \mathbb {C} }is arepresentationofSL2(Z){\displaystyle {\text{SL}}_{2}(\mathbb {Z} )}onZ{\displaystyle \mathbb {Z} }hence such representations can be tensored together, showingL⊗k⊗L⊗l≅L⊗(k+l){\displaystyle {\mathcal {L}}^{\otimes k}\otimes {\mathcal {L}}^{\otimes l}\cong {\mathcal {L}}^{\otimes (k+l)}}. The sections ofL⊗k{\displaystyle {\mathcal {L}}^{\otimes k}}are then functions sectionsf∈Γ(C×h){\displaystyle f\in \Gamma (\mathbb {C} \times {\mathfrak {h}})}compatible with the action ofSL2(Z){\displaystyle {\text{SL}}_{2}(\mathbb {Z} )}, or equivalently, functionsf:h→C{\displaystyle f:{\mathfrak {h}}\to \mathbb {C} }such thatf((abcd)⋅τ)=(cτ+d)kf(τ){\displaystyle f\left({\begin{pmatrix}a&b\\c&d\end{pmatrix}}\cdot \tau \right)=(c\tau +d)^{k}f(\tau )}This is exactly the condition for a holomorphic function to be modular.
The modular forms are the modular functions which can be extended to the compactificationL⊗k¯→M¯1,1{\displaystyle {\overline {{\mathcal {L}}^{\otimes k}}}\to {\overline {\mathcal {M}}}_{1,1}}this is because in order to compactify the stackM1,1{\displaystyle {\mathcal {M}}_{1,1}}, a point at infinity must be added, which is done through a gluing process by gluing theq{\displaystyle q}-disk (where a modular function has itsq{\displaystyle q}-expansion)[2]pgs 29-33.
Constructing the universal curvesE→M1,1{\displaystyle {\mathcal {E}}\to {\mathcal {M}}_{1,1}}is a two step process: (1) construct a versal curveEh→h{\displaystyle {\mathcal {E}}_{\mathfrak {h}}\to {\mathfrak {h}}}and then (2) show this behaves well with respect to theSL2(Z){\displaystyle {\text{SL}}_{2}(\mathbb {Z} )}-action onh{\displaystyle {\mathfrak {h}}}. Combining these two actions together yields the quotient stack[(SL2(Z)⋉Z2)∖C×h]{\displaystyle [({\text{SL}}_{2}(\mathbb {Z} )\ltimes \mathbb {Z} ^{2})\backslash \mathbb {C} \times {\mathfrak {h}}]}
Every rank 2Z{\displaystyle \mathbb {Z} }-lattice inC{\displaystyle \mathbb {C} }induces a canonicalZ2{\displaystyle \mathbb {Z} ^{2}}-action onC{\displaystyle \mathbb {C} }. As before, since every lattice is homothetic to a lattice of the form(1,τ){\displaystyle (1,\tau )}then the action(m,n){\displaystyle (m,n)}sends a pointz∈C{\displaystyle z\in \mathbb {C} }to(m,n)⋅z↦z+m⋅1+n⋅τ{\displaystyle (m,n)\cdot z\mapsto z+m\cdot 1+n\cdot \tau }Because theτ{\displaystyle \tau }inh{\displaystyle {\mathfrak {h}}}can vary in this action, there is an inducedZ2{\displaystyle \mathbb {Z} ^{2}}-action onC×h{\displaystyle \mathbb {C} \times {\mathfrak {h}}}(m,n)⋅(z,τ)↦(z+m⋅1+n⋅τ,τ){\displaystyle (m,n)\cdot (z,\tau )\mapsto (z+m\cdot 1+n\cdot \tau ,\tau )}giving the quotient spaceEh→h{\displaystyle {\mathcal {E}}_{\mathfrak {h}}\to {\mathfrak {h}}}by projecting ontoh{\displaystyle {\mathfrak {h}}}.
There is aSL2(Z){\displaystyle {\text{SL}}_{2}(\mathbb {Z} )}-action onZ2{\displaystyle \mathbb {Z} ^{2}}which is compatible with the action onh{\displaystyle {\mathfrak {h}}}, meaning given a pointz∈h{\displaystyle z\in {\mathfrak {h}}}and ag∈SL2(Z){\displaystyle g\in {\text{SL}}_{2}(\mathbb {Z} )}, the new latticeg⋅z{\displaystyle g\cdot z}and an induced action fromZ2⋅g{\displaystyle \mathbb {Z} ^{2}\cdot g}, which behaves as expected. This action is given by(abcd):(m,n)↦(m,n)⋅(abcd){\displaystyle {\begin{pmatrix}a&b\\c&d\end{pmatrix}}:(m,n)\mapsto (m,n)\cdot {\begin{pmatrix}a&b\\c&d\end{pmatrix}}}which is matrix multiplication on the right, so(m,n)⋅(abcd)=(am+cn,bm+dn){\displaystyle (m,n)\cdot {\begin{pmatrix}a&b\\c&d\end{pmatrix}}=(am+cn,bm+dn)}
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https://en.wikipedia.org/wiki/Moduli_stack_of_elliptic_curves
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Inmathematics, theNagell–Lutz theoremis a result in thediophantine geometryofelliptic curves, which describesrationaltorsionpoints on elliptic curves over the integers. It is named forTrygve NagellandÉlisabeth Lutz.
Suppose that the equation
defines anon-singularcubic curveEwith integercoefficientsa,b,c, and letDbe thediscriminantof the cubicpolynomialon the right side:
IfP=(x,y){\displaystyle P=(x,y)}is arational pointof finiteorderonE, for theelliptic curve group law, then:
The Nagell–Lutz theorem generalizes to arbitrary number fields and more
general cubic equations.[1]For curves over the rationals, the generalization says that, for a nonsingular cubic curve whose Weierstrass form
has integer coefficients, any rational pointP=(x,y){\displaystyle P=(x,y)}of finite
order must have integer coordinates, or else have order 2 and
coordinates of the formx=m/4{\displaystyle x=m/4},y=n/8{\displaystyle y=n/8}, formandnintegers.
The result is named for its two independent discoverers, the NorwegianTrygve Nagell(1895–1988) who published it in 1935, andÉlisabeth Lutz(1937).
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https://en.wikipedia.org/wiki/Nagell%E2%80%93Lutz_theorem
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Inmathematics, theRiemann–Hurwitz formula, named afterBernhard RiemannandAdolf Hurwitz, describes the relationship of theEuler characteristicsof twosurfaceswhen one is aramified coveringof the other. It therefore connectsramificationwithalgebraic topology, in this case. It is a prototype result for many others, and is often applied in the theory ofRiemann surfaces(which is its origin) andalgebraic curves.
For acompact,connected,orientablesurfaceS{\displaystyle S}, the Euler characteristicχ(S){\displaystyle \chi (S)}is
wheregis thegenus(thenumber of handles). This follows, as theBetti numbersare1,2g,1,0,0,…{\displaystyle 1,2g,1,0,0,\dots }.
For the case of an (unramified)covering mapof surfaces
that is surjective and of degreeN{\displaystyle N}, we have the formula
That is because each simplex ofS{\displaystyle S}should be covered by exactlyN{\displaystyle N}inS′{\displaystyle S'}, at least if we use a fine enoughtriangulationofS{\displaystyle S}, as we are entitled to do since the Euler characteristic is atopological invariant. What the Riemann–Hurwitz formula does is to add in a correction to allow for ramification (sheets coming together).
Now assume thatS{\displaystyle S}andS′{\displaystyle S'}areRiemann surfaces, and that the mapπ{\displaystyle \pi }iscomplex analytic. The mapπ{\displaystyle \pi }is said to beramifiedat a pointPinS′ if there exist analytic coordinates nearPand π(P) such that π takes the form π(z) =zn, andn> 1. An equivalent way of thinking about this is that there exists a small neighborhoodUofPsuch that π(P) has exactly one preimage inU, but the image of any other point inUhas exactlynpreimages inU. The numbernis called theramification indexat Pand is denoted byeP. In calculating the Euler characteristic ofS′ we notice the loss ofeP− 1 copies ofPabove π(P) (that is, in the inverse image of π(P)). Now let us choose triangulations ofSandS′with vertices at the branch and ramification points, respectively, and use these to compute the Euler characteristics. ThenS′will have the same number ofd-dimensional faces forddifferent from zero, but fewer than expected vertices. Therefore, we find a "corrected" formula
or as it is also commonly written, using thatχ(X)=2−2g(X){\displaystyle \chi (X)=2-2g(X)}and multiplying through by −1:
(all but finitely manyPhaveeP= 1, so this is quite safe). This formula is known as theRiemann–Hurwitz formulaand also asHurwitz's theorem.
Another useful form of the formula is:
wherebis the number of branch points inS(images of ramification points) and b' is the size of the union of the fibers of branch points (this contains all ramification points and perhaps some non-ramified points). Indeed, to obtain this formula, remove disjoint disc neighborhoods of the branch points fromSand their preimages inS'so that the restriction ofπ{\displaystyle \pi }is a covering. Removing a disc from a surface lowers its Euler characteristic by 1 by the formula for connected sum, so we finish by the formula for a non-ramified covering.
We can also see that this formula is equivalent to the usual form,
as we have
since for anyQ∈S{\displaystyle Q\in S}we haveN=∑P∈π−1(Q)eP{\displaystyle N=\sum _{P\in \pi ^{-1}(Q)}e_{P}}
TheWeierstrass℘{\displaystyle \wp }-function, considered as ameromorphic functionwith values in theRiemann sphere, yields a map from anelliptic curve(genus 1) to theprojective line(genus 0). It is adouble cover(N= 2), with ramification at four points only, at whiche= 2. The Riemann–Hurwitz formula then reads
with the summation taken over four ramification points.
The formula may also be used to calculate the genus ofhyperelliptic curves.
As another example, the Riemann sphere maps to itself by the functionzn, which has ramification indexnat 0, for any integern> 1. There can only be other ramification at the point at infinity. In order to balance the equation
we must have ramification indexnat infinity, also.
Several results in algebraic topology and complex analysis follow.
Firstly, there are no ramified covering maps from a curve of lower genus to a curve of higher genus – and thus, since non-constant meromorphic maps of curves are ramified covering spaces, there are no non-constant meromorphic maps from a curve of lower genus to a curve of higher genus.
As another example, it shows immediately that a curve of genus 0 has no cover withN> 1 that is unramified everywhere: because that would give rise to an Euler characteristic > 2.
For acorrespondenceof curves, there is a more general formula,Zeuthen's theorem, which gives the ramification correction to the first approximation that the Euler characteristics are in the inverse ratio to the degrees of the correspondence.
Anorbifoldcovering of degree N between orbifold surfaces S' and S is a branched covering, so the Riemann–Hurwitz formula implies the usual formula for coverings
denoting withχ{\displaystyle \chi \,}the orbifold Euler characteristic.
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https://en.wikipedia.org/wiki/Riemann%E2%80%93Hurwitz_formula
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Wiles's proof of Fermat's Last Theoremis aproofby British mathematicianSir Andrew Wilesof a special case of themodularity theoremforelliptic curves. Together withRibet's theorem, it provides a proof forFermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using previous knowledge by almost all living mathematicians at the time.[1]: 203–205, 223, 226
Wiles first announced his proof on 23 June 1993 at a lecture inCambridgeentitled "Modular Forms, Elliptic Curves and Galois Representations".[2]However, in September 1993 the proof was found to contain an error. One year later on 19 September 1994, in what he would call "the most important moment of [his] working life", Wiles stumbled upon a revelation that allowed him to correct the proof to the satisfaction of the mathematical community. The corrected proof was published in 1995.[3]
Wiles's proof uses many techniques fromalgebraic geometryandnumber theoryand has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry such as thecategoryofschemes, significant number theoretic ideas fromIwasawa theory, and other 20th-century techniques which were not available to Fermat. The proof's method of identification of adeformation ringwith aHecke algebra(now referred to as anR=T theorem) to provemodularity liftingtheorems has been an influential development inalgebraic number theory.
Together, the two papers which contain the proof are 129 pages long[4][5]and consumed more than seven years of Wiles's research time.John Coatesdescribed the proof as one of the highest achievements of number theory, andJohn Conwaycalled it "the proof of the [20th] century."[6]Wiles's path to proving Fermat's Last Theorem, by way of proving the modularity theorem for the special case ofsemistable elliptic curves, established powerful modularity lifting techniques and opened up entire new approaches to numerous other problems. For proving Fermat's Last Theorem, he wasknighted, and received other honours such as the 2016Abel Prize. When announcing that Wiles had won the Abel Prize, theNorwegian Academy of Science and Lettersdescribed his achievement as a "stunning proof".[3]
Fermat's Last Theorem, formulated in 1637, states that no three positive integersa,b, andccan satisfy the equation
ifnis an integer greater than two (n> 2).
Over time, this simple assertion became one of the most famousunproved claimsin mathematics. Between its publication and Andrew Wiles's eventual solution more than 350 years later, many mathematicians and amateurs attempted to prove this statement, either for all values ofn> 2, or for specific cases. It spurred the development of entire new areas withinnumber theory. Proofs were eventually found for all values ofnup to around 4 million, first by hand, and later by computer. However, no general proof was found that would be valid for all possible values ofn, nor even a hint how such a proof could be undertaken.
Separately from anything related to Fermat's Last Theorem, in the 1950s and 1960s Japanese mathematicianGoro Shimura, drawing on ideas posed byYutaka Taniyama, conjectured that a connection might exist betweenelliptic curvesandmodular forms. These were mathematical objects with no known connection between them. Taniyama and Shimura posed the question whether, unknown to mathematicians, the two kinds of object were actually identical mathematical objects, just seen in different ways.
They conjectured that everyrationalelliptic curve is alsomodular. This became known as the Taniyama–Shimura conjecture. In the West, this conjecture became well known through a 1967 paper byAndré Weil, who gave conceptual evidence for it; thus, it is sometimes called the Taniyama–Shimura–Weil conjecture.
By around 1980, much evidence had been accumulated to form conjectures about elliptic curves, and many papers had been written which examined the consequences if the conjecture were true, but the actual conjecture itself was unproven and generally considered inaccessible—meaning that mathematicians believed a proof of the conjecture was probably impossible using current knowledge.
For decades, the conjecture remained an important but unsolved problem in mathematics. Around 50 years after first being proposed, the conjecture was finally proven and renamed themodularity theorem, largely as a result of Andrew Wiles's work described below.
On yet another separate branch of development, in the late 1960s, Yves Hellegouarch came up with the idea of associating hypothetical solutions (a,b,c) of Fermat's equation with a completely different mathematical object: an elliptic curve.[7]The curve consists of all points in the plane whose coordinates (x,y) satisfy the relation
Such an elliptic curve would enjoy very special properties due to the appearance of high powers of integers in its equation and the fact thatan+bn=cnwould be annth power as well.
In 1982–1985,Gerhard Freycalled attention to the unusual properties of this same curve, now called aFrey curve. He showed that it was likely that the curve could link Fermat and Taniyama, since anycounterexampleto Fermat's Last Theorem would probably also imply that an elliptic curve existed that was notmodular. Frey showed that there were good reasons to believe that any set of numbers (a,b,c,n) capable of disproving Fermat's Last Theorem could also probably be used to disprove the Taniyama–Shimura–Weil conjecture. Therefore, if the Taniyama–Shimura–Weil conjecture were true, no set of numbers capable of disproving Fermat could exist, so Fermat's Last Theorem would have to be true as well.
The conjecture says that each elliptic curve withrationalcoefficients can be constructed in an entirely different way, not by giving its equation but by usingmodular functionstoparametrisecoordinatesxandyof the points on it. Thus, according to the conjecture, any elliptic curve overQwould have to be amodular elliptic curve, yet if a solution to Fermat's equation with non-zeroa,b,candngreater than 2 existed, the corresponding curve would not be modular, resulting in a contradiction. If the link identified by Frey could be proven, then in turn, it would mean that a disproof of Fermat's Last Theorem would disprove the Taniyama–Shimura–Weil conjecture, or by contraposition, a proof of the latter would prove the former as well.[8]
To complete this link, it was necessary to show that Frey's intuition was correct: that a Frey curve, if it existed, could not be modular. In 1985,Jean-Pierre Serreprovided a partial proof that a Frey curve could not be modular. Serre did not provide a complete proof of his proposal; the missing part (which Serre had noticed early on[9]: 1) became known as the epsilon conjecture (sometimes written ε-conjecture; now known asRibet's theorem). Serre's main interest was in an even more ambitious conjecture,Serre's conjectureon modularGalois representations, which would imply the Taniyama–Shimura–Weil conjecture. However his partial proof came close to confirming the link between Fermat and Taniyama.
In the summer of 1986,Ken Ribetsucceeded in proving the epsilon conjecture, now known asRibet's theorem. His article was published in 1990. In doing so, Ribet finally proved the link between the two theorems by confirming, as Frey had suggested, that a proof of the Taniyama–Shimura–Weil conjecture for the kinds of elliptic curves Frey had identified, together with Ribet's theorem, would also prove Fermat's Last Theorem.
In mathematical terms, Ribet's theorem showed that if the Galois representation associated with an elliptic curve has certain properties (which Frey's curve has), then that curve cannot be modular, in the sense that there cannot exist a modular form which gives rise to the same Galois representation.[10]
Following the developments related to the Frey curve, and its link to both Fermat and Taniyama, a proof of Fermat's Last Theorem would follow from a proof of the Taniyama–Shimura–Weil conjecture—or at least a proof of the conjecture for the kinds of elliptic curves that included Frey's equation (known assemistable elliptic curves).
However, despite the progress made by Serre and Ribet, this approach to Fermat was widely considered unusable as well, since almost all mathematicians saw the Taniyama–Shimura–Weil conjecture itself as completely inaccessible to proof with current knowledge.[1]: 203–205, 223, 226For example, Wiles's ex-supervisorJohn Coatesstated that it seemed "impossible to actually prove",[1]: 226and Ken Ribet considered himself "one of the vast majority of people who believed [it] was completely inaccessible".[1]: 223
Hearing of Ribet's 1986 proof of the epsilon conjecture, English mathematician Andrew Wiles, who had studied elliptic curves and had a childhood fascination with Fermat, decided to begin working in secret towards a proof of the Taniyama–Shimura–Weil conjecture, since it was now professionally justifiable,[11]as well as because of the enticing goal of proving such a long-standing problem.
Ribet later commented that "Andrew Wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove [it]."[1]: 223
Wiles initially presented his proof in 1993. It was finally accepted as correct, and published, in 1995, following the correction of a subtle error in one part of his original paper. His work was extended to a full proof of the modularity theorem over the following six years by others, who built on Wiles's work.
During 21–23 June 1993, Wiles announced and presented his proof of the Taniyama–Shimura conjecture for semistable elliptic curves, and hence of Fermat's Last Theorem, over the course of three lectures delivered at theIsaac Newton Institute for Mathematical SciencesinCambridge, England.[2]There was a relatively large amount of press coverage afterwards.[12]
After the announcement,Nick Katzwas appointed as one of the referees toreviewWiles's manuscript. In the course of his review, he asked Wiles a series of clarifying questions that led Wiles to recognise that the proof contained a gap. There was an error in one critical portion of the proof which gave a bound for the order of a particular group: theEuler systemused to extendKolyvaginandFlach's method was incomplete. The error would not have rendered his work worthless—each part of Wiles's work was highly significant and innovative by itself, as were the many developments and techniques he had created in the course of his work, and only one part was affected.[1]: 289, 296–297Without this part proved, however, there was no actual proof of Fermat's Last Theorem.
Wiles spent almost a year trying to repair his proof, initially by himself and then in collaboration with his former studentRichard Taylor, without success.[13][14][15]By the end of 1993, rumours had spread that under scrutiny, Wiles's proof had failed, but how seriously was not known. Mathematicians were beginning to pressure Wiles to disclose his work whether or not complete, so that the wider community could explore and use whatever he had managed to accomplish. Instead of being fixed, the problem, which had originally seemed minor, now seemed very significant, far more serious, and less easy to resolve.[16]
Wiles states that on the morning of 19 September 1994, he was on the verge of giving up and was almost resigned to accepting that he had failed, and to publishing his work so that others could build on it and find the error. He states that he was having a final look to try to understand the fundamental reasons why his approach could not be made to work, when he had a sudden insight that the specific reason why the Kolyvagin–Flach approach would not work directly also meant that his original attempt usingIwasawa theorycould be made to work if he strengthened it using experience gained from the Kolyvagin–Flach approach since then. Each was inadequate by itself, but fixing one approach with tools from the other would resolve the issue and produce aclass number formula(CNF) valid for all cases that were not already proven by his refereed paper:[13][17]
I was sitting at my desk examining the Kolyvagin–Flach method. It wasn't that I believed I could make it work, but I thought that at least I could explain why it didn't work. Suddenly I had this incredible revelation. I realised that, the Kolyvagin–Flach method wasn't working, but it was all I needed to make my original Iwasawa theory work from three years earlier. So out of the ashes of Kolyvagin–Flach seemed to rise the true answer to the problem. It was so indescribably beautiful; it was so simple and so elegant. I couldn't understand how I'd missed it and I just stared at it in disbelief for twenty minutes. Then during the day I walked around the department, and I'd keep coming back to my desk looking to see if it was still there. It was still there. I couldn't contain myself, I was so excited. It was the most important moment of my working life. Nothing I ever do again will mean as much.
On 6 October Wiles asked three colleagues (includingGerd Faltings) to review his new proof,[19]and on 24 October 1994 Wiles submitted two manuscripts, "Modular elliptic curves and Fermat's Last Theorem"[4]and "Ring theoretic properties of certain Hecke algebras",[5]the second of which Wiles had written with Taylor and proved that certain conditions were met which were needed to justify the corrected step in the main paper.
The two papers were vetted and finally published as the entirety of the May 1995 issue of theAnnals of Mathematics. The new proof was widely analysed and became accepted as likely correct in its major components.[6][10][11]These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured.
Fermat claimed to "... have discovered a truly marvelous proof of this, which this margin is too narrow to contain".[20][21]Wiles's proof is very complex, and incorporates the work of so many other specialists that it was suggested in 1994 that only a small number of people were capable of fully understanding at that time all the details of what he had done.[2][22]The complexity of Wiles's proof motivated a 10-day conference atBoston University; the resulting book of conference proceedings aimed to make the full range of required topics accessible to graduate students in number theory.[9]
As noted above, Wiles proved the Taniyama–Shimura–Weil conjecture for the special case of semistable elliptic curves, rather than for all elliptic curves. Over the following years,Christophe Breuil,Brian Conrad,Fred Diamond, andRichard Taylor(sometimes abbreviated as "BCDT") carried the work further, ultimately proving the Taniyama–Shimura–Weil conjecture for all elliptic curves in a 2001 paper.[23]Now proven, the conjecture became known as themodularity theorem.
In 2005, Dutchcomputer scientistJan Bergstraposed the problem of formalizing Wiles's proof in such a way that it could beverified by computer.[24]
Wiles proved the modularity theorem for semistable elliptic curves, from which Fermat’s last theorem follows usingproof by contradiction. In this proof method, one assumes the opposite of what is to be proved, and shows if that were true, it would create a contradiction. The contradiction shows that the assumption (that the conclusion is wrong) must have been incorrect, requiring the conclusion to hold.
The proof falls roughly in two parts: In the first part, Wiles proves a general result about "lifts", known as the "modularity lifting theorem". This first part allows him to prove results about elliptic curves by converting them to problems aboutGalois representationsof elliptic curves. He then uses this result to prove that all semistable curves are modular, by proving that theGalois representationsof these curves are modular.
Wiles aims first of all to prove a result about these representations, that he will use later: that if a semistable elliptic curveEhas a Galois representationρ(E,p)that is modular, the elliptic curve itself must be modular.
Proving this is helpful in two ways: it makes counting and matching easier, and, significantly, to prove the representation is modular, we would only have to prove it for one single prime numberp, and we can do this usingany primethat makes our work easy – it does not matter which prime we use.
This is the most difficult part of the problem – technically it means proving that if the Galois representationρ(E,p)is a modular form, so are all the other related Galois representationsρ(E,p∞)for all powers ofp.[3]This is the so-called "modular liftingproblem", and Wiles approached it usingdeformations.
Together, these allow us to work with representations of curves rather than directly with elliptic curves themselves. Our original goal will have been transformed into proving the modularity of geometric Galois representations of semistable elliptic curves, instead. Wiles described this realization as a "key breakthrough".
A Galois representation of an elliptic curve isG→ GL(Zp). To show that a geometric Galois representation of an elliptic curve is a modular form, we need to find anormalized eigenformwhoseeigenvalues(which are also itsFourier seriescoefficients) satisfy acongruence relationshipfor all but a finite number of primes.
This is Wiles'slifting theorem(ormodularity lifting theorem), a major and revolutionary accomplishment at the time.
So we can try to prove all of our elliptic curves are modular by using one prime number asp- but if we do not succeed in proving this for all elliptic curves, perhaps we can prove the rest by choosing different prime numbers as 'p' for the difficult cases.
The proof must cover the Galois representations of all semistable elliptic curvesE, but for each individual curve, we only need to prove it is modular using one prime numberp.)
From above, it does not matter which prime is chosen for the representations. We can use any one prime number that is easiest. 3 is the smallest prime number more than 2, and some work has already been done on representations of elliptic curves usingρ(E, 3), so choosing 3 as our prime number is a helpful starting point.
Wiles found that it was easier to prove the representation was modular by choosing a primep= 3in the cases where the representationρ(E, 3)is irreducible, but the proof whenρ(E, 3)is reducible was easier to prove by choosingp= 5. So, the proof splits in two at this point.
The switch betweenp= 3andp= 5has since opened a significant area of study in its own right(seeSerre's modularity conjecture).
Wiles uses his modularity lifting theorem to make short work of this case:
This existing result forp= 3is crucial to Wiles's approach and is one reason for initially usingp= 3.
Wiles found that when the representation of an elliptic curve usingp= 3is reducible, it was easier to work withp= 5and use his new lifting theorem to prove thatρ(E, 5)will always be modular, than to try and prove directly thatρ(E, 3)itself is modular (remembering that we only need to prove it for one prime).
Wiles showed that in this case, one could always find another semistable elliptic curveFsuch that the representationρ(F, 3)is irreducible and also the representationsρ(E, 5)andρ(F, 5)areisomorphic(they have identical structures).
This proves:
Wiles opted to attempt to match elliptic curves to acountableset of modular forms. He found that this direct approach was not working, so he transformed the problem by instead matching theGalois representationsof the elliptic curves to modular forms. Wiles denotes this matching (or mapping) that, more specifically, is aring homomorphism:
R{\displaystyle R}is a deformation ring andT{\displaystyle \mathbf {T} }is aHecke ring.
Wiles had the insight that in many cases this ringhomomorphismcould be a ringisomorphism(Conjecture 2.16 in Chapter 2, §3 of the 1995 paper[4]). He realised that the map betweenR{\displaystyle R}andT{\displaystyle \mathbf {T} }is an isomorphism if and only if twoabelian groupsoccurring in the theory are finite and have the samecardinality. This is sometimes referred to as the "numerical criterion". Given this result, Fermat's Last Theorem is reduced to the statement that two groups have the same order. Much of the text of the proof leads into topics and theorems related toring theoryandcommutation theory. Wiles's goal was to verify that the mapR→T{\displaystyle R\rightarrow \mathbf {T} }is an isomorphism and ultimately thatR=T{\displaystyle R=\mathbf {T} }. In treating deformations, Wiles defined four cases, with theflatdeformation case requiring more effort to prove and treated in a separate article in the same volume entitled "Ring-theoretic properties of certain Hecke algebras".
Gerd Faltings, in his bulletin, gives the followingcommutative diagram(p. 745):
or ultimately thatR=T{\displaystyle R=\mathbf {T} }, indicating acomplete intersection. Since Wiles could not show thatR=T{\displaystyle R=\mathbf {T} }directly, he did so throughZ3,F3{\displaystyle \mathbf {Z} _{3},\mathbf {F} _{3}}andT/m{\displaystyle \mathbf {T} /{\mathfrak {m}}}vialifts.
In order to perform this matching, Wiles had to create aclass number formula(CNF). He first attempted to use horizontalIwasawa theorybut that part of his work had an unresolved issue such that he could not create a CNF. At the end of the summer of 1991, he learned about anEuler systemrecently developed byVictor KolyvaginandMatthias Flachthat seemed "tailor made" for the inductive part of his proof, which could be used to create a CNF, and so Wiles set his Iwasawa work aside and began working to extend Kolyvagin and Flach's work instead, in order to create the CNF his proof would require.[25]By the spring of 1993, his work had covered all but a few families of elliptic curves, and in early 1993, Wiles was confident enough of his nearing success to let one trusted colleague into his secret. Since his work relied extensively on using the Kolyvagin–Flach approach, which was new to mathematics and to Wiles, and which he had also extended, in January 1993 he asked his Princeton colleague,Nick Katz, to help him review his work for subtle errors. Their conclusion at the time was that the techniques Wiles used seemed to work correctly.[1]: 261–265[26]
Wiles's use of Kolyvagin–Flach would later be found to be the point of failure in the original proof submission, and he eventually had to revert to Iwasawa theory and a collaboration with Richard Taylor to fix it. In May 1993, while reading a paper by Mazur, Wiles had the insight that the 3/5 switch would resolve the final issues and would then cover all elliptic curves.
Given an elliptic curveE{\displaystyle E}over the fieldQ{\displaystyle \mathbb {Q} }of rational numbers, for every prime powerℓn{\displaystyle \ell ^{n}}, there exists ahomomorphismfrom theabsolute Galois group
to
the group ofinvertible2 by 2 matrices whose entries are integers moduloℓn{\displaystyle \ell ^{n}}. This is becauseE(Q¯){\displaystyle E({\bar {\mathbb {Q} }})}, the points ofE{\displaystyle E}overQ¯{\displaystyle {\bar {\mathbb {Q} }}}, form anabelian groupon whichGal(Q¯/Q){\displaystyle \operatorname {Gal} ({\bar {\mathbb {Q} }}/\mathbb {Q} )}acts; the subgroup of elementsx{\displaystyle x}such thatℓnx=0{\displaystyle \ell ^{n}x=0}is just(Z/ℓnZ)2{\displaystyle (\mathbb {Z} /\ell ^{n}\mathbb {Z} )^{2}}, and anautomorphismof this group is a matrix of the type described.
Less obvious is that given a modular form of a certain special type, aHecke eigenformwith eigenvalues inQ{\displaystyle \mathbb {Q} }, one also gets a homomorphism
This goes back to Eichler and Shimura. The idea is that the Galois group acts first on the modular curve on which the modular form is defined, thence on theJacobian varietyof the curve, and finally on the points ofℓn{\displaystyle \ell ^{n}}power order on that Jacobian. The resulting representation is not usually 2-dimensional, but theHecke operatorscut out a 2-dimensional piece. It is easy to demonstrate that these representations come from some elliptic curve but the converse is the difficult part to prove.
Instead of trying to go directly from the elliptic curve to the modular form, one can first pass to themodℓn{\displaystyle {\bmod {\ell ^{n}}}}representation for someℓ{\displaystyle \ell }andn{\displaystyle n}, and from that to the modular form. In the case whereℓ=3{\displaystyle \ell =3}andn=1{\displaystyle n=1}, results of theLanglands–Tunnell theoremshow that themod3{\displaystyle {\bmod {3}}}representation of any elliptic curve overQ{\displaystyle \mathbb {Q} }comes from a modular form. The basic strategy is to use induction onn{\displaystyle n}to show that this is true forℓ=3{\displaystyle \ell =3}and anyn{\displaystyle n}, that ultimately there is a single modular form that works for alln. To do this, one uses a counting argument, comparing the number of ways in which one canlifta modℓn{\displaystyle \ell ^{n}}Galois representation to one modℓn+1{\displaystyle \ell ^{n+1}}and the number of ways in which one can lift a modℓn{\displaystyle \ell ^{n}}modular form. An essential point is to impose a sufficient set of conditions on the Galois representation; otherwise, there will be too many lifts and most will not be modular. These conditions should be satisfied for the representations coming from modular forms and those coming from elliptic curves.
If the original(mod3){\displaystyle (\mathrm {mod} \,3)}representation has an image which is too small, one runs into trouble with the lifting argument, and in this case, there is a final trick which has since been studied in greater generality in the subsequent work on theSerre modularity conjecture. The idea involves the interplay between the(mod3){\displaystyle (\mathrm {mod} \,3)}and(mod5){\displaystyle (\mathrm {mod} \,5)}representations. In particular, if the mod-5 Galois representationρ¯E,5{\displaystyle {\overline {\rho }}_{E,5}}associated to an semistable elliptic curveEoverQis irreducible, then there is another semistable elliptic curveE'overQsuch that its associated mod-5 Galois representationρ¯E′,5{\displaystyle {\overline {\rho }}_{E',5}}is isomorphic toρ¯E,5{\displaystyle {\overline {\rho }}_{E,5}}andsuch that its associated mod-3 Galois representationρ¯E,3{\displaystyle {\overline {\rho }}_{E,3}}is irreducible (and therefore modular by Langlands–Tunnell).[27]
In his 108-page article published in 1995, Wiles divides the subject matter up into the following chapters (preceded here by page numbers):
Gerd Faltingssubsequently provided some simplifications to the 1995 proof, primarily in switching from geometric constructions to rather simpler algebraic ones.[19][28]The book of the Cornell conference also contained simplifications to the original proof.[9]
Wiles's paper is more than 100 pages long and often uses the specialised symbols and notations ofgroup theory,algebraic geometry,commutative algebra, andGalois theory. The mathematicians who helped to lay the groundwork for Wiles often created new specialised concepts and technicaljargon.
Among the introductory presentations are an email which Ribet sent in 1993;[29][30]Hesselink's quick review of top-level issues, which gives just the elementary algebra and avoids abstract algebra;[24]or Daney's web page, which provides a set of his own notes and lists the current books available on the subject. Weston attempts to provide a handy map of some of the relationships between the subjects.[31]F. Q. Gouvêa's 1994 article "A Marvelous Proof", which reviews some of the required topics, won a Lester R. Ford award from theMathematical Association of America.[32][33]Faltings' 5-page technical bulletin on the matter is a quick and technical review of the proof for the non-specialist.[34]For those in search of a commercially available book to guide them, he recommended that those familiar with abstract algebra read Hellegouarch, then read the Cornell book,[9]which is claimed to be accessible to "a graduate student in number theory". The Cornell book does not cover the entirety of the Wiles proof.[12]
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Acryptocurrency(colloquiallycrypto) is adigital currencydesigned to work through acomputer networkthat is not reliant on any central authority, such as agovernmentorbank, to uphold or maintain it.[2]
Individual coin ownership records are stored in a digitalledgerorblockchain, which is a computerizeddatabasethat uses a consensus mechanism to securetransactionrecords, control the creation of additional coins, and verify the transfer of coin ownership.[3][4][5]The two most common consensus mechanisms areproof of workandproof of stake.[6]Despite the name, which has come to describe many of thefungibleblockchain tokens that have been created, cryptocurrencies are not considered to becurrenciesin the traditional sense, and varying legal treatments have been applied to them in various jurisdictions, including classification ascommodities,securities, and currencies. Cryptocurrencies are generally viewed as a distinct asset class in practice.[7][8][9]
The first cryptocurrency wasbitcoin, which was first released as open-source software in 2009. As of June 2023, there were more than 25,000other cryptocurrenciesin the marketplace, of which more than 40 had amarket capitalizationexceeding $1 billion.[10]As of April 2025, the cryptocurrency market capitalization was already estimated at $2.76 trillion.[11]
In 1983, AmericancryptographerDavid Chaumconceived of a type of cryptographicelectronic moneycalledecash.[12][13]Later, in 1995, he implemented it throughDigicash,[14]an early form of cryptographic electronic payments. Digicash required user software in order to withdraw notes from a bank and designate specific encrypted keys before they could be sent to a recipient. This allowed the digital currency to be untraceable by a third party.
In 1996, theNational Security Agencypublished a paper entitledHow to Make a Mint: The Cryptography of Anonymous Electronic Cash, describing a cryptocurrency system. The paper was first published in anMITmailing list (October 1996) and later (April 1997) inThe American Law Review.[15]
In 1998,Wei Daidescribed "b-money," an anonymous, distributed electronic cash system.[16]Shortly thereafter,Nick Szabodescribedbit gold.[17]Like bitcoin and other cryptocurrencies that would follow it, bit gold (not to be confused with the later gold-based exchange BitGold) was described as an electronic currency system that required users to complete aproof of workfunction with solutions being cryptographically put together and published.
In January 2009, bitcoin was created bypseudonymousdeveloperSatoshi Nakamoto. It usedSHA-256, a cryptographic hash function, in itsproof-of-workscheme.[18][19]In April 2011,Namecoinwas created as an attempt at forming a decentralizedDNS. In October 2011,Litecoinwas released, which usedscryptas its hash function instead of SHA-256.Peercoin, created in August 2012, used a hybrid of proof-of-work andproof-of-stake.[20]
Cryptocurrency has undergone several periods of growth and retraction, including severalbubblesand market crashes, such as in 2011, 2013–2014/15, 2017–2018, and 2021–2023.[21][22]
On 6 August 2014, the UK announced itsTreasuryhad commissioned a study of cryptocurrencies and what role, if any, they could play in the UK economy. The study was also to report on whether regulation should be considered.[23]Its final report was published in 2018,[24]and it issued a consultation on cryptoassets andstablecoinsin January 2021.[25]
In June 2021,El Salvadorbecame the first country to accept bitcoin aslegal tender, after theLegislative Assemblyhad voted 62–22 to pass a bill submitted by PresidentNayib Bukeleclassifying the cryptocurrency as such.[26]
In August 2021,Cubafollowed with Resolution 215 to recognize and regulate cryptocurrencies such as bitcoin.[27]
In September 2021, thegovernment of China, the single largest market for cryptocurrency, declared all cryptocurrency transactions illegal. This completed a crackdown on cryptocurrency that had previously banned the operation of intermediaries and miners within China.[28]
On 15 September 2022, the world's second largest cryptocurrency at that time,Ethereum, transitioned itsconsensus mechanismfromproof-of-work(PoW) toproof-of-stake(PoS) in an upgrade process known as "the Merge". According to the Ethereum Founder, the upgrade would cut both Ethereum's energy use and carbon-dioxide emissions by 99.9%.[29]
On 11 November 2022,FTX Trading Ltd., acryptocurrency exchange, which also operated a cryptohedge fund, and had been valued at $18 billion,[30]filedforbankruptcy.[31]The financial impact of the collapse extended beyond the immediate FTX customer base, as reported,[32]while, at aReutersconference, financial industry executives said that "regulators must step in to protect crypto investors."[33]Technology analyst Avivah Litan commented on the cryptocurrency ecosystem that "everything...needs to improve dramatically in terms of user experience, controls, safety, customer service."[34]
According to Jan Lansky, a cryptocurrency is a system that meets six conditions:[35]
In March 2018, the wordcryptocurrencywas added to theMerriam-Webster Dictionary.[36]
After the early innovation of bitcoin in 2008 and the earlynetwork effectgained by bitcoin, tokens, cryptocurrencies, and other digital assets that were not bitcoin became collectively known during the 2010s as alternative cryptocurrencies,[37][38][39]or "altcoins".[40]Sometimes the term "alt coins" was used,[41][42]or disparagingly, "shitcoins".[43]Paul Vigna ofThe Wall Street Journaldescribed altcoins in 2020 as "alternative versions of Bitcoin"[44]given its role as the model protocol for cryptocurrency designers. APolytechnic University of Cataloniathesis in 2021 used a broader description, including not only alternative versions of bitcoin but every cryptocurrency other than bitcoin. As of early 2020, there were more than 5,000 cryptocurrencies.
Altcoins often have underlying differences when compared to bitcoin. For example,Litecoinaims to process a block every 2.5 minutes, rather than bitcoin's 10 minutes which allows Litecoin to confirm transactions faster than bitcoin.[20]Another example isEthereum, which hassmart contractfunctionality that allows decentralized applications to be run on its blockchain.[45]Ethereum was the most used blockchain in 2020, according to Bloomberg News.[46]In 2016, it had the largest "following" of any altcoin, according to theNew York Times.[47]
Significant market price rallies across multiple altcoin markets are often referred to as an "altseason".[48][49]
Stablecoinsare cryptocurrencies designed to maintain a stable level ofpurchasing power.[50]Notably, these designs are not foolproof, as a number of stablecoins have crashed or lost theirpeg. For example, on 11 May 2022,Terra's stablecoin UST fell from $1 to 26 cents.[51][52]The subsequent failure ofTerraform Labsresulted in the loss of nearly $40B invested in the Terra and Luna coins.[53]In September 2022, South Korean prosecutors requested the issuance of anInterpol Red Noticeagainst the company's founder,Do Kwon.[54]In Hong Kong, the expected regulatory framework for stablecoins in 2023/24 is being shaped and includes a few considerations.[55]
Memecoinsare a category of cryptocurrencies that originated fromInternet memesor jokes. The most notable example isDogecoin, a memecoin featuring theShiba Inudog from theDogememe.[56]Memecoins are known for extreme volatility; for example, the record-high value for a Dogecoin was 73 cents, but that had plunged to 13 cents by mid-2024.[56]Scams are prolific among memecoins.[56]
Physical cryptocurrency coins have been made as promotional items and some have become collectibles.[57]Some of these have a private key embedded in them to access crypto worth a few dollars. There have also been attempts to issue bitcoin "bank notes".[58]
The term "physical bitcoin" is used in the finance industry when investment funds that hold crypto purchased from crypto exchanges put their crypto holdings in a specialised bank called a "custodian".[59]
These physical representations of cryptocurrency do not hold any value by themselves; these are only utilized for collectable purposes. For example, the first incarnation of the bitcoin Casascius, coins made of silver, brass or aluminum sometimes with gold plating, or Titan Bitcoin, which in silver or gold versions are sought after bynumismatists.[60]
Cryptocurrency is produced by an entire cryptocurrency system collectively, at a rate that is defined when the system is created and that is publicly stated. In centralized banking and economic systems such as the USFederal Reserve System, corporate boards or governments control the supply of currency.[citation needed]In the case of cryptocurrency, companies or governments cannot produce new units and have not so far provided backing for other firms, banks, or corporate entities that hold asset value measured in it. The underlying technical system upon which cryptocurrencies are based was created bySatoshi Nakamoto.[61]
Within aproof-of-worksystem such as bitcoin, the safety, integrity, and balance ofledgersare maintained by a community of mutually distrustful parties referred to asminers. Miners use their computers to help validate and timestamp transactions, adding them to the ledger in accordance with a particular timestamping scheme.[18]In aproof-of-stakeblockchain, transactions are validated by holders of the associated cryptocurrency, sometimes grouped together in stake pools.
Most cryptocurrencies are designed to gradually decrease the production of that currency, placing a cap on the total amount of that currency that will ever be in circulation.[62]Compared with ordinary currencies held by financial institutions or kept ascashon hand, cryptocurrencies can be more difficult forseizureby law enforcement.[3]
The validity of each cryptocurrency's coins is provided by ablockchain. A blockchain is a continuously growing list ofrecords, calledblocks, which are linked and secured using cryptography.[61][63]Each block typically contains ahashpointer as a link to a previous block,[63]atimestamp, and transaction data.[64]By design, blockchains are inherently resistant to modification of the data. A blockchain is "an open,distributed ledgerthat can record transactions between two parties efficiently and in a verifiable and permanent way".[65]For use as a distributed ledger, a blockchain is typically managed by apeer-to-peernetwork collectively adhering to a protocol for validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without the alteration of all subsequent blocks, which requires collusion of the network majority.
Blockchains aresecure by designand are an example of a distributed computing system with highByzantine fault tolerance.Decentralizedconsensus has therefore been achieved with a blockchain.[66]
Anodeis a computer that connects to a cryptocurrency network. The node supports the cryptocurrency's network through either relaying transactions, validation, or hosting a copy of the blockchain. In terms of relaying transactions, each network computer (node) has a copy of the blockchain of the cryptocurrency it supports. When a transaction is made, the node creating the transaction broadcasts details of the transaction using encryption to other nodes throughout the node network so that the transaction (and every other transaction) is known.
Node owners are either volunteers, those hosted by the organization or body responsible for developing the cryptocurrency blockchain network technology, or those who are enticed to host a node to receive rewards from hosting the node network.[67]
Cryptocurrencies use various timestamping schemes to "prove" the validity of transactions added to the blockchain ledger without the need for a trusted third party.
The first timestamping scheme invented was theproof-of-workscheme. The most widely used proof-of-work schemes are based on SHA-256 andscrypt.[20]
Some other hashing algorithms that are used for proof-of-work includeCryptoNote,Blake,SHA-3, andX11.
Another method is called theproof-of-stakescheme. Proof-of-stake is a method of securing a cryptocurrency network and achieving distributed consensus through requesting users to show ownership of a certain amount of currency. It is different from proof-of-work systems that run difficult hashing algorithms to validate electronic transactions. The scheme is largely dependent on the coin, and there is currently no standard form of it. Some cryptocurrencies use a combined proof-of-work and proof-of-stake scheme.[20]
On a blockchain,miningis the validation of transactions. For this effort, successful miners obtain new cryptocurrency as a reward. The reward decreasestransaction feesby creating a complementary incentive to contribute to the processing power of the network. The rate of generating hashes, which validate any transaction, has been increased by the use of specialized hardware such asFPGAsandASICsrunning complex hashing algorithms like SHA-256 andscrypt.[68]This arms race for cheaper-yet-efficient machines has existed since bitcoin was introduced in 2009.[68]Mining is measured byhash rate, typically in TH/s.[69]A 2023IMFworking paper found that crypto mining could generate 450 million tons of CO2emissions by 2027, accounting for 0.7 percent of global emissions, or 1.2 percent of the world total[70]
With more people entering the world of virtual currency, generating hashes for validation has become more complex over time, forcing miners to invest increasingly large sums of money to improve computing performance. Consequently, the reward for finding a hash has diminished and often does not justify the investment in equipment and cooling facilities (to mitigate the heat the equipment produces) and the electricity required to run them.[71]Popular regions for mining include those with inexpensive electricity, a cold climate, and jurisdictions with clear and conducive regulations. By July 2019, bitcoin's electricity consumption was estimated to be approximately 7 gigawatts, around 0.2% of the global total, or equivalent to the energy consumed nationally by Switzerland.[72]
Someminers pool resources, sharing theirprocessing powerover a network to split the reward equally, according to the amount of work they contributed to the probability of finding ablock. A "share" is awarded to members of the mining pool who present a valid partial proof-of-work.
As of February 2018[update], the Chinese government has halted trading of virtual currency, banned initial coin offerings, and shut down mining. Many Chinese miners have since relocated to Canada[73]and Texas.[74]One company is operating data centers for mining operations at Canadian oil and gas field sites due to low gas prices.[75]In June 2018,Hydro Quebecproposed to the provincial government to allocate 500 megawatts of power to crypto companies for mining.[76]According to a February 2018 report fromFortune, Iceland has become a haven for cryptocurrency miners in part because of its cheap electricity.[77]
In March 2018, the city ofPlattsburgh, New Yorkput an 18-monthmoratoriumon all cryptocurrency mining in an effort to preserve natural resources and the "character and direction" of the city.[78]In 2021,Kazakhstanbecame the second-biggest crypto-currency mining country, producing 18.1% of the globalexahashrate. The country built a compound containing 50,000 computers nearEkibastuz.[79]
An increase in cryptocurrency mining increased the demand forgraphics cards(GPU) in 2017.[80]The computing power of GPUs makes them well-suited to generating hashes. Popular favorites of cryptocurrency miners, such as Nvidia'sGTX 1060andGTX 1070graphics cards, as well as AMD's RX 570 and RX 580 GPUs, doubled or tripled in price – or were out of stock.[81]A GTX 1070 Ti, which was released at a price of $450, sold for as much as $1,100. Another popular card, the GTX 1060 (6 GB model), was released at anMSRPof $250 and sold for almost $500. RX 570 and RX 580 cards fromAMDwere out of stock for almost a year. Miners regularly buy up the entire stock of new GPUs as soon as they are available.[82]
Nvidiahas asked retailers to do what they can when it comes to selling GPUs to gamers instead of miners. Boris Böhles, PR manager for Nvidia in the German region, said: "Gamers come first for Nvidia."[83]
Numerous companies developed dedicated crypto-mining accelerator chips, capable of price-performance far higher than that of CPU orGPU mining. At one point,Intelmarketed its own brand of crypto accelerator chip, namedBlockscale.[84]
Acryptocurrency walletis a means of storing thepublic and private "keys"(address) or seed, which can be used to receive or spend the cryptocurrency.[85]With the private key, it is possible to write in the public ledger, effectively spending the associated cryptocurrency. With the public key, it is possible for others to send currency to the wallet.
There exist multiple methods of storing keys or seed in a wallet. These methods range from using paper wallets (which are public, private, or seed keys written on paper), to using hardware wallets (which are hardware to store your wallet information), to a digital wallet (which is a computer with software hosting your wallet information), to hosting your wallet using an exchange where cryptocurrency is traded, or by storing your wallet information on a digital medium such as plaintext.[86]
Bitcoin ispseudonymous, rather thananonymous; the cryptocurrency in a wallet is not tied to a person but rather to one or more specific keys (or "addresses").[87]Thereby, bitcoin owners are not immediately identifiable, but all transactions are publicly available in the blockchain.[88]Still,cryptocurrency exchangesare often required by law to collect the personal information of their users.[89]
Some cryptocurrencies, such asMonero,Zerocoin,Zerocash, andCryptoNote, implement additional measures to increase privacy, such as by usingzero-knowledge proofs.[90][91]
A recent 2020 study presented different attacks on privacy in cryptocurrencies. The attacks demonstrated how the anonymity techniques are not sufficient safeguards. In order to improve privacy, researchers suggested several different ideas, including new cryptographic schemes and mechanisms for hiding theIP addressof the source.[92]
Cryptocurrencies are used primarily outside banking and governmental institutions and are exchanged over the Internet.
Proof-of-work cryptocurrencies, such as bitcoin, offer block rewards incentives for miners. There has been an implicit belief that whether miners are paid by block rewards or transaction fees does not affect the security of the blockchain, but a study suggests that this may not be the case under certain circumstances.[93]
The rewards paid to miners increase the supply of the cryptocurrency. By making sure that verifying transactions is a costly business, the integrity of the network can be preserved as long as benevolent nodes control a majority of computing power. The verification algorithm requires a lot of processing power, and thus electricity, in order to make verification costly enough to accurately validate the public blockchain. Not only do miners have to factor in the costs associated with expensive equipment necessary to stand a chance of solving a hash problem, they must further consider the significant amount of electrical power in search of the solution. Generally, the block rewards outweigh electricity and equipment costs, but this may not always be the case.[94]
The current value, not the long-term value, of the cryptocurrency supports the reward scheme to incentivize miners to engage in costly mining activities.[95]In 2018, bitcoin's design caused a 1.4% welfare loss compared to an efficient cash system, while a cash system with 2% money growth has a minor 0.003% welfare cost. The main source for this inefficiency is the large mining cost, which is estimated to be US$360 million per year. This translates into users being willing to accept a cash system with an inflation rate of 230% before being better off using bitcoin as a means of payment. However, the efficiency of the bitcoin system can be significantly improved by optimizing the rate of coin creation and minimizing transaction fees. Another potential improvement is to eliminate inefficient mining activities by changing the consensus protocol altogether.[96]
Transaction fees (sometimes also referred to asminer feesorgas fees) for cryptocurrency depend mainly on thesupplyof network capacity at the time, versus thedemandfrom the currency holder for a faster transaction.[97]The ability for the holder to be allowed to set the fee manually often depends on the wallet software used, and centralexchanges for cryptocurrency(CEX) usually do not allow the customer to set a custom transaction fee for the transaction.[citation needed]Their wallet software, such asCoinbaseWallet, however, might support adjusting the fee.[98]
Select cryptocurrency exchanges have offered to let the user choose between different presets of transaction fee values during the currency conversion. One of those exchanges, namelyLiteBit, previously headquartered in the Netherlands, was forced to cease all operations on August 13th, 2023, "due to market changes and regulatory pressure".[99]
The "recommended fee" suggested by the network will often depend on the time of day (due to depending on network load).
ForEthereum, transaction fees differ by computational complexity, bandwidth use, and storage needs, while bitcoin transaction fees differ by transaction size and whether the transaction usesSegWit. In February 2023, the median transaction fee for Ether corresponded to $2.2845,[100]while for bitcoin it corresponded to $0.659.[101]
Some cryptocurrencies have no transaction fees, the most well-known example beingNano (XNO), and instead rely onclient-sideproof-of-work as the transaction prioritization and anti-spam mechanism.[102][103][104]
Cryptocurrency exchangesallow customers to trade cryptocurrencies[105]for other assets, such as conventionalfiat money, or to trade between different digital currencies.
Crypto marketplaces do not guarantee that an investor is completing a purchase or trade at the optimal price. As a result, as of 2020, it was possible toarbitrageto find the difference in price across several markets.[106]
Atomic swaps are a mechanism where one cryptocurrency can be exchanged directly for another cryptocurrency without the need for a trusted third party, such as an exchange.[107]
Jordan Kelley, founder ofRobocoin, launched the firstbitcoin ATMin the United States on 20 February 2014. The kiosk installed in Austin, Texas, is similar to bank ATMs but has scanners to read government-issued identification such as a driver's license or a passport to confirm users' identities.[108]
Aninitial coin offering(ICO) is a controversial means of raising funds for a new cryptocurrency venture. An ICO may be used by startups with the intention of avoiding regulation. However, securities regulators in many jurisdictions, including in the U.S. and Canada, have indicated that if a coin or token is an "investment contract" (e.g., under the Howey test, i.e., an investment of money with a reasonable expectation of profit based significantly on the entrepreneurial or managerial efforts of others), it is a security and is subject to securities regulation. In an ICO campaign, a percentage of the cryptocurrency (usually in the form of "tokens") is sold to early backers of the project in exchange for legal tender or other cryptocurrencies, often bitcoin or Ether.[109][110][111]
According toPricewaterhouseCoopers, four of the 10 biggest proposed initial coin offerings have usedSwitzerlandas a base, where they are frequently registered as non-profit foundations. The Swiss regulatory agencyFINMAstated that it would take a "balanced approach" to ICO projects and would allow "legitimate innovators to navigate the regulatory landscape and so launch their projects in a way consistent with national laws protecting investors and the integrity of the financial system." In response to numerous requests by industry representatives, a legislative ICO working group began to issue legal guidelines in 2018, which are intended to remove uncertainty from cryptocurrency offerings and to establish sustainable business practices.[112]
Themarket capitalizationof a cryptocurrency is calculated by multiplying the price by the number of coins in circulation. The total cryptocurrency market cap has historically been dominated by bitcoin accounting for at least 50% of the market cap value where altcoins have increased and decreased in market cap value in relation to bitcoin. Bitcoin's value is largely determined by speculation among other technological limiting factors known as blockchain rewards coded into the architecture technology of bitcoin itself. The cryptocurrency market cap follows a trend known as the "halving", which is when the block rewards received from bitcoin are halved due to technological mandated limited factors instilled into bitcoin which in turn limits the supply of bitcoin. As the date reaches near of a halving (twice thus far historically) the cryptocurrency market cap increases, followed by a downtrend.[113]
By June 2021, cryptocurrency had begun to be offered by some wealth managers in the US for401(k)s.[114][115][116]
Cryptocurrency prices are much more volatile than established financial assets such asstocks. For example, over one week in May 2022, bitcoin lost 20% of its value and Ethereum lost 26%, whileSolanaandCardanolost 41% and 35% respectively. The falls were attributed to warnings about inflation. By comparison, in the same week, theNasdaqtech stock index fell 7.6 per cent and theFTSE 100was 3.6 per cent down.[117]
In the longer term, of the10 leading cryptocurrenciesidentified by the total value of coins in circulation in January 2018, only four (bitcoin, Ethereum, Cardano andRipple(XRP)) were still in that position in early 2022.[118]The total value of all cryptocurrencies was $2 trillion at the end of 2021, but had halved nine months later.[119][120]TheWall Street Journalhas commented that the crypto sector has become "intertwined" with the rest of the capital markets and "sensitive to the same forces that drive tech stocks and other risk assets," such as inflation forecasts.[121]
There are alsocentralizeddatabases, outside of blockchains, that store crypto market data. Compared to the blockchain, databases perform fast as there is no verification process. Four of the most popular cryptocurrency market databases are CoinMarketCap, CoinGecko, BraveNewCoin, and Cryptocompare.[122]
According to Alan Feuer ofThe New York Times,libertariansandanarcho-capitalistswere attracted to the philosophical idea behind bitcoin. Early bitcoin supporterRoger Versaid: "At first, almost everyone who got involved did so for philosophical reasons. We saw bitcoin as a great idea, as a way to separate money from the state."[123]EconomistPaul Krugmanargues that cryptocurrencies like bitcoin are "something of a cult" based in "paranoid fantasies" of government power.[124]
David Golumbiasays that the ideas influencing bitcoin advocates emerge from right-wing extremist movements such as theLiberty Lobbyand theJohn Birch Societyand their anti-Central Bank rhetoric, or, more recently,Ron PaulandTea Party-style libertarianism.[125]Steve Bannon, who owns a "good stake" in bitcoin, sees cryptocurrency as a form of disruptive populism, taking control back from central authorities.[126]
Bitcoin's founder,Satoshi Nakamoto, supported the idea that cryptocurrencies go well with libertarianism. "It's very attractive to the libertarian viewpoint if we can explain it properly," Nakamoto said in 2008.[127]
According to theEuropean Central Bank, the decentralization of money offered by bitcoin has its theoretical roots in theAustrian school of economics, especially withFriedrich von Hayekin his bookDenationalisation of Money: The Argument Refined,[128]in which Hayek advocates a completefree marketin the production, distribution and management of money to end the monopoly ofcentral banks.[129][130]
The rise in the popularity of cryptocurrencies and their adoption by financial institutions has led some governments to assess whether regulation is needed to protect users. TheFinancial Action Task Force(FATF) has defined cryptocurrency-related services as "virtual asset service providers" (VASPs) and recommended that they be regulated with the samemoney laundering(AML) andknow your customer(KYC) requirements as financial institutions.[131]
In May 2020, the Joint Working Group on interVASP Messaging Standards published "IVMS 101", a universal common language for communication of required originator and beneficiary information between VASPs. The FATF and financial regulators were informed as the data model was developed.[132]
In June 2020, FATF updated its guidance to include the "Travel Rule" for cryptocurrencies, a measure which mandates that VASPs obtain, hold, and exchange information about the originators and beneficiaries of virtual asset transfers.[133]Subsequent standardized protocol specifications recommended usingJSONfor relaying data between VASPs and identity services. As of December 2020, the IVMS 101 data model has yet to be finalized and ratified by the three global standard setting bodies that created it.[134]
The European Commission published a digital finance strategy in September 2020. This included a draft regulation on Markets in Crypto-Assets (MiCA), which aimed to provide a comprehensive regulatory framework for digital assets in the EU.[135][136]
On 10 June 2021, theBasel Committee on Banking Supervisionproposed that banks that held cryptocurrency assets must set aside capital to cover all potential losses. For instance, if a bank were to hold bitcoin worth $2 billion, it would be required to set aside enough capital to cover the entire $2 billion. This is a more extreme standard than banks are usually held to when it comes to other assets. However, this is a proposal and not a regulation.
The IMF is seeking a coordinated, consistent and comprehensive approach to supervising cryptocurrencies.Tobias Adrian, the IMF's financial counsellor and head of its monetary and capital markets department said in a January 2022 interview that "Agreeing global regulations is never quick. But if we start now, we can achieve the goal of maintaining financial stability while also enjoying the benefits which the underlying technological innovations bring,"[137]
In May 2024, 15 years after the advent of the first blockchain, bitcoin, theUS Congressadvanced a bill to the fullHouse of Representativesto provide regulatory clarity for digital assets. TheFinancial Innovation and Technology for the 21st Century Act, which defines responsibilities between various US agencies, notably between theCommodity Futures Trading Commission(CFTC) for decentralized blockchains and theSecurities and Exchange Commission(SEC) for blockchains that are functional but not decentralized.Stablecoinsare excluded from both CFTC and SEC regulation in this bill, "except for fraud and certain activities by registered firms."[138]
In September 2017, China bannedICOsto causeabnormal returnfrom cryptocurrency decreasing during announcement window. The liquidity changes by banning ICOs in China was temporarily negative while the liquidity effect became positive after news.[139]
On 18 May 2021, China banned financial institutions and payment companies from being able to provide cryptocurrency transaction related services.[140]This led to a sharp fall in the price of the biggestproof of workcryptocurrencies. For instance,bitcoinfell 31%,Ethereumfell 44%,Binance Coinfell 32% andDogecoinfell 30%.[141]Proof of work mining was the next focus, with regulators in popular mining regions citing the use of electricity generated from highly polluting sources such as coal to create bitcoin and Ethereum.[142]
In September 2021, the Chinese government declared all cryptocurrency transactions of any kind illegal, completing its crackdown on cryptocurrency.[28]
In April 2024,TVNZ's1Newsreported that theCook Islandsgovernment was proposing legislation that would allow "recovery agents" to use various means including hacking to investigate or find cryptocurrency that may have been used for illegal means or is the "proceeds of crime." The Tainted Cryptocurrency Recovery Bill was drafted by two lawyers hired by US-based debt collection company Drumcliffe. The proposed legislation was criticised by Cook Islands Crown Law's deputy solicitor general David Greig, who described it as "flawed" and said that some provisions were "clearly unconstitutional". The Cook Islands Financial Services Development Authority described Drumcliffe's involvement as a conflict of interest.[143]
Similar criticism was echoed byAuckland University of Technologycryptocurrency specialist and senior lecturer Jeff Nijsse andUniversity of Otagopolitical scientistProfessorRobert Patman, who described it as government overreach and described it as inconsistent with international law. Since the Cook Islands is anassociated statethat is part of theRealm of New Zealand, Patman said that the law would have "implications for New Zealand's governance arrangements." A spokesperson forNew Zealand Foreign MinisterWinston Petersconfirmed that New Zealand officials were discussing the legislation with their Cook Islands counterparts.Cook Islands Prime MinisterMark Browndefended the legislation as part of the territory's fight against international cybercrime.[143]
On 9 June 2021,El Salvadorannounced that it will adoptbitcoinas legal tender, becoming the first country to do so.[144]
The EU defines crypto assets as "a digital representation of a value or of a right that is able to be transferred and stored electronically using distributed ledger technology or similar technology."[145]The EU regulation Markets in Crypto-Assets (MiCA) covering asset-referenced tokens (ARTs) and electronic money tokens (EMTs) (also known as stablecoins) came into force on 30 June 2024. As of 17 January 2025, theEuropean Securities and Markets Authority(ESMA) issued guidance to crypto-asset service providers (CASPs) allowing them to maintain crypto-asset services for non-compliant ARTs and EMTs until the end of March 2025.[146][147]
The rest of MiCA came into force as of 30 December 2024, covering crypto-assets other than ART and EMT and CASPs. MiCA excludes crypto-assets if they qualify as financial instruments according to ESMA guidelines published on 17 December 2024 as well as crypto-assets that are unique and not fungible with other crypto-assets.[148][149]
At present, India neither prohibits nor allows investment in the cryptocurrency market. In 2020, the Supreme Court of India had lifted the ban on cryptocurrency, which was imposed by the Reserve Bank of India.[150][151][152][153]Since then, an investment in cryptocurrency is considered legitimate, though there is still ambiguity about the issues regarding the extent and payment of tax on the income accrued thereupon and also its regulatory regime. But it is being contemplated that the Indian Parliament will soon pass a specific law to either ban or regulate the cryptocurrency market in India.[154]Expressing his public policy opinion on the Indian cryptocurrency market to a well-known online publication, a leadingpublic policylawyer and Vice President ofSAARCLAW(South Asian Association for Regional Co-operation in Law)Hemant Batrahas said that the "cryptocurrency market has now become very big with involvement of billions of dollars in the market hence, it is now unattainable and irreconcilable for the government to completely ban all sorts of cryptocurrency and its trading and investment".[155]He mooted regulating the cryptocurrency market rather than completely banning it. He favoured followingIMFandFATFguidelines in this regard.
South Africa, which has seen a large number of scams related to cryptocurrency, is said to be putting a regulatory timeline in place that will produce a regulatory framework.[156]The largest scam occurred in April 2021, where the two founders of an African-based cryptocurrency exchange called Africrypt, Raees Cajee and Ameer Cajee, disappeared with $3.8 billion worth ofbitcoin.[157]Additionally,Mirror Trading Internationaldisappeared with $170 million worth of cryptocurrency in January 2021.[157]
In March 2021, South Korea implemented new legislation to strengthen their oversight of digital assets. This legislation requires all digital asset managers, providers and exchanges to be registered with the Korea Financial Intelligence Unit in order to operate in South Korea.[158]Registering with this unit requires that all exchanges are certified by the Information Security Management System and that they ensure all customers have real name bank accounts. It also requires that the CEO and board members of the exchanges have not been convicted of any crimes and that the exchange holds sufficient levels of deposit insurance to cover losses arising from hacks.[158]
Switzerland was one of the first countries to implement the FATF's Travel Rule. FINMA, the Swiss regulator, issued its own guidance to VASPs in 2019. The guidance followed the FATF's Recommendation 16, however with stricter requirements. According to FINMA's[159]requirements, VASPs need to verify the identity of the beneficiary of the transfer.
On 30 April 2021, theCentral Bank of the Republic of Turkeybanned the use of cryptocurrencies andcryptoassetsfor making purchases on the grounds that the use of cryptocurrencies for such payments poses significant transaction risks.[160]
In the United Kingdom, as of 10 January 2021, all cryptocurrency firms, such as exchanges, advisors and professionals that have either a presence, market product or provide services within the UK market must register with theFinancial Conduct Authority. Additionally, on 27 June 2021, the financial watchdog demanded thatBinancecease all regulated activities in the UK.[161]
The incoming Labour government confirmed in November 2024 that it will proceed with the regulation of cryptoassets and new UK requirements are expected to come into force in 2026.[162]
In 2021, 17 states in the US passed laws and resolutions concerning cryptocurrency regulation.[163]This led the Securities and Exchange Commission to start considering what steps to take. On 8 July 2021,Senator Elizabeth Warren, part of theSenate Banking Committee, wrote to the chairman of the SEC and demanded answers on cryptocurrency regulation due to the increase in cryptocurrency exchange use and the danger this posed to consumers. On 5 August 2021, the chairman,Gary Gensler, responded to Warren's letter and called for legislation focused on "crypto trading, lending and DeFi platforms," because of how vulnerable investors could be when they traded on crypto trading platforms without a broker. He also argued that many tokens in the crypto market may be unregistered securities without required disclosures or market oversight. Additionally, Gensler did not hold back in his criticism of stablecoins. These tokens, which are pegged to the value of fiat currencies, may allow individuals to bypass important public policy goals related to traditional banking and financial systems, such as anti-money laundering, tax compliance, and sanctions.[164]
On 19 October 2021, the first bitcoin-linked exchange-traded fund (ETF) fromProSharesstarted trading on the NYSE under the ticker "BITO."ProSharesCEO Michael L. Sapir said the ETF would expose bitcoin to a wider range of investors without the hassle of setting up accounts with cryptocurrency providers. Ian Balina, the CEO of Token Metrics, stated that SEC approval of the ETF was a significant endorsement for the crypto industry because many regulators globally were not in favor of crypto, and retail investors were hesitant to accept crypto. This event would eventually open more opportunities for new capital and new people in this space.[165]
TheDepartment of the Treasury, on 20 May 2021, announced that it would require any transfer worth $10,000 or more to be reported to theInternal Revenue Servicesince cryptocurrency already posed a problem where illegal activity like tax evasion was facilitated broadly. This release from the IRS was a part of efforts to promote better compliance and consider more severe penalties for tax evaders.[166]
On 17 February 2022, theDepartment of Justicenamed Eun Young Choi as the first director of a National Cryptocurrency Enforcement Team to help identify and deal with misuse of cryptocurrencies and other digital assets.[167]
The Biden administration faced a dilemma as it tried to develop regulations for the cryptocurrency industry. On one hand, officials were hesitant to restrict a growing industry. On the other hand, they were committed to preventing illegal cryptocurrency transactions. To reconcile these conflicting goals, on 9 March 2022, Biden issued an executive order.[168]Followed this, on 16 September 2022, the Comprehensive Framework for Responsible Development of Digital Assets document was released[169]to support development of cryptocurrencies and restrict their illegal use. The executive order included all digital assets, but cryptocurrencies posed both the greatest security risks and potential economic benefits. Though this might not address all of the challenges in crypto industry, it was a significant milestone in the US cryptocurrency regulation history.[170]
In February 2023, the SEC ruled that cryptocurrency exchangeKraken's estimated $42 billion in staked assets globally operated as an illegal securities seller. The company agreed to a $30 million settlement with the SEC and to cease selling its staking service in the US. The case would impact other major crypto exchanges operating staking programs.[171]
On 23 March 2023, the SEC issued an alert to investors stating that firms offering crypto asset securities might not be complying with US laws. The SEC argued that unregistered offerings of crypto asset securities might not include important information.[172]
On 23 January 2025, President Donald Trump signedExecutive Order 14178,Strengthening American Leadership in Digital Financial Technology[173]revokingExecutive Order 14067of 9 March 2022,Ensuring Responsible Development of Digital Assetsand the Department of the Treasury'sFramework for International Engagement on Digital Assetsof 7 July 2022.
In addition the order prohibits the establishment, issuance or promotion ofCentral bank digital currencyand establishes a group tasked with proposing a federal regulatory framework for digital assets within 180 days.[174]
Thelegal status of cryptocurrenciesvaries substantially from country to country and is still undefined or changing in many of them. At least one study has shown that broad generalizations about the use of bitcoin in illicit finance are significantly overstated and that blockchain analysis is an effective crime fighting and intelligence gathering tool.[175]While some countries have explicitly allowed their use and trade,[176]others have banned or restricted it. According to theLibrary of Congressin 2021,
an "absolute ban" on trading or using cryptocurrencies applies in 9 countries:
Algeria, Bangladesh, Bolivia, China, Egypt, Iraq, Morocco, Nepal, and the United Arab Emirates. An "implicit ban" applies in another 39 countries or regions, which include: Bahrain, Benin, Burkina Faso, Burundi, Cameroon, Chad, Cote d’Ivoire, the Dominican Republic, Ecuador, Gabon, Georgia, Guyana, Indonesia, Iran, Jordan, Kazakhstan, Kuwait, Lebanon, Lesotho, Macau, Maldives, Mali, Moldova, Namibia, Niger, Nigeria, Oman, Pakistan, Palau, Republic of Congo, Saudi Arabia, Senegal, Tajikistan, Tanzania, Togo, Turkey, Turkmenistan, Qatar and Vietnam.[177]In the United States and Canada, state and provincial securities regulators, coordinated through theNorth American Securities Administrators Association, are investigating "Bitcoin scams" andICOsin 40 jurisdictions.[178]
Various government agencies, departments, and courts have classified bitcoin differently.China Central Bankbanned the handling of bitcoins by financial institutions inChinain early 2014.
In Russia, though owning cryptocurrency is legal, its residents are only allowed to purchase goods from other residents using theRussian rublewhile nonresidents are allowed to use foreign currency.[179]Regulations and bans that apply to bitcoin probably extend to similar cryptocurrency systems.[180]
In August 2018, theBank of Thailandannounced its plans to create its own cryptocurrency, the Central Bank Digital Currency (CBDC).[181]
Cryptocurrency advertisements have been banned on the following platforms:
On 25 March 2014, the United StatesInternal Revenue Service(IRS) ruled that bitcoin will be treated as property for tax purposes. Therefore, virtual currencies are considered commodities subject to capital gains tax.[189]
As the popularity and demand for online currencies has increased since the inception of bitcoin in 2009,[190]so have concerns that such an unregulated person to person global economy that cryptocurrencies offer may become a threat to society. Concerns abound that altcoins may become tools for anonymous web criminals.[191]
Cryptocurrency networks display a lack of regulation that has been criticized as enabling criminals who seek to evade taxes andlaunder money. Money laundering issuesare also present in regular bank transfers, however with bank-to-bank wire transfers for instance, the account holder must at leastprovide a proven identity.
Transactions that occur through the use and exchange of these altcoins are independent from formal banking systems, and therefore can make tax evasion simpler for individuals. Since charting taxable income is based upon what a recipient reports to the revenue service, it becomes extremely difficult to account for transactions made using existing cryptocurrencies, a mode of exchange that is complex and difficult to track.[191]
Systems of anonymity that most cryptocurrencies offer can also serve as a simpler means to launder money. Rather than laundering money through an intricate net of financial actors and offshore bank accounts, laundering money through altcoins can be achieved through anonymous transactions.[191]
Cryptocurrency makes legal enforcement against extremist groups more complicated, which consequently strengthens them.[192]White supremacistRichard Spencerwent as far as to declare bitcoin the "currency of the alt-right".[193]
In February 2014, the world's largest bitcoin exchange,Mt. Gox, declaredbankruptcy. Likely due to theft, the company claimed that it had lost nearly 750,000 bitcoins belonging to their clients. This added up to approximately 7% of all bitcoins in existence, worth a total of $473 million. Mt. Gox blamed hackers, who had exploited thetransaction malleability problemsin the network. The price of a bitcoin fell from a high of about $1,160 in December to under $400 in February.[194]
On 21 November 2017,Tetherannounced that it had been hacked, losing $31 million in USDT from its core treasury wallet.[195]
On 7 December 2017, Slovenian cryptocurrency exchangeNicehashreported that hackers had stolen over $70 million using a hijacked company computer.[196]
On 19 December 2017, Yapian, the owner of South Korean exchange Youbit, filed for bankruptcy after suffering two hacks that year.[197][198]Customers were still granted access to 75% of their assets.
In May 2018,Bitcoin Goldhad its transactions hijacked and abused by unknown hackers.[199]Exchanges lost an estimated $18m and bitcoin Gold was delisted from Bittrex after it refused to pay its share of the damages.
On 13 September 2018, Homero Josh Garza was sentenced to 21 months of imprisonment, followed by three years of supervised release.[200]Garza had founded the cryptocurrency startups GAW Miners and ZenMiner in 2014, acknowledged in aplea agreementthat the companies were part of apyramid scheme, and pleaded guilty towire fraudin 2015. The SEC separately brought a civil enforcement action in the US against Garza, who was eventually ordered to pay a judgment of $9.1 million plus $700,000 in interest. The SEC's complaint stated that Garza, through his companies, had fraudulently sold "investment contracts representing shares in the profits they claimed would be generated" from mining.[201]
In January 2018, Japanese exchangeCoincheckreported that hackers had stolen cryptocurrency worth $530 million.[202]
In June 2018, South Korean exchange Coinrail was hacked, losing over $37 million in crypto.[203]The hack worsened a cryptocurrency selloff by an additional $42 billion.[204]
On 9 July 2018, the exchange Bancor, whose code and fundraising had been subjects of controversy, had $23.5 million in crypto stolen.[205]
A 2020 EU report found that users had lost crypto-assets worth hundreds of millions of US dollars in security breaches at exchanges and storage providers. Between 2011 and 2019, reported breaches ranged from four to twelve a year. In 2019, more than a billion dollars worth of cryptoassets was reported stolen. Stolen assets "typically find their way to illegal markets and are used to fund further criminal activity".[206]
According to a 2020 report produced by theUnited States Attorney General's Cyber-Digital Task Force, three categories make up the majority of illicit cryptocurrency uses: "(1) financial transactions associated with the commission of crimes; (2)money launderingand theshielding of legitimate activity from tax, reporting, or other legal requirements; or (3) crimes, such as theft, directly implicating the cryptocurrency marketplace itself." The report concluded that "for cryptocurrency to realize its truly transformative potential, it is imperative that these risks be addressed" and that "the government has legal and regulatory tools available at its disposal to confront the threats posed by cryptocurrency's illicit uses".[207][208]
According to the UK 2020 national risk assessment—a comprehensive assessment of money laundering and terrorist financing risk in the UK—the risk of using cryptoassets such as bitcoin for money laundering and terrorism financing is assessed as "medium" (from "low" in the previous 2017 report).[209]Legal scholars suggested that the money laundering opportunities may be more perceived than real.[210]Blockchain analysiscompany Chainalysis concluded that illicit activities likecybercrime,money launderingandterrorism financingmade up only 0.15% of all crypto transactions conducted in 2021, representing a total of $14 billion.[211][212][213]
In December 2021, Monkey Kingdom, a NFT project based in Hong Kong, lost US$1.3 million worth of cryptocurrencies via a phishing link used by the hacker.[214]
On November 2, 2023,Sam Bankman-Friedwas pronounced guilty on seven counts of fraud related toFTX.[215]Federal criminal court sentencing experts speculated on the potential amount of prison time likely to be meted out.[216][217][218]On March 28, 2024, the court sentenced Bankman-Fried to 25 years in prison.[219]
According to blockchain data companyChainalysis, criminals launderedUS$8,600,000,000 worth of cryptocurrency in 2021, up by 30% from the previous year.[220]The data suggests that rather than managing numerous illicit havens, cybercriminals make use of a small group of purpose built centralized exchanges for sending and receiving illicit cryptocurrency. In 2021, those exchanges received 47% of funds sent by crime linked addresses.[221]Almost $2.2bn worth of cryptocurrencies was embezzled from DeFi protocols in 2021, which represents 72% of all cryptocurrency theft in 2021.
According toBloombergand theNew York Times, Federation Tower, a two skyscraper complex in the heart of Moscow City, is home to many cryptocurrency businesses under suspicion of facilitating extensive money laundering, including accepting illicit cryptocurrency funds obtained through scams, darknet markets, and ransomware.[222]Notable businesses includeGarantex,[223]Eggchange, Cashbank, Buy-Bitcoin, Tetchange, Bitzlato, and Suex, which was sanctioned by the U.S. in 2021. Bitzlato founder and owner Anatoly Legkodymov was arrested following money-laundering charges by the United States Department of Justice.[224]
Dark money has also been flowing into Russia through a dark web marketplace called Hydra, which is powered by cryptocurrency, and enjoyed more than $1 billion in sales in 2020, according to Chainalysis.[225]The platform demands that sellers liquidate cryptocurrency only through certain regional exchanges, which has made it difficult for investigators to trace the money.
Almost 74% of ransomware revenue in 2021 — over $400 million worth of cryptocurrency — went to software strains likely affiliated with Russia, where oversight is notoriously limited.[222]However, Russians are also leaders in the benign adoption of cryptocurrencies, as the ruble is unreliable, andPresident Putinfavours the idea of "overcoming the excessive domination of the limited number of reserve currencies."[226]
In 2022, RenBridge - an unregulated alternative to exchanges for transferring value between blockchains - was found to be responsible for the laundering of at least $540 million since 2020. It is especially popular with people attempting to launder money from theft. This includes a cyberattack on Japanese crypto exchange Liquid that has been linked toNorth Korea.[227]
Properties of cryptocurrencies gave them popularity in applications such as a safe haven in banking crises and means of payment, which also led to the cryptocurrency use in controversial settings in the form ofonline black markets, such asSilk Road.[191]The original Silk Road was shut down in October 2013 and there have been two more versions in use since then. In the year following the initial shutdown of Silk Road, the number of prominent dark markets increased from four to twelve, while the amount of drug listings increased from 18,000 to 32,000.[191]
Darknet markets present challenges in regard to legality. Cryptocurrency used in dark markets are not clearly or legally classified in almost all parts of the world. In the US, bitcoins are regarded as "virtual assets".[citation needed]This type of ambiguous classification puts pressure on law enforcement agencies around the world to adapt to the shifting drug trade of dark markets.[228][unreliable source?]
Various studies have found that crypto-trading is rife withwash trading. Wash trading is a process, illegal in some jurisdictions, involving buyers and sellers being the same person or group, and may be used to manipulate the price of a cryptocurrency or inflate volume artificially. Exchanges with higher volumes can demand higher premiums from token issuers.[229]A study from 2019 concluded that up to 80% of trades on unregulated cryptocurrency exchanges could be wash trades.[229]A 2019 report by Bitwise Asset Management claimed that 95% of all bitcoin trading volume reported on major website CoinMarketCap had been artificially generated, and of 81 exchanges studied, only 10 provided legitimate volume figures.[230]
In 2022, cryptocurrencies attracted attention when Western nations imposed severe economic sanctions on Russia in the aftermath ofits invasion of Ukrainein February. However, American sources warned in March that some crypto-transactions could potentially be used to evade economic sanctions against Russia and Belarus.[231]
In April 2022, the computer programmerVirgil Griffithreceived a five-year prison sentence in the US for attending a Pyongyang cryptocurrency conference, where he gave a presentation on blockchains which might be used for sanctions evasion.[232]
TheBank for International Settlementssummarized several criticisms of cryptocurrencies in Chapter V of their 2018 annual report. The criticisms include the lack of stability in their price, the high energy consumption, high and variable transactions costs, the poor security and fraud at cryptocurrency exchanges, vulnerability to debasement (from forking), and the influence of miners.[233][234][235]
Cryptocurrencies have been compared toPonzi schemes,pyramid schemes[236]andeconomic bubbles,[237]such ashousing market bubbles.[238]Howard MarksofOaktree Capital Managementstated in 2017 that digital currencies were "nothing but an unfounded fad (or perhaps even a pyramid scheme), based on a willingness to ascribe value to something that has little or none beyond what people will pay for it", and compared them to thetulip mania(1637),South Sea Bubble(1720), anddot-com bubble(1999), which all experienced profound price booms and busts.[239]
Regulators in several countries have warned against cryptocurrency and some have taken measures to dissuade users.[240]However, research in 2021 by the UK's financial regulator suggests such warnings either went unheard, or were ignored. Fewer than one in 10 potential cryptocurrency buyers were aware of consumer warnings on theFCAwebsite, and 12% of crypto users were not aware that their holdings were not protected bystatutory compensation.[241][242]Of 1,000 respondents between the ages of eighteen and forty, almost 70% wrongly assumed cryptocurrencies were regulated, 75% of younger crypto investors claimed to be driven by competition with friends and family, 58% said that social media enticed them to make high risk investments.[243]The FCA recommends making use of its warning list, which flags unauthorized financial firms.[244]
Many banks do not offer virtual currency services themselves and can refuse to do business with virtual currency companies.[245]In 2014, Gareth Murphy, a senior banking officer, suggested that the widespread adoption of cryptocurrencies may lead to too much money beingobfuscated, blinding economists who would use such information to better steer the economy.[246]While traditional financial products have strong consumer protections in place, there is no intermediary with the power to limit consumer losses if bitcoins are lost or stolen. One of the features cryptocurrency lacks in comparison to credit cards, for example, is consumer protection against fraud, such aschargebacks.
The French regulatorAutorité des marchés financiers(AMF) lists 16 websites of companies that solicit investment in cryptocurrency without being authorized to do so in France.[247]
An October 2021 paper by theNational Bureau of Economic Researchfound that bitcoin suffers from systemic risk as the top 10,000 addresses control about one-third of all bitcoin in circulation.[248]It is even worse for miners, with 0.01% controlling 50% of the capacity. According to researcher Flipside Crypto, less than 2% of anonymous accounts control 95% of all available bitcoin supply.[249]This is considered risky as a great deal of the market is in the hands of a few entities.
A paper by John Griffin, a finance professor at theUniversity of Texas, and Amin Shams, a graduate student found that in 2017 the price of bitcoin had been substantially inflated using another cryptocurrency, Tether.[250]
Roger Lowenstein, author of "Bank of America: The Epic Struggle to Create the Federal Reserve," says in a New York Times story that FTX will face over $8 billion in claims.[251]
Non-fungible tokens(NFTs) are digital assets that represent art, collectibles, gaming, etc. Like crypto, their data is stored on the blockchain. NFTs are bought and traded using cryptocurrency. The Ethereum blockchain was the first place where NFTs were implemented, but now many other blockchains have created their own versions of NFTs.
According to Vanessa Grellet, renowned panelist in blockchain conferences,[252]there was an increasing interest from traditionalstock exchangesin crypto-assets at the end of the 2010s, while crypto-exchanges such asCoinbasewere gradually entering the traditionalfinancial markets. This convergence marked a significant trend where conventional financial actors were adopting blockchain technology to enhance operational efficiency, while the crypto world introduced innovations likeSecurity Token Offering(STO), enabling new ways offundraising. Tokenization, turning assets such asreal estate,investment funds, andprivate equityinto blockchain-based tokens, had the potential to make traditionally illiquid assets more accessible to investors. Despite the regulatory risks associated with such developments, major financial institutions, includingJPMorgan Chase, were actively working on blockchain initiatives, exemplified by the creation of Quorum, a private blockchain platform.[253]
As the first big Wall Street bank to embrace cryptocurrencies,Morgan Stanleyannounced on 17 March 2021 that they will be offering access to bitcoin funds for their wealthy clients through three funds which enable bitcoin ownership for investors with an aggressive risk tolerance.[254]BNY Mellon on 11 February 2021 announced that it would begin offering cryptocurrency services to its clients.[255]
On 20 April 2021,[256]Venmoadded support to its platform to enable customers to buy, hold and sell cryptocurrencies.[257]
In October 2021, financial services companyMastercardannounced it is working with digital asset managerBakkton a platform that would allow any bank or merchant on the Mastercard network to offer cryptocurrency services.[258]
Mining forproof-of-workcryptocurrencies requires enormous amounts of electricity and consequently comes with a largecarbon footprintdue to causinggreenhouse gas emissions.[259]Proof-of-work blockchains such as bitcoin,Ethereum,Litecoin, andMonerowere estimated to have added between 3 million and 15 million tons ofcarbon dioxide (CO2) to the atmospherein the period from 1 January 2016 to 30 June 2017.[260]By November 2018, bitcoin was estimated to have an annualenergy consumptionof 45.8TWh, generating 22.0 to 22.9 million tons of CO2, rivalling nations likeJordanandSri Lanka.[261]By the end of 2021, bitcoin was estimated to produce 65.4 million tons of CO2, as much asGreece,[262]and consume between 91 and 177 terawatt-hours annually.[263][264]
Critics have also identified a largeelectronic wasteproblem in disposing ofmining rigs.[265]Mining hardware is improving at a fast rate, quickly resulting in older generations of hardware.[266]
Bitcoin is the least energy-efficient cryptocurrency, using 707.6 kilowatt-hours of electricity per transaction.[267]
Before June 2021, China was the primary location for bitcoin mining. However, due to concerns over power usage and other factors, China forced out bitcoin operations, at least temporarily. As a result, the United States promptly emerged as the top global leader in the industry. An example of a gross amount of electronic waste associated with bitcoin mining operations in the US is a facility that located in Dalton, Georgia which is consuming nearly the same amount of electricity as the combined power usage of 97,000 households in its vicinity. Another example is that Riot Platforms operates a bitcoin mining facility in Rockdale, Texas, which consumes approximately as much electricity as the nearby 300,000 households. This makes it the most energy-intensive bitcoin mining operation in the United States.[268]
The world's second-largest cryptocurrency, Ethereum, uses 62.56 kilowatt-hours of electricity per transaction.[269]XRPis the world's most energy efficient cryptocurrency, using 0.0079 kilowatt-hours of electricity per transaction.[270]
Although the biggest PoW blockchains consume energy on the scale of medium-sized countries, the annual power demand from proof-of-stake (PoS) blockchains is on a scale equivalent to a housing estate.The Timesidentified six "environmentally friendly" cryptocurrencies:Chia,IOTA,Cardano,Nano, Solarcoin and Bitgreen.[271]Academics and researchers have used various methods for estimating the energy use and energy efficiency of blockchains. A study of the six largest proof-of-stake networks in May 2021 concluded:
In terms of annual consumption (kWh/yr), the figures were: Polkadot (70,237),Tezos(113,249),Avalanche(489,311),Algorand(512,671), Cardano (598,755) and Solana (1,967,930). This equates to Polkadot consuming 7 times the electricity of an average U.S. home, Cardano 57 homes and Solana 200 times as much. The research concluded that PoS networks consumed 0.001% the electricity of the bitcoin network.[272]University College London researchers reached a similar conclusion.[273]
Variable renewable energypower stations could invest in bitcoin mining to reducecurtailment,hedgeelectricity price risk, stabilize the grid, increase theprofitability of renewable energypower stations and therefore acceleratetransition to sustainable energy.[274][275][276][277][278]
There are also purely technical elements to consider. For example, technological advancement in cryptocurrencies such as bitcoin result in high up-front costs to miners in the form of specializedhardwareandsoftware.[279]Cryptocurrency transactions are normally irreversible after a number of blocks confirm the transaction. Additionally, cryptocurrency private keys can be permanently lost from local storage due to malware, data loss or the destruction of the physical media. This precludes the cryptocurrency from being spent, resulting in its effective removal from the markets.[280]
In September 2015, the establishment of thepeer-reviewedacademic journalLedger(ISSN2379-5980) was announced. It covers studies of cryptocurrencies and related technologies, and is published by theUniversity of Pittsburgh.[281]
The journal encourages authors todigitally signafile hashof submitted papers, which will then betimestampedinto the bitcoinblockchain. Authors are also asked to include a personal bitcoin address in the first page of their papers.[282][283]
A number ofaid agencieshave started accepting donations in cryptocurrencies, includingUNICEF.[284]Christopher Fabian, principal adviser at UNICEF Innovation, said the children's fund would uphold donor protocols, meaning that people making donations online would have to pass checks before they were allowed to deposit funds.[285][286]
However, in 2021, there was a backlash against donations in bitcoin because of the environmental emissions it caused. Some agencies stopped accepting bitcoin and others turned to "greener" cryptocurrencies.[287]TheU.S. arm of Greenpeacestopped accepting bitcoin donations after seven years. It said: "As the amount of energy needed to run bitcoin became clearer, this policy became no longer tenable."[288]
In 2022, theUkrainian governmentraised overUS$10,000,000 worth of aid through cryptocurrency following the2022 Russian invasion of Ukraine.[289]
Bitcoinhas been characterized as aspeculative bubbleby eightwinners of the Nobel Memorial Prize in Economic Sciences:Paul Krugman,[290]Robert J. Shiller,[291]Joseph Stiglitz,[292]Richard Thaler,[293]James Heckman,[294]Thomas Sargent,[294]Angus Deaton,[294]andOliver Hart;[294]and by central bank officials includingAlan Greenspan,[295]Agustín Carstens,[296]Vítor Constâncio,[297]andNout Wellink.[298]
InvestorsWarren BuffettandGeorge Soroshave respectively characterized it as a "mirage"[299]and a "bubble";[300]while business executivesJack MaandJP Morgan ChaseCEOJamie Dimonhave called it a "bubble"[301]and a "fraud",[302]respectively, although Jamie Dimon later said he regretted dubbing bitcoin a fraud.[303]BlackRockCEOLaurence D. Finkcalled bitcoin an "index ofmoney laundering".[304]
In June 2022, business magnateBill Gatessaid that cryptocurrencies are "100% based ongreater fool theory".[305]
Legal scholars criticize the lack of regulation, which hinders conflict resolution when crypto assets are at the center of a legal dispute, for example a divorce or an inheritance. In Switzerland, jurists generally deny that cryptocurrencies are objects that fall underproperty law, as cryptocurrencies do not belong to any class of legally defined objects (Typenzwang, the legalnumerus clausus). Therefore, it is debated whether anybody could even be sued forembezzlementof cryptocurrency if he/she had access to someone's wallet. However, in thelaw of obligationsandcontract law, any kind of object would be legally valid, but the object would have to be tied to an identifiedcounterparty. However, as the more popular cryptocurrencies can be freely and quickly exchanged into legal tender, they are financial assets and have to be taxed and accounted for as such.[306][307]
In 2018, an increase in crypto-related suicides was noticed after the cryptocurrency market crashed in August. The situation was particularly critical in Korea as crypto traders were on "suicide watch". A cryptocurrency forum on Reddit even started providing suicide prevention support to affected investors.[308][309]The May 2022 collapse of the Luna currency operated byTerraalso led to reports of suicidal investors in crypto-related subreddits.[310]
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Incryptography,Curve25519is anelliptic curveused inelliptic-curve cryptography(ECC) offering 128bits of security(256-bitkey size) and designed for use with theElliptic-curve Diffie–Hellman(ECDH) key agreement scheme. It is one of the fastest curves in ECC, and is not covered by any known patents.[1]Thereference implementationispublic domain software.[2][3]
The original Curve25519 paper defined it as aDiffie–Hellman(DH) function.Daniel J. Bernsteinhas since proposed that the name Curve25519 be used for the underlying curve, and the nameX25519for the DH function.[4]
The curve used isy2=x3+486662x2+x{\displaystyle y^{2}=x^{3}+486662x^{2}+x}, aMontgomery curve, over theprime fielddefined by thepseudo-Mersenne prime number[5]2255−19{\displaystyle 2^{255}-19}(hence the numeric "25519" in the name), and it uses the base pointx=9{\displaystyle x=9}. This point generates a cyclic subgroup whoseorderis the prime2252+27742317777372353535851937790883648493{\displaystyle 2^{252}+27742317777372353535851937790883648493}. This subgroup has a co-factor of8, meaning the number of elements in the subgroup is1/8that of the elliptic curve group. Using a prime order subgroup prevents mounting aPohlig–Hellman algorithmattack.[6]
The protocol uses compressed elliptic point (onlyXcoordinates), so it allows efficient use of theMontgomery ladderforECDH, using onlyXZcoordinates.[7]
Curve25519 is constructed such that it avoids many potential implementation pitfalls.[8]
The curve isbirationally equivalentto atwisted Edwards curveused in theEd25519[9][10]signature scheme.[11]
In 2005, Curve25519 was first released byDaniel J. Bernstein.[6]
In 2013, interest began to increase considerably when it was discovered that theNSAhad potentially implemented abackdoorinto the P-256 curve basedDual_EC_DRBGalgorithm.[12]While not directly related,[13]suspicious aspects of the NIST's P curve constants[14]led to concerns[15]that the NSA had chosen values that gave them an advantage in breaking the encryption.[16][17]
"I no longer trust the constants. I believe the NSA has manipulated them through their relationships with industry."
Since 2013, Curve25519 has become thede factoalternative to P-256, being used in a wide variety of applications.[18]Starting in 2014,OpenSSH[19]defaults to Curve25519-basedECDHandGnuPGadds support forEd25519keys for signing and encryption.[20]The use of the curve was eventually standardized for both key exchange and signature in 2020.[21][22]
In 2017, NIST announced that Curve25519 andCurve448would be added to Special Publication 800-186, which specifies approved elliptic curves for use by the US Federal Government.[23]Both are described in RFC 7748.[24]A 2019 draft of "FIPS 186-5" notes the intention to allow usage ofEd25519[25]for digital signatures. The 2023 update of Special Publication 800-186 allows usage of Curve25519.[26]
In February 2017, theDNSSECspecification for using Ed25519 and Ed448 was published asRFC8080, assigning algorithm numbers 15 and 16.[27]
In 2018,DKIMspecification was amended so as to allow signatures with this algorithm.[28]Also in 2018, RFC 8446 was published as the newTransport Layer Security v1.3standard. It recommends support forX25519,Ed25519,X448, andEd448algorithms.[29]
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Incryptography,FourQis anelliptic curvedeveloped byMicrosoft Research. It is designed for key agreements schemes (elliptic-curve Diffie–Hellman) and digital signatures (Schnorr), and offers about 128bits of security.[1]It is equipped with areference implementationmade by the authors of the original paper. Theopen sourceimplementation is calledFourQliband runs onWindowsandLinuxand is available for x86, x64, and ARM.[2]It is licensed under theMIT Licenseand the source code is available onGitHub.[3]
Its name is derived from the four dimensional Gallant–Lambert–Vanstone scalar multiplication, which allows high performance calculations.[4]The curve is defined over a two dimensionalextensionof theprimefield defined by theMersenne prime2127−1{\displaystyle 2^{127}-1}.
The curve was published in 2015 by Craig Costello and Patrick Longa fromMicrosoft ResearchonePrint.[1]
The paper was presented inAsiacryptin 2015 inAuckland, New Zealand, and consequently areference implementationwas published onMicrosoft's website.[2]
There were some efforts to standardize usage of the curve underIETF; these efforts were withdrawn in late 2017.[5]
The curve is defined by atwisted Edwards equation
d{\displaystyle d}is a non-square inFp2{\displaystyle \mathbb {F} _{p^{2}}}, wherep{\displaystyle p}is theMersenne prime2127−1{\displaystyle 2^{127}-1}.
In order to avoidsmall subgroup attacks,[6]all points are verified to lie in anN-torsionsubgroup of theelliptic curve, whereNis specified as a 246-bitprimedividing theorderof the group.
The curve is equipped with two nontrivialendomorphisms:ψ{\displaystyle \psi }related to thep{\displaystyle p}-powerFrobenius map, andϕ{\displaystyle \phi }, a low degree efficiently computable endomorphism (seecomplex multiplication).
The currently best knowndiscrete logarithmattack is the genericPollard's rho algorithm, requiring about2122.5{\displaystyle 2^{122.5}}group operations on average. Therefore, it typically belongs to the 128 bit security level.
In order to preventtiming attacks, all group operations are done in constant time, i.e. without disclosing information about key material.[1]
Most cryptographic primitives, and most notablyECDH, require fast computation of scalar multiplication, i.e.[k]P{\displaystyle [k]P}for a pointP{\displaystyle P}on the curve and an integerk{\displaystyle k}, which is usually thought as distributed uniformly at random over{0,…,N−1}{\displaystyle \{0,\ldots ,N-1\}}.
Since we look at aprimeordercyclicsubgroup, one can write scalarsλψ,λϕ{\displaystyle \lambda _{\psi },\lambda _{\phi }}such thatψ(P)=[λψ]P{\displaystyle \psi (P)=[\lambda _{\psi }]P}andϕ(P)=[λϕ]P{\displaystyle \phi (P)=[\lambda _{\phi }]P}for every pointP{\displaystyle P}in theN-torsion subgroup.
Hence, for a givenk{\displaystyle k}we may write
If we find smallai{\displaystyle a_{i}}, we may compute[k]P{\displaystyle [k]P}quickly by utilizing the implied equation
Babai roundingtechnique[7]is used to find smallai{\displaystyle a_{i}}. For FourQ it turns that one can guarantee an efficiently computable solution withai<264{\displaystyle a_{i}<2^{64}}.
Moreover, as thecharacteristicof the field is aMersenne prime, modulations can be carried efficiently.
Both properties (four dimensional decomposition and Mersenne prime characteristic), alongside usage of fast multiplication formulae (extended twisted Edwardscoordinates), make FourQ the currently fastest elliptic curve for the 128 bit security level.
FourQ is implemented in the cryptographic libraryCIRCL, published byCloudflare.[8]
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DNSCurveis a proposed secure protocol for theDomain Name System(DNS), designed byDaniel J. Bernstein. It encrypts and authenticates DNSpacketsbetweenresolversand authoritative servers.
DNSCurve claims advantages over previous DNS services of:[1]
DNSCurve usesCurve25519elliptic curve cryptographyto establish the identity of authoritative servers.[2]Public keysfor remote authoritative servers are encoded in NS records as the host name component of the server's fully qualified domain name, so recursive resolvers know whether the server supports DNSCurve. Keys begin with the magic stringuz5and are followed by a 51-byteBase32encoding of the server's 255-bit public key. E.g., inBINDformat:
The identity is used to establish keys used by anauthenticated encryptionscheme consisting ofSalsa20andPoly1305.The cryptographic setup is called acryptographic box, specificallycrypto_box_curve25519xsalsa20poly1305.[3]
Thecryptographic boxtool used in DNSCurve are the same used inCurveCP, aUDP-based protocol which is similar toTCPbut uses elliptic-curve cryptography to encrypt and authenticate data. An analogy is that whileDNSSECis like signing a webpage withPretty Good Privacy(PGP), CurveCP and DNSCurve are like encrypting and authenticating the channel usingTransport Layer Security(TLS). Just as PGP-signed webpages can be sent over an encrypted channel using SSL, DNSSEC data can be protected using DNSCurve.[4]
The resolver first retrieves the public key from the NS record, see§ Structureabove.
The resolver then sends to the server a packet containing its DNSCurve public key, a 96-bitnonce, and a cryptographic box containing the query. The cryptographic box is created using the resolver's private key, the server's public key, and the nonce. The response from the server contains a different 96-bit nonce and its own cryptographic box containing the answer to the query.
DNSCurve uses 256-bit elliptic-curve cryptography, whichNISTestimates to be roughly equivalent to 3072-bit RSA.[5]ECRYPTreports a similar equivalence.[6]It uses per-query public-key crypto (like SSH and SSL), and 96-bit nonces to protect against replay attacks. Adam Langley, security officer at Google, says "With very high probability, no one will ever solve a single instance of Curve25519 without a large, quantum computer."[7]
Adam Langley has posted speed tests on his personal website showing Curve25519, used by DNSCurve, to be the fastest among elliptic curves tested.[8]According to the U.S.National Security Agency(NSA), elliptic curve cryptography offers vastly superior performance over RSA and Diffie–Hellman at a geometric rate as key sizes increase.[9]
DNSCurve first gained recursive support in dnscache via a patch[10]by Matthew Dempsky. Dempsky also has aGitHubrepository which includes Python DNS lookup tools and a forwarder in C.[11]Adam Langley has a GitHub repository as well.[12]There is an authoritative forwarder called CurveDNS[13]which allows DNS administrators to protect existing installations without patching.
Jan Mojžíš has released curveprotect,[14]a software suite which implements DNSCurve and CurveCP protection for common services like DNS, SSH, HTTP, and SMTP.
DNSCurve.io (2023) recommends two implementations: Jan Mojžíš's dqcache for recursive resolvers, CurveDNS for authoritative servers.[15]
OpenDNS, which has 50 million users, announced support for DNSCurve on its recursive resolvers on February 23, 2010. In other words, its recursive resolvers now use DNSCurve to communicate to authoritative servers if available.[16]On December 6, 2011, OpenDNS announced a new tool, calledDNSCrypt.[17]DNSCrypt is based on similar cryptographic tools as DNSCurve, but instead protects the channel between OpenDNS and its users.[18]
No equally large authoritative DNS providers have yet deployed DNSCurve.
DNSCurve is intended to secure communication between a resolver and an authoritative server.
For securing communication between DNS clients and resolvers, there are several options:
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Patent-related uncertainty aroundelliptic curve cryptography(ECC), orECC patents, is one of the main factors limiting its wide acceptance. For example, theOpenSSLteam accepted an ECC patch only in 2005 (in OpenSSL version 0.9.8), despite the fact that it was submitted in 2002.
According toBruce Schneieras of May 31, 2007, "Certicom certainly can claim ownership of ECC. The algorithm was developed and patented by the company's founders, and the patents are well written and strong. I don't like it, but they can claim ownership."[1]Additionally,NSAhas licensedMQVand other ECC patents fromCerticomin a US$25 million deal forNSA Suite Balgorithms.[2](ECMQV is no longer part of Suite B.)
However, according toRSA Laboratories, "in all of these cases, it is the implementation technique that is patented, not the prime or representation, and there are alternative, compatible implementation techniques that are not covered by the patents."[3]Additionally,Daniel J. Bernsteinhas stated that he is "not aware of" patents that cover theCurve25519elliptic curve Diffie–Hellmanalgorithm or its implementation.[4]RFC6090, published in February 2011, documents ECC techniques, some of which were published so long ago that even if they were patented, any such patents for these previously published techniques would now be expired.
According to the NSA, Certicom holds over 130 patents relating to elliptic curves and public key cryptography in general.[5]
It is difficult to create a complete list of patents that are related to ECC. Still, a good starting point isthe Standards for Efficient Cryptography Group (SECG)– a group devoted exclusively to developing standards based on ECC, however,https://www.secg.org/the group's official website has an indicator that states "shut down for repairs" since 2014. It states that "The site is being restored" since then. There is controversy over the validity of some of the patent claims.[4]
On May 30, 2007, Certicom filed a lawsuit againstSonyinUnited States District Court for the Eastern District of TexasMarshalloffice, claiming that Sony's use of ECC inAdvanced Access Content SystemandDigital Transmission Content Protectionviolates Certicom's patents for that cryptographic method. In particular, Certicom alleged violation ofU.S. patent 6,563,928andU.S. patent 6,704,870. The lawsuit was dismissed on May 27, 2009.[6]The stipulation states, "Whereas Certicom and Sony have entered into a settlement agreement according to which they have agreed to a dismissal without prejudice, these parties, therefore jointly move to dismiss all claims and counterclaims asserted in this suit, without prejudice to the right to pursue any such claims and counterclaims in the future."[7]
As for theprior art, Sony claimed:[8]
According toDaniel J. Bernstein, theCurve25519and efficient implementations thereof can be free from patent encumbrance.[9]
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Elliptic-curve Diffie–Hellman(ECDH) is akey agreementprotocol that allows two parties, each having anelliptic-curvepublic–private key pair, to establish ashared secretover aninsecure channel.[1][2][3]This shared secret may be directly used as a key, or toderive another key. The key, or the derived key, can then be used to encrypt subsequent communications using asymmetric-key cipher. It is a variant of theDiffie–Hellmanprotocol usingelliptic-curve cryptography.
The following example illustrates how a shared key is established. SupposeAlicewants to establish a shared key withBob, but the only channel available for them may be eavesdropped by a third party. Initially, thedomain parameters(that is,(p,a,b,G,n,h){\displaystyle (p,a,b,G,n,h)}in the prime case or(m,f(x),a,b,G,n,h){\displaystyle (m,f(x),a,b,G,n,h)}in the binary case) must be agreed upon. Also, each party must have a key pair suitable for elliptic curve cryptography, consisting of a private keyd{\displaystyle d}(a randomly selected integer in the interval[1,n−1]{\displaystyle [1,n-1]}) and a public key represented by a pointQ{\displaystyle Q}(whereQ=d⋅G{\displaystyle Q=d\cdot G}, that is, the result ofaddingG{\displaystyle G}to itselfd{\displaystyle d}times). Let Alice's key pair be(dA,QA){\displaystyle (d_{\text{A}},Q_{\text{A}})}and Bob's key pair be(dB,QB){\displaystyle (d_{\text{B}},Q_{\text{B}})}. Each party must know the other party's public key prior to execution of the protocol.
Alice computes point(xk,yk)=dA⋅QB{\displaystyle (x_{k},y_{k})=d_{\text{A}}\cdot Q_{\text{B}}}. Bob computes point(xk,yk)=dB⋅QA{\displaystyle (x_{k},y_{k})=d_{\text{B}}\cdot Q_{\text{A}}}. The shared secret isxk{\displaystyle x_{k}}(thexcoordinate of the point). Most standardized protocols based on ECDH derive a symmetric key fromxk{\displaystyle x_{k}}using some hash-based key derivation function.
The shared secret calculated by both parties is equal, becausedA⋅QB=dA⋅dB⋅G=dB⋅dA⋅G=dB⋅QA{\displaystyle d_{\text{A}}\cdot Q_{\text{B}}=d_{\text{A}}\cdot d_{\text{B}}\cdot G=d_{\text{B}}\cdot d_{\text{A}}\cdot G=d_{\text{B}}\cdot Q_{\text{A}}}.
The only information about her key that Alice initially exposes is her public key. So, no party except Alice can determine Alice's private key (Alice of course knows it by having selected it), unless that party can solve the elliptic curvediscrete logarithmproblem. Bob's private key is similarly secure. No party other than Alice or Bob can compute the shared secret, unless that party can solve the elliptic curveDiffie–Hellman problem.
The public keys are either static (and trusted, say via a certificate) or ephemeral (also known asECDHE, where final 'E' stands for "ephemeral").Ephemeral keysare temporary and not necessarily authenticated, so if authentication is desired, authenticity assurances must be obtained by other means. Authentication is necessary to avoidman-in-the-middle attacks. If one of either Alice's or Bob's public keys is static, then man-in-the-middle attacks are thwarted. Static public keys provide neitherforward secrecynor key-compromise impersonation resilience, among other advanced security properties. Holders of static private keys should validate the other public key, and should apply a securekey derivation functionto the raw Diffie–Hellman shared secret to avoid leaking information about the static private key. For schemes with other security properties, seeMQV.
If Alice maliciously chooses invalid curve points for her key and Bob does not validate that Alice's points are part of the selected group, she can collect enough residues of Bob's key to derive his private key. SeveralTLSlibraries were found to be vulnerable to this attack.[4]
The shared secret is uniformly distributed on a subset of[0,p){\displaystyle [0,p)}of size(n+1)/2{\displaystyle (n+1)/2}. For this reason, the secret should not be used directly as a symmetric key, but it can be used as entropy for a key derivation function.
LetA,B∈Fp{\displaystyle A,B\in F_{p}}such thatB(A2−4)≠0{\displaystyle B(A^{2}-4)\neq 0}. The Montgomery form elliptic curveEM,A,B{\displaystyle E_{M,A,B}}is the set of all(x,y)∈Fp×Fp{\displaystyle (x,y)\in F_{p}\times F_{p}}satisfying the equationBy2=x(x2+Ax+1){\displaystyle By^{2}=x(x^{2}+Ax+1)}along with the point at infinity denoted as∞{\displaystyle \infty }. This is called the affine form of the curve. The set of allFp{\displaystyle F_{p}}-rational points ofEM,A,B{\displaystyle E_{M,A,B}}, denoted asEM,A,B(Fp){\displaystyle E_{M,A,B}(F_{p})}is the set of all(x,y)∈Fp×Fp{\displaystyle (x,y)\in F_{p}\times F_{p}}satisfyingBy2=x(x2+Ax+1){\displaystyle By^{2}=x(x^{2}+Ax+1)}along with∞{\displaystyle \infty }. Under a suitably defined addition operation,EM,A,B(Fp){\displaystyle E_{M,A,B}(F_{p})}is a group with∞{\displaystyle \infty }as the identity element. It is known that the order of this group is a multiple of 4. In fact, it is usually possible to obtainA{\displaystyle A}andB{\displaystyle B}such that the order ofEM,A,B{\displaystyle E_{M,A,B}}is4q{\displaystyle 4q}for a primeq{\displaystyle q}. For more extensive discussions of Montgomery curves and their arithmetic one may follow.[5][6][7]
For computational efficiency, it is preferable to work with projective coordinates. The projective form of the Montgomery curveEM,A,B{\displaystyle E_{M,A,B}}isBY2Z=X(X2+AXZ+Z2){\displaystyle BY^{2}Z=X(X^{2}+AXZ+Z^{2})}. For a pointP=[X:Y:Z]{\displaystyle P=[X:Y:Z]}onEM,A,B{\displaystyle E_{M,A,B}}, thex{\displaystyle x}-coordinate mapx{\displaystyle x}is the following:[7]x(P)=[X:Z]{\displaystyle x(P)=[X:Z]}ifZ≠0{\displaystyle Z\neq 0}andx(P)=[1:0]{\displaystyle x(P)=[1:0]}ifP=[0:1:0]{\displaystyle P=[0:1:0]}.Bernstein[8][9]introduced the mapx0{\displaystyle x_{0}}as follows:x0(X:Z)=XZp−2{\displaystyle x_{0}(X:Z)=XZ^{p-2}}which is defined for all values ofX{\displaystyle X}andZ{\displaystyle Z}inFp{\displaystyle F_{p}}. Following Miller,[10]Montgomery[5]and Bernstein,[9]the Diffie-Hellman key agreement can be carried out on a Montgomery curve as follows. LetQ{\displaystyle Q}be a generator of a prime order subgroup ofEM,A,B(Fp){\displaystyle E_{M,A,B}(F_{p})}. Alice chooses a secret keys{\displaystyle s}and has public keyx0(sQ){\displaystyle x_{0}(sQ)};
Bob chooses a secret keyt{\displaystyle t}and has public keyx0(tQ){\displaystyle x_{0}(tQ)}. The shared secret key of Alice and Bob isx0(stQ){\displaystyle x_{0}(stQ)}. Using classical computers, the best known method of obtainingx0(stQ){\displaystyle x_{0}(stQ)}fromQ,x0(sQ){\displaystyle Q,x_{0}(sQ)}andx0(tQ){\displaystyle x_{0}(tQ)}requires aboutO(p1/2){\displaystyle O(p^{1/2})}time using thePollards rho algorithm.[11]
The most famous example of Montgomery curve isCurve25519which was introduced by Bernstein.[9]For Curve25519,p=2255−19,A=486662{\displaystyle p=2^{255}-19,A=486662}andB=1{\displaystyle B=1}.
The other Montgomery curve which is part of TLS 1.3 isCurve448which was introduced
by Hamburg.[12]For Curve448,p=2448−2224−1,A=156326{\displaystyle p=2^{448}-2^{224}-1,A=156326}andB=1{\displaystyle B=1}. Couple of Montgomery curves named M[4698] and M[4058] competitive toCurve25519andCurve448respectively have been proposed in.[13]For M[4698],p=2251−9,A=4698,B=1{\displaystyle p=2^{251}-9,A=4698,B=1}and for M[4058],p=2444−17,A=4058,B=1{\displaystyle p=2^{444}-17,A=4058,B=1}. At 256-bit security level, three Montgomery curves named M[996558], M[952902] and M[1504058] have been proposed in.[14]For M[996558],p=2506−45,A=996558,B=1{\displaystyle p=2^{506}-45,A=996558,B=1}, for M[952902],p=2510−75,A=952902,B=1{\displaystyle p=2^{510}-75,A=952902,B=1}and for M[1504058],p=2521−1,A=1504058,B=1{\displaystyle p=2^{521}-1,A=1504058,B=1}respectively. Apart from these two, other proposals of Montgomery curves can be found at.[15]
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Inpublic-key cryptography,Edwards-curve Digital Signature Algorithm(EdDSA) is adigital signaturescheme using a variant ofSchnorr signaturebased ontwisted Edwards curves.[1]It is designed to be faster than existing digital signature schemes without sacrificing security. It was developed by a team includingDaniel J. Bernstein, Niels Duif,Tanja Lange, Peter Schwabe, and Bo-Yin Yang.[2]Thereference implementationispublic-domain software.[3]
The following is a simplified description of EdDSA, ignoring details of encoding integers and curve points as bit strings; the full details are in the papers and RFC.[4][2][1]
AnEdDSA signature schemeis a choice:[4]: 1–2[2]: 5–6[1]: 5–7
These parameters are common to all users of the EdDSA signature scheme. The security of the EdDSA signature scheme depends critically on the choices of parameters, except for the arbitrary choice of base point—for example,Pollard's rho algorithm for logarithmsis expected to take approximatelyℓπ/4{\displaystyle {\sqrt {\ell \pi /4}}}curve additions before it can compute a discrete logarithm,[5]soℓ{\displaystyle \ell }must be large enough for this to be infeasible, and is typically taken to exceed2200.[6]The choice ofℓ{\displaystyle \ell }is limited by the choice ofq{\displaystyle q}, since byHasse's theorem,#E(Fq)=2cℓ{\displaystyle \#E(\mathbb {F} _{q})=2^{c}\ell }cannot differ fromq+1{\displaystyle q+1}by more than2q{\displaystyle 2{\sqrt {q}}}. The hash functionH{\displaystyle H}is normally modelled as arandom oraclein formal analyses of EdDSA's security.
Within an EdDSA signature scheme,
2cSB=2cR+2cH(R∥A∥M)A.{\displaystyle 2^{c}SB=2^{c}R+2^{c}H(R\parallel A\parallel M)A.}
2cSB=2c(r+H(R∥A∥M)s)B=2crB+2cH(R∥A∥M)sB=2cR+2cH(R∥A∥M)A.{\displaystyle {\begin{aligned}2^{c}SB&=2^{c}(r+H(R\parallel A\parallel M)s)B\\&=2^{c}rB+2^{c}H(R\parallel A\parallel M)sB\\&=2^{c}R+2^{c}H(R\parallel A\parallel M)A.\end{aligned}}}
Ed25519is the EdDSA signature scheme usingSHA-512(SHA-2) and an elliptic curve related toCurve25519[2]where
−x2+y2=1−121665121666x2y2,{\displaystyle -x^{2}+y^{2}=1-{\frac {121665}{121666}}x^{2}y^{2},}
Thetwisted Edwards curveE/Fq{\displaystyle E/\mathbb {F} _{q}}is known asedwards25519,[7][1]and isbirationally equivalentto theMontgomery curveknown asCurve25519.
The equivalence is[2][7][8]x=uv−486664,y=u−1u+1.{\displaystyle x={\frac {u}{v}}{\sqrt {-486664}},\quad y={\frac {u-1}{u+1}}.}
The original team has optimized Ed25519 for thex86-64Nehalem/Westmereprocessor family. Verification can be performed in batches of 64 signatures for even greater throughput. Ed25519 is intended to provide attack resistance comparable to quality 128-bitsymmetric ciphers.[9]
Public keys are 256 bits long and signatures are 512 bits long.[10]
Ed25519 is designed to avoid implementations that use branch conditions or array indices that depend on secret data,[2]: 2[1]: 40in order to mitigateside-channel attacks.
As with other discrete-log-based signature schemes, EdDSA uses a secret value called anonceunique to each signature. In the signature schemesDSAandECDSA, this nonce is traditionally generated randomly for each signature—and if the random number generator is ever broken and predictable when making a signature, the signature can leak the private key, as happened with theSony PlayStation 3firmware update signing key.[11][12][13][14]
In contrast, EdDSA chooses the nonce deterministically as the hash of a part of the private key and the message. Thus, once a private key is generated, EdDSA has no further need for a random number generator in order to make signatures, and there is no danger that a broken random number generator used to make a signature will reveal the private key.[2]: 8
Note that there are two standardization efforts for EdDSA, one from IETF, an informationalRFC8032and one from NIST as part of FIPS 186-5.[15]The differences between the standards have been analyzed,[16][17]and test vectors are available.[18]
Notable uses of Ed25519 includeOpenSSH,[19]GnuPG[20]and various alternatives, and thesignifytool byOpenBSD.[21]Usage of Ed25519 (and Ed448) in the SSH protocol has been standardized.[22]In 2023 the final version of theFIPS186-5 standard included deterministic Ed25519 as an approved signature scheme.[15]
Ed448is the EdDSA signature scheme defined inRFC8032using the hash functionSHAKE256and the elliptic curveedwards448, an (untwisted)Edwards curverelated toCurve448inRFC7748.
Ed448 has also been approved in the final version of the FIPS 186-5 standard.[15]
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MQV(Menezes–Qu–Vanstone) is anauthenticatedprotocolforkey agreementbased on theDiffie–Hellmanscheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitraryfinite group, and, in particular,elliptic curvegroups, where it is known aselliptic curve MQV (ECMQV).
MQV was initially proposed byAlfred Menezes, Minghua Qu andScott Vanstonein 1995. It was later modified in joint work with Laurie Law and Jerry Solinas.[1]There are one-, two- and three-pass variants.
MQV is incorporated in the public-key standardIEEE P1363and NIST's SP800-56A standard.[2]
Some variants of MQV are claimed in patents assigned toCerticom.
ECMQV has been dropped from the National Security Agency'sSuite Bset of cryptographic standards.
Alice has a key pair(A,a){\displaystyle (A,a)}withA{\displaystyle A}her public key anda{\displaystyle a}her private key and Bob has the key pair(B,b){\displaystyle (B,b)}withB{\displaystyle B}his public key andb{\displaystyle b}his private key.
In the followingR¯{\displaystyle {\bar {R}}}has the following meaning. LetR=(x,y){\displaystyle R=(x,y)}be a point on an elliptic curve. ThenR¯=(xmod2L)+2L{\displaystyle {\bar {R}}=(x\,{\bmod {\,}}2^{L})+2^{L}}whereL=⌈⌈log2n⌉2⌉{\displaystyle L=\left\lceil {\frac {\lceil \log _{2}n\rceil }{2}}\right\rceil }andn{\displaystyle n}is the order of the used generator pointP{\displaystyle P}. SoR¯{\displaystyle {\bar {R}}}are the firstLbits of the first coordinate ofR{\displaystyle R}.
Note: for the algorithm to be secure some checks have to be performed. See Hankerson et al.
Bob calculates:K=h⋅Sb(X+X¯A)=h⋅Sb(xP+X¯aP)=h⋅Sb(x+X¯a)P=h⋅SbSaP{\displaystyle K=h\cdot S_{b}(X+{\bar {X}}A)=h\cdot S_{b}(xP+{\bar {X}}aP)=h\cdot S_{b}(x+{\bar {X}}a)P=h\cdot S_{b}S_{a}P}
Alice calculates:K=h⋅Sa(Y+Y¯B)=h⋅Sa(yP+Y¯bP)=h⋅Sa(y+Y¯b)P=h⋅SbSaP{\displaystyle K=h\cdot S_{a}(Y+{\bar {Y}}B)=h\cdot S_{a}(yP+{\bar {Y}}bP)=h\cdot S_{a}(y+{\bar {Y}}b)P=h\cdot S_{b}S_{a}P}
So the shared secretsK{\displaystyle K}are indeed the same withK=h⋅SbSaP{\displaystyle K=h\cdot S_{b}S_{a}P}
The original MQV protocol does not include user identities of the communicating parties in the key exchange flows. User identities are only included in the subsequent explicit key confirmation process. However, explicit key confirmation is optional in MQV (and in theIEEE P1363specification). In 2001, Kaliski presented an unknown key-share attack that exploited the missing identities in the MQV key exchange protocol.[3]The attack works against implicitly authenticated MQV that does not have explicit key confirmation. In this attack, the user establishes a session key with another user but is tricked into believing that he shares the key with a different user. In 2006, Menezes and Ustaoglu proposed to address this attack by including user identities in the key derivation function at the end of the MQV key exchange.[4]The explicit key confirmation process remains optional.
In 2005, Krawczyk proposed a hash variant of MQV, called HMQV.[5]The HMQV protocol was designed to address Kaliski's attack (without mandating explicit key confirmation), with the additional goals of achieving provable security and better efficiency. HMQV made three changes to MQV:
HMQV claims to be superior to MQV in performance because it dispenses with the operations in 2) and 3) above, which are mandatory in MQV. The HMQV paper provides "formal security proofs" to support that dispensing with these operations is safe.
In 2005, Menezes first presented a small subgroup confinement attack against HMQV.[6]This attack exploits the exact missing of public key validations in 2) and 3). It shows that when engaged with an active attacker, the HMQV protocol leaks information about the user's long-term private key, and depending on the underlying cryptographic group setting, the entire private key may be recovered by the attacker. Menezes proposed to address this attack by at least mandating public key validations in 2) and 3).
In 2006, in response to Menezes's attack, Krawczyk revised HMQV inthe submissionto IEEE P1363 (included in theIEEE P1363 D1-pre draft). However, instead of validating the long-term and ephemeral public keys in 2) and 3) respectively as two separate operations, Krawczyk proposed to validate them together in one combined operation during the key exchange process. This would save cost. With the combined public key validation in place, Menezes's attack would be prevented. The revised HMQV could still claim to be more efficient than MQV.
In 2010, Hao presented two attacks on the revised HMQV (as specified in the IEEE P1363 D1-pre draft).[7]The first attack exploits the fact that HMQV allows any data string other than 0 and 1 to be registered as a long-term public key. Hence, a small subgroup element is allowed to be registered as a "public key". With the knowledge of this "public key", a user is able to pass all verification steps in HMQV and is fully "authenticated" in the end. This contradicts the common understanding that "authentication" in an authenticated key exchange protocol is defined based on proving the knowledge of a private key. In this case, the user is "authenticated" but without having a private key (in fact, the private key does not exist). This issue is not applicable to MQV. The second attack exploits the self-communication mode, which is explicitly supported in HMQV to allow a user to communicate with himself using the same public key certificate. In this mode, HMQV is shown to be vulnerable to an unknown key-share attack. To address the first attack, Hao proposed to perform public key validations in 2) and 3) separately, as initially suggested by Menezes. However, this change would diminish the efficiency advantages of HMQV over MQV. To address the second attack, Hao proposed to include additional identities to distinguish copies of self, or to disable the self-communication mode.
Hao's two attacks were discussed by members of the IEEE P1363 working group in 2010. However, there was no consensus on how HMQV should be revised. As a result, the HMQV specification in the IEEE P1363 D1-pre draft was unchanged, but the standardisation of HMQV in IEEE P1363 has stopped progressing since.[citation needed]
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Elliptic curve scalar multiplicationis the operation of successively adding a point along anelliptic curveto itself repeatedly. It is used inelliptic curve cryptography(ECC).
The literature presents this operation asscalar multiplication, as written inHessian form of an elliptic curve. A widespread name for this operation is alsoelliptic curve point multiplication, but this can convey the wrong impression of being a multiplication between two points.
Given a curve,E, defined by some equation in afinite field(such asE:y2=x3+ax+b), point multiplication is defined as the repeated addition of a point along that curve. Denote asnP=P+P+P+ … +Pfor some scalar (integer)nand a pointP= (x,y)that lies on the curve,E. This type of curve is known as a Weierstrass curve.
The security of modern ECC depends on the intractability of determiningnfromQ=nPgiven known values ofQandPifnis large (known as theelliptic curve discrete logarithmproblem by analogy to othercryptographic systems). This is because the addition of two points on an elliptic curve (or the addition of one point to itself) yields a third point on the elliptic curve whose location has no immediately obvious relationship to the locations of the first two, and repeating this many times over yields a pointnPthat may be essentially anywhere. Intuitively, this is not dissimilar to the fact that if you had a pointPon a circle, adding 42.57 degrees to its angle may still be a point "not too far" fromP, but adding 1000 or 1001 times 42.57 degrees will yield a point that requires a bit more complex calculation to find the original angle. Reversing this process, i.e., givenQ=nPandP, and determiningn, can only be done by trying out all possiblen—an effort that is computationally intractable ifnis large.
There are three commonly defined operations for elliptic curve points: addition, doubling and negation.
Point at infinityO{\displaystyle {\mathcal {O}}}is theidentity elementof elliptic curve arithmetic. Adding it to any point results in that other point, including adding point at infinity to itself.
That is:
Point at infinity is also written as0.
Point negation is finding such a point, that adding it to itself will result in point at infinity (O{\displaystyle {\mathcal {O}}}).
For elliptic curves of the formE:y2=x3+ax+b, negation is a point with the samexcoordinate but negatedycoordinate:
With 2 distinct points,PandQ, addition is defined as the negation of the point resulting from the intersection of the curve,E, and the straight line defined by the pointsPandQ, giving the point,R.[1]
Assuming the elliptic curve,E, is given byy2=x3+ax+b, this can be calculated as:
These equations are correct when neither point is the point at infinity,O{\displaystyle {\mathcal {O}}}, and if the points have different x coordinates (they're not mutual inverses). This is important for theECDSA verification algorithmwhere the hash value could be zero.
Where the pointsPandQare coincident (at the same coordinates), addition is similar, except that there is no well-defined straight line throughP, so the operation is closed using a limiting case, the tangent to the curve,E, atP.
This is calculated as above, taking derivatives (dE/dx)/(dE/dy):[1]
whereais from the defining equation of the curve,E, above.
The straightforward way of computing a point multiplication is through repeated addition. However, there are more efficient approaches to computing the multiplication.
The simplest method is the double-and-add method,[2]similar tosquare-and-multiplyin modular exponentiation. The algorithm works as follows:
To computesP, start with the binary representation fors:s=s0+2s1+22s2+⋯+2n−1sn−1{\displaystyle s=s_{0}+2s_{1}+2^{2}s_{2}+\cdots +2^{n-1}s_{n-1}}, wheres0..sn−1∈{0,1},n=⌈log2s⌉{\displaystyle s_{0}~..~s_{n-1}\in \{0,1\},n=\lceil \log _{2}{s}\rceil }.
eA
Note that both of the iterative methods above are vulnerable to timing analysis. See Montgomery Ladder below for an alternative approach.
wherefis the function for multiplying,Pis the coordinate to multiply,dis the number of times to add the coordinate to itself. Example:100Pcan be written as2(2[P + 2(2[2(P + 2P)])])and thus requires six point double operations and two point addition operations.100Pwould be equal tof(P, 100).
This algorithm requires log2(d) iterations of point doubling and addition to compute the full point multiplication. There are many variations of this algorithm such as using a window, sliding window, NAF, NAF-w, vector chains, and Montgomery ladder.
In the windowed version of this algorithm,[2]one selects a window sizewand computes all2w{\displaystyle 2^{w}}values ofdP{\displaystyle dP}ford=0,1,2,…,2w−1{\displaystyle d=0,1,2,\dots ,2^{w}-1}. The algorithm now uses the representationd=d0+2wd1+22wd2+⋯+2mwdm{\displaystyle d=d_{0}+2^{w}d_{1}+2^{2w}d_{2}+\cdots +2^{mw}d_{m}}and becomes
This algorithm has the same complexity as the double-and-add approach with the benefit of using fewer point additions (which in practice are slower than doubling). Typically, the value ofwis chosen to be fairly small making thepre-computationstage a trivial component of the algorithm. For the NIST recommended curves,w=4{\displaystyle w=4}is usually the best selection. The entire complexity for an-bit number is measured asn+1{\displaystyle n+1}point doubles and2w−2+nw{\displaystyle 2^{w}-2+{\tfrac {n}{w}}}point additions.
In the sliding-window version, we look to trade off point additions for point doubles. We compute a similar table as in the windowed version except we only compute the pointsdP{\displaystyle dP}ford=2w−1,2w−1+1,…,2w−1{\displaystyle d=2^{w-1},2^{w-1}+1,\dots ,2^{w}-1}. Effectively, we are only computing the values for which the most significant bit of the window is set. The algorithm then uses the original double-and-add representation ofd=d0+2d1+22d2+⋯+2mdm{\displaystyle d=d_{0}+2d_{1}+2^{2}d_{2}+\cdots +2^{m}d_{m}}.
This algorithm has the benefit that the pre-computation stage is roughly half as complex as the normal windowed method while also trading slower point additions for point doublings. In effect, there is little reason to use the windowed method over this approach, except that the former can be implemented in constant time. The algorithm requiresw−1+n{\displaystyle w-1+n}point doubles and at most2w−1−1+nw{\displaystyle 2^{w-1}-1+{\tfrac {n}{w}}}point additions.
In thenon-adjacent formwe aim to make use of the fact that point subtraction is just as easy as point addition to perform fewer (of either) as compared to a sliding-window method. The NAF of the multiplicandd{\displaystyle d}must be computed first with the following algorithm
Where the signed modulo functionmodsis defined as
This produces the NAF needed to now perform the multiplication. This algorithm requires the pre-computation of the points{1,3,5,…,2w−1−1}P{\displaystyle \lbrace 1,3,5,\dots ,2^{w-1}-1\rbrace P}and their negatives, whereP{\displaystyle P}is the point to be multiplied. On typical Weierstrass curves, ifP={x,y}{\displaystyle P=\lbrace x,y\rbrace }then−P={x,−y}{\displaystyle -P=\lbrace x,-y\rbrace }. So in essence the negatives are cheap to compute. Next, the following algorithm computes the multiplicationdP{\displaystyle dP}:
The wNAF guarantees that on average there will be a density of1w+1{\displaystyle {\tfrac {1}{w+1}}}point additions (slightly better than the unsigned window). It requires 1 point doubling and2w−2−1{\displaystyle 2^{w-2}-1}point additions for precomputation. The algorithm then requiresn{\displaystyle n}point doublings andnw+1{\displaystyle {\tfrac {n}{w+1}}}point additions for the rest of the multiplication.
One property of the NAF is that we are guaranteed that every non-zero elementdi{\displaystyle d_{i}}is followed by at leastw−1{\displaystyle w-1}additional zeroes. This is because the algorithm clears out the lowerw{\displaystyle w}bits ofd{\displaystyle d}with every subtraction of the output of themodsfunction. This observation can be used for several purposes. After every non-zero element the additional zeroes can be implied and do not need to be stored. Secondly, the multiple serial divisions by 2 can be replaced by a division by2w{\displaystyle 2^{w}}after every non-zerodi{\displaystyle d_{i}}element and divide by 2 after every zero.
It has been shown that through application of a FLUSH+RELOAD side-channel attack onOpenSSL, the full private key can be revealed after performing cache-timing against as few as 200 signatures performed.[3]
The Montgomery ladder[4]approach computes the point multiplication in afixednumber of operations. This can be beneficial when timing, power consumption, or branch measurements are exposed to an attacker performing aside-channel attack. The algorithm uses the same representation as from double-and-add.
This algorithm has in effect the same speed as the double-and-add approach except that it computes the same number of point additions and doubles regardless of the value of the multiplicandd. This means that at this level the algorithm does not leak any information through branches or power consumption.
However, it has been shown that through application of a FLUSH+RELOAD side-channel attack on OpenSSL, the full private key can be revealed after performing cache-timing against only one signature at a very low cost.[5]
Rust code for Montgomery Ladder:[6]
The security of a cryptographic implementation is likely to face the threat of the so calledtiming attackswhich exploits the data-dependent timing characteristics of the implementation. Machines running cryptographic
implementations consume variable amounts of time to process different inputs and so the timings
vary based on the encryption key. To resolve this issue, cryptographic algorithms are implemented
in a way which removes data dependent variable timing characteristic from the implementation leading
to the so called constant-time implementations. Software implementations are considered to be constant-time in the
following sense as stated in:[7]“avoids all input-dependent branches, all input-dependent arrayindices, and other instructions with input-dependent timings.” The GitHub page[8]lists coding rules
for implementations of cryptographic operations, and more generally for operations involving secret or
sensitive values.
The Montgomery ladder is anx{\displaystyle x}-coordinate only algorithm for elliptic curve point multiplication
and is based on the double and add rules over a specific set of curves known asMontgomery curve. The algorithm has a conditional branching
such that the condition depends on a secret bit. So a straightforward implementation of the ladder won't be
constant time and has the potential to leak the secret bit. This problem has been addressed in literature[9][10]and several constant time implementations are known. The constant time Montgomery ladder algorithm is as given below which uses two functions CSwap and Ladder-Step. In the return value of the algorithm Z2p-2is the value of Z2−1computed using theFermat's little theorem.
The Ladder-Step function (given below) used within the ladder is the core of the algorithm and is a combined form of the differential add and doubling operations. The field
constant a24is defined as a24=(A+2)/4{\displaystyle (A+2)/4}, whereA{\displaystyle A}is a parameter of the underlyingMontgomery curve.
The CSwap function manages the conditional branching and helps the ladder to run following the requirements of a constant time implementation. The function swaps the pair of field elements⟨{\displaystyle \langle }X2,Z2⟩{\displaystyle \rangle }and⟨{\displaystyle \langle }X3,Z3⟩{\displaystyle \rangle }only ifb{\displaystyle b}= 1 and
this is done without leaking any information about the secret bit. Various methods of implementing CSwap have been proposed in literature.[9][10]A lesser costly option to manage the constant time requirement of the Montgomery ladder is conditional select which is formalised through a function CSelect. This function has been used in various optimisations and has been formally discussed in[11]
Since the inception of the standard Montgomery curveCurve25519at 128-bit security level, there has been various software implementations to compute the ECDH on various architectures and to achieve best possible performance cryptographic developers have resorted to write the implementations using assembly language of the underlying architecture. The work[12]provided a couple of 64-bit assembly implementations targeting the AMD64 architecture. The implementations were developed using a tool known asqhasm[13]which can generate high-speed assembly language cryptographic programs. It is to be noted that the function CSwap was used in the implementations of these ladders. After that there has been several attempts to optimise the ladder implementation through hand-written assembly programs out of which the notion of CSelect was first used in[14]and then in.[15]Apart from using sequential instructions, vector instructions have also been used to optimise the ladder computation through various works.[16][17][18][19]Along with AMD64, attempts have also been made to achieve efficient implementations on other architectures like ARM. The works[20]and[21]provides efficient implementations targeting the ARM architecture. The libraries lib25519[22]and[23]are two state-of-art libraries containing efficient implementations of the Montgomery ladder forCurve25519. Nevertheless, the libraries have implementations of other cryptographic primitives as well.
Apart fromCurve25519, there have been several attempts to compute the ladder over other curves at various security levels. Efficient implementations of the ladder over the standard curveCurve448at 224-bit security level have also been studied in literature.[14][17][19]A curve named Curve41417 providing security just over 200 bits was proposed[24]in which a variant of Karatsuba strategy was used to implement the field multiplication needed for the related ECC software. In pursuit of searching Montgomery curves that are competitive toCurve25519andCurve448research has been done and couple of curves were proposed along with efficient sequential[15]and vectorised implementations[19]of the corresponding ladders. At 256-bit security level efficient implementations of the ladder have also been addressed through three different Montgomery curves.[25]
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Network codinghas been shown to optimally usebandwidthin a network, maximizing information flow but the scheme is very inherently vulnerable to pollution attacks by malicious nodes in the network. A node injecting garbage can quickly affect many receivers. The pollution ofnetwork packetsspreads quickly since the output of (even an) honest node is corrupted if at least one of the incoming packets is corrupted.
An attacker can easily corrupt a packet even if it is encrypted by either forging the signature or by producing a collision under thehash function. This will give an attacker access to the packets and the ability to corrupt them. Denis Charles, Kamal Jain and Kristin Lauter designed a newhomomorphic encryptionsignature scheme for use with network coding to prevent pollution attacks.[1]
The homomorphic property of the signatures allows nodes to sign any linear combination of the incoming packets without contacting the signing authority. In this scheme it is computationally infeasible for a node to sign a linear combination of the packets without disclosing whatlinear combinationwas used in the generation of the packet. Furthermore, we can prove that the signature scheme is secure under well knowncryptographicassumptions of the hardness of thediscrete logarithmproblem and the computationalElliptic curve Diffie–Hellman.
LetG=(V,E){\displaystyle G=(V,E)}be adirected graphwhereV{\displaystyle V}is a set, whose elements are called vertices ornodes, andE{\displaystyle E}is a set ofordered pairsof vertices, called arcs, directed edges, or arrows. A sources∈V{\displaystyle s\in V}wants to transmit a fileD{\displaystyle D}to a setT⊆V{\displaystyle T\subseteq V}of the vertices. One chooses avector spaceW/Fp{\displaystyle W/\mathbb {F} _{p}}(say of dimensiond{\displaystyle d}), wherep{\displaystyle p}is a prime, and views the data to be transmitted as a bunch of vectorsw1,…,wk∈W{\displaystyle w_{1},\ldots ,w_{k}\in W}. The source then creates the augmented vectorsv1,…,vk{\displaystyle v_{1},\ldots ,v_{k}}by settingvi=(0,…,0,1,…,0,wi1,…,wid){\displaystyle v_{i}=(0,\ldots ,0,1,\ldots ,0,w_{i_{1}},\ldots ,w{i_{d}})}wherewij{\displaystyle w_{i_{j}}}is thej{\displaystyle j}-th coordinate of the vectorwi{\displaystyle w_{i}}. There are(i−1){\displaystyle (i-1)}zeros before the first '1' appears invi{\displaystyle v_{i}}. One can assume without loss of generality that the vectorsvi{\displaystyle v_{i}}arelinearly independent. We denote thelinear subspace(ofFpk+d{\displaystyle \mathbb {F} _{p}^{k+d}}) spanned by these vectors byV{\displaystyle V}. Each outgoing edgee∈E{\displaystyle e\in E}computes a linear combination,y(e){\displaystyle y(e)}, of the vectors entering the vertexv=in(e){\displaystyle v=in(e)}where the edge originates, that is to say
whereme(f)∈Fp{\displaystyle m_{e}(f)\in \mathbb {F} _{p}}. We consider the source as havingk{\displaystyle k}input edges carrying thek{\displaystyle k}vectorswi{\displaystyle w_{i}}. Byinduction, one has that the vectory(e){\displaystyle y(e)}on any edge is a linear combinationy(e)=∑1≤i≤k(gi(e)vi){\displaystyle y(e)=\sum _{1\leq i\leq k}(g_{i}(e)v_{i})}and is a vector inV{\displaystyle V}. The k-dimensional vectorg(e)=(g1(e),…,gk(e)){\displaystyle g(e)=(g_{1}(e),\ldots ,g_{k}(e))}is simply the firstkcoordinates of the vectory(e){\displaystyle y(e)}. We call thematrixwhose rows are the vectorsg(e1),…,g(ek){\displaystyle g(e_{1}),\ldots ,g(e_{k})}, whereei{\displaystyle e_{i}}are the incoming edges for a vertext∈T{\displaystyle t\in T}, the global encoding matrix fort{\displaystyle t}and denote it asGt{\displaystyle G_{t}}. In practice the encoding vectors are chosen at random so the matrixGt{\displaystyle G_{t}}is invertible with high probability. Thus, any receiver, on receivingy1,…,yk{\displaystyle y_{1},\ldots ,y_{k}}can findw1,…,wk{\displaystyle w_{1},\ldots ,w_{k}}by solving
where theyi′{\displaystyle y_{i}'}are the vectors formed by removing the firstk{\displaystyle k}coordinates of the vectoryi{\displaystyle y_{i}}.
Eachreceiver,t∈T{\displaystyle t\in T}, getsk{\displaystyle k}vectorsy1,…,yk{\displaystyle y_{1},\ldots ,y_{k}}which are random linear combinations of thevi{\displaystyle v_{i}}’s.
In fact, if
then
Thus we can invert the linear transformation to find thevi{\displaystyle v_{i}}’s with highprobability.
Krohn, Freedman and Mazieres proposed a theory[2]in 2004 that if we have a hash functionH:V⟶G{\displaystyle H:V\longrightarrow G}such that:
Then server can securely distributeH(vi){\displaystyle H(v_{i})}to each receiver, and to check if
we can check whether
The problem with this method is that the server needs to transfer secure information to each of the receivers. The hash functionsH{\displaystyle H}needs to be transmitted to all the nodes in the network through a separate secure channel.H{\displaystyle H}is expensive to compute and secure transmission ofH{\displaystyle H}is not economical either.
The homomorphic property of the signatures allows nodes to sign any linear combination of the incoming packets without contacting the signing authority.
Elliptic curve cryptographyover a finite field is an approach topublic-key cryptographybased on the algebraic structure ofelliptic curvesoverfinite fields.
LetFq{\displaystyle \mathbb {F} _{q}}be a finite field such thatq{\displaystyle q}is not a power of 2 or 3. Then an elliptic curveE{\displaystyle E}overFq{\displaystyle \mathbb {F} _{q}}is a curve given by an equation of the form
wherea,b∈Fq{\displaystyle a,b\in \mathbb {F} _{q}}such that4a3+27b2≠0{\displaystyle 4a^{3}+27b^{2}\not =0}
LetK⊇Fq{\displaystyle K\supseteq \mathbb {F} _{q}}, then,
forms anabelian groupwith O as identity. Thegroup operationscan be performed efficiently.
Weil pairingis a construction ofroots of unityby means of functions on anelliptic curveE{\displaystyle E}, in such a way as to constitute apairing(bilinear form, though withmultiplicative notation) on thetorsion subgroupofE{\displaystyle E}. LetE/Fq{\displaystyle E/\mathbb {F} _{q}}be an elliptic curve and letF¯q{\displaystyle \mathbb {\bar {F}} _{q}}be an algebraic closure ofFq{\displaystyle \mathbb {F} _{q}}. Ifm{\displaystyle m}is an integer, relatively prime to the characteristic of the fieldFq{\displaystyle \mathbb {F} _{q}}, then the group ofm{\displaystyle m}-torsion points,E[m]=P∈E(F¯q):mP=O{\displaystyle E[m]={P\in E(\mathbb {\bar {F}} _{q}):mP=O}}.
IfE/Fq{\displaystyle E/\mathbb {F} _{q}}is an elliptic curve andgcd(m,q)=1{\displaystyle \gcd(m,q)=1}then
There is a mapem:E[m]∗E[m]→μm(Fq){\displaystyle e_{m}:E[m]*E[m]\rightarrow \mu _{m}(\mathbb {F} _{q})}such that:
Also,em{\displaystyle e_{m}}can be computed efficiently.[3]
Letp{\displaystyle p}be a prime andq{\displaystyle q}a prime power. LetV/Fp{\displaystyle V/\mathbb {F} _{p}}be a vector space of dimensionD{\displaystyle D}andE/Fq{\displaystyle E/\mathbb {F} _{q}}be an elliptic curve such thatP1,…,PD∈E[p]{\displaystyle P_{1},\ldots ,P_{D}\in E[p]}.
Defineh:V⟶E[p]{\displaystyle h:V\longrightarrow E[p]}as follows:h(u1,…,uD)=∑1≤i≤D(uiPi){\displaystyle h(u_{1},\ldots ,u_{D})=\sum _{1\leq i\leq D}(u_{i}P_{i})}.
The functionh{\displaystyle h}is an arbitrary homomorphism fromV{\displaystyle V}toE[p]{\displaystyle E[p]}.
The server choosess1,…,sD{\displaystyle s_{1},\ldots ,s_{D}}secretly inFp{\displaystyle \mathbb {F} _{p}}and publishes a pointQ{\displaystyle Q}of p-torsion such thatep(Pi,Q)≠1{\displaystyle e_{p}(P_{i},Q)\not =1}and also publishes(Pi,siQ){\displaystyle (P_{i},s_{i}Q)}for1≤i≤D{\displaystyle 1\leq i\leq D}.
The signature of the vectorv=u1,…,uD{\displaystyle v=u_{1},\ldots ,u_{D}}isσ(v)=∑1≤i≤D(uisiPi){\displaystyle \sigma (v)=\sum _{1\leq i\leq D}(u_{i}s_{i}P_{i})}Note: This signature is homomorphic since the computation of h is a homomorphism.
Givenv=u1,…,uD{\displaystyle v=u_{1},\ldots ,u_{D}}and its signatureσ{\displaystyle \sigma }, verify that
The verification crucially uses the bilinearity of the Weil-pairing.
The server computesσ(vi){\displaystyle \sigma (v_{i})}for each1≤i≤k{\displaystyle 1\leq i\leq k}. Transmitsvi,σ(vi){\displaystyle v_{i},\sigma (v_{i})}.
At each edgee{\displaystyle e}while computingy(e)=∑f∈E:out(f)=in(e)(me(f)y(f)){\displaystyle y(e)=\sum _{f\in E:\mathrm {out} (f)=\mathrm {in} (e)}(m_{e}(f)y(f))}also computeσ(y(e))=∑f∈E:out(f)=in(e)(me(f)σ(y(f))){\displaystyle \sigma (y(e))=\sum _{f\in E:\mathrm {out} (f)=\mathrm {in} (e)}(m_{e}(f)\sigma (y(f)))}on the elliptic curveE{\displaystyle E}.
The signature is a point on the elliptic curve with coordinates inFq{\displaystyle \mathbb {F} _{q}}. Thus the size of the signature is2logq{\displaystyle 2\log q}bits (which is some constant timeslog(p){\displaystyle log(p)}bits, depending on the relative size ofp{\displaystyle p}andq{\displaystyle q}), and this is the transmission overhead. The computation of the signatureh(e){\displaystyle h(e)}at each vertex requiresO(dinlogplog1+ϵq){\displaystyle O(d_{in}\log p\log ^{1+\epsilon }q)}bit operations, wheredin{\displaystyle d_{in}}is the in-degree of the vertexin(e){\displaystyle in(e)}. The verification of a signature requiresO((d+k)log2+ϵq){\displaystyle O((d+k)\log ^{2+\epsilon }q)}bit operations.
Attacker can produce a collision under the hash function.
If given(P1,…,Pr){\displaystyle (P_{1},\ldots ,P_{r})}points inE[p]{\displaystyle E[p]}finda=(a1,…,ar)∈Fpr{\displaystyle a=(a_{1},\ldots ,a_{r})\in \mathbb {F} _{p}^{r}}andb=(b1,…,br)∈Fpr{\displaystyle b=(b_{1},\ldots ,b_{r})\in \mathbb {F} _{p}^{r}}
such thata≠b{\displaystyle a\not =b}and
Proposition: There is a polynomial time reduction from discrete log on thecyclic groupof orderp{\displaystyle p}on elliptic curves to Hash-Collision.
Ifr=2{\displaystyle r=2}, then we getxP+yQ=uP+vQ{\displaystyle xP+yQ=uP+vQ}. Thus(x−u)P+(y−v)Q=0{\displaystyle (x-u)P+(y-v)Q=0}.
We claim thatx≠u{\displaystyle x\not =u}andy≠v{\displaystyle y\not =v}. Suppose thatx=u{\displaystyle x=u}, then we would have(y−v)Q=0{\displaystyle (y-v)Q=0}, butQ{\displaystyle Q}is a point of orderp{\displaystyle p}(a prime) thusy−u≡0modp{\displaystyle y-u\equiv 0{\bmod {p}}}. In other wordsy=v{\displaystyle y=v}inFp{\displaystyle \mathbb {F} _{p}}. This contradicts the assumption that(x,y){\displaystyle (x,y)}and(u,v){\displaystyle (u,v)}are distinct pairs inF2{\displaystyle \mathbb {F} _{2}}. Thus we have thatQ=−(x−u)(y−v)−1P{\displaystyle Q=-(x-u)(y-v)^{-1}P}, where the inverse is taken as modulop{\displaystyle p}.
If we have r > 2 then we can do one of two things. Either we can takeP1=P{\displaystyle P_{1}=P}andP2=Q{\displaystyle P_{2}=Q}as before and setPi=O{\displaystyle P_{i}=O}fori{\displaystyle i}> 2 (in this case the proof reduces to the case whenr=2{\displaystyle r=2}), or we can takeP1=r1P{\displaystyle P_{1}=r_{1}P}andPi=riQ{\displaystyle P_{i}=r_{i}Q}whereri{\displaystyle r_{i}}are chosen at random fromFp{\displaystyle \mathbb {F} _{p}}. We get one equation in one unknown (the discrete log ofQ{\displaystyle Q}). It is quite possible that the equation we get does not involve the unknown. However, this happens with very small probability as we argue next. Suppose the algorithm for Hash-Collision gave us that
Then as long as∑2≤i≤rbiri≢0modp{\displaystyle \sum _{2\leq i\leq r}b_{i}r_{i}\not \equiv 0{\bmod {p}}}, we can solve for the discrete log of Q. But theri{\displaystyle r_{i}}’s are unknown to the oracle for Hash-Collision and so we can interchange the order in which this process occurs. In other words, givenbi{\displaystyle b_{i}}, for2≤i≤r{\displaystyle 2\leq i\leq r}, not all zero, what is the probability that theri{\displaystyle r_{i}}’s we chose satisfies∑2≤i≤r(biri)=0{\displaystyle \sum _{2\leq i\leq r}(b_{i}r_{i})=0}? It is clear that the latter probability is1p{\displaystyle 1 \over p}. Thus with high probability we can solve for the discrete log ofQ{\displaystyle Q}.
We have shown that producing hash collisions in this scheme is difficult. The other method by which an adversary can foil our system is by forging a signature. This scheme for the signature is essentially the Aggregate Signature version of the Boneh-Lynn-Shacham signature scheme.[4]Here it is shown that forging a signature is at least as hard as solving theelliptic curve Diffie–Hellmanproblem. The only known way to solve this problem on elliptic curves is via computing discrete-logs. Thus forging a signature is at least as hard as solving the computational co-Diffie–Hellman on elliptic curves and probably as hard as computing discrete-logs.
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https://en.wikipedia.org/wiki/Homomorphic_signatures_for_network_coding
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Hyperelliptic curve cryptographyis similar toelliptic curve cryptography(ECC) insofar as theJacobianof ahyperelliptic curveis anabelian groupin which to do arithmetic, just as we use thegroupof points on an elliptic curve in ECC.
An(imaginary) hyperelliptic curveofgenusg{\displaystyle g}over a fieldK{\displaystyle K}is given by the equationC:y2+h(x)y=f(x)∈K[x,y]{\displaystyle C:y^{2}+h(x)y=f(x)\in K[x,y]}whereh(x)∈K[x]{\displaystyle h(x)\in K[x]}is a polynomial of degree not larger thang{\displaystyle g}andf(x)∈K[x]{\displaystyle f(x)\in K[x]}is a monic polynomial of degree2g+1{\displaystyle 2g+1}. From this definition it follows that elliptic curves are hyperelliptic curves of genus 1. In hyperelliptic curve cryptographyK{\displaystyle K}is often afinite field. The Jacobian ofC{\displaystyle C}, denotedJ(C){\displaystyle J(C)}, is aquotient group, thus the elements of the Jacobian are not points, they are equivalence classes ofdivisorsof degree 0 under the relation oflinear equivalence. This agrees with the elliptic curve case, because it can be shown that the Jacobian of an elliptic curve is isomorphic with the group of points on the elliptic curve.[1]The use of hyperelliptic curves in cryptography came about in 1989 fromNeal Koblitz. Although introduced only 3 years after ECC, not many cryptosystems implement hyperelliptic curves because the implementation of the arithmetic isn't as efficient as with cryptosystems based on elliptic curves or factoring (RSA). The efficiency of implementing the arithmetic depends on the underlying finite fieldK{\displaystyle K}, in practice it turns out that finite fields ofcharacteristic2 are a good choice for hardware implementations while software is usually faster in odd characteristic.[2]
The Jacobian on a hyperelliptic curve is an Abelian group and as such it can serve as group for thediscrete logarithm problem(DLP). In short, suppose we have an Abelian groupG{\displaystyle G}andg{\displaystyle g}an element ofG{\displaystyle G}, the DLP onG{\displaystyle G}entails finding the integera{\displaystyle a}given two elements ofG{\displaystyle G}, namelyg{\displaystyle g}andga{\displaystyle g^{a}}. The first type of group used was the multiplicative group of a finite field, later also Jacobians of (hyper)elliptic curves were used. If the hyperelliptic curve is chosen with care, thenPollard's rho methodis the most efficient way to solve DLP. This means that, if the Jacobian hasn{\displaystyle n}elements, that the running time is exponential inlog(n){\displaystyle \log(n)}. This makes it possible to use Jacobians of a fairly smallorder, thus making the system more efficient. But if the hyperelliptic curve is chosen poorly, the DLP will become quite easy to solve. In this case there are known attacks which are more efficient than generic discrete logarithm solvers[3]or even subexponential.[4]Hence these hyperelliptic curves must be avoided. Considering various attacks on DLP, it is possible to list the features of hyperelliptic curves that should be avoided.
Allgeneric attackson thediscrete logarithm problemin finite abelian groups such as thePohlig–Hellman algorithmandPollard's rho methodcan be used to attack the DLP in the Jacobian of hyperelliptic curves. The Pohlig-Hellman attack reduces the difficulty of the DLP by looking at the order of the group we are working with. Suppose the groupG{\displaystyle G}that is used hasn=p1r1⋯pkrk{\displaystyle n=p_{1}^{r_{1}}\cdots p_{k}^{r_{k}}}elements, wherep1r1⋯pkrk{\displaystyle p_{1}^{r_{1}}\cdots p_{k}^{r_{k}}}is the prime factorization ofn{\displaystyle n}. Pohlig-Hellman reduces the DLP inG{\displaystyle G}to DLPs in subgroups of orderpi{\displaystyle p_{i}}fori=1,...,k{\displaystyle i=1,...,k}. So forp{\displaystyle p}the largest prime divisor ofn{\displaystyle n}, the DLP inG{\displaystyle G}is just as hard to solve as the DLP in the subgroup of orderp{\displaystyle p}. Therefore, we would like to chooseG{\displaystyle G}such that the largest prime divisorp{\displaystyle p}of#G=n{\displaystyle \#G=n}is almost equal ton{\displaystyle n}itself. Requiringnp≤4{\textstyle {\frac {n}{p}}\leq 4}usually suffices.
Theindex calculus algorithmis another algorithm that can be used to solve DLP under some circumstances. For Jacobians of (hyper)elliptic curves there exists an index calculus attack on DLP. If the genus of the curve becomes too high, the attack will be more efficient than Pollard's rho. Today it is known that even a genus ofg=3{\displaystyle g=3}cannot assure security.[5]Hence we are left with elliptic curves and hyperelliptic curves of genus 2.
Another restriction on the hyperelliptic curves we can use comes from the Menezes-Okamoto-Vanstone-attack / Frey-Rück-attack. The first, often called MOV for short, was developed in 1993, the second came about in 1994. Consider a (hyper)elliptic curveC{\displaystyle C}over a finite fieldFq{\displaystyle \mathbb {F} _{q}}whereq{\displaystyle q}is the power of a prime number. Suppose the Jacobian of the curve hasn{\displaystyle n}elements andp{\displaystyle p}is the largest prime divisor ofn{\displaystyle n}. Fork{\displaystyle k}the smallest positive integer such thatp|qk−1{\displaystyle p|q^{k}-1}there exists a computableinjectivegroup homomorphismfrom the subgroup ofJ(C){\displaystyle J(C)}of orderp{\displaystyle p}toFqk∗{\displaystyle \mathbb {F} _{q^{k}}^{*}}. Ifk{\displaystyle k}is small, we can solve DLP inJ(C){\displaystyle J(C)}by using the index calculus attack inFqk∗{\textstyle \mathbb {F} _{q^{k}}^{*}}. For arbitrary curvesk{\displaystyle k}is very large (around the size ofqg{\displaystyle q^{g}}); so even though the index calculus attack is quite fast for multiplicative groups of finite fields this attack is not a threat for most curves. The injective function used in this attack is apairingand there are some applications in cryptography that make use of them. In such applications it is important to balance the hardness of the DLP inJ(C){\displaystyle J(C)}andFqk∗{\textstyle \mathbb {F} _{q^{k}}^{*}}; depending on thesecurity levelvalues ofk{\displaystyle k}between 6 and 12 are useful.
The subgroup ofFqk∗{\textstyle \mathbb {F} _{q^{k}}^{*}}is atorus. There exists some independent usage intorus based cryptography.
We also have a problem, ifp{\displaystyle p}, the largest prime divisor of the order of the Jacobian, is equal to the characteristic ofFq.{\displaystyle \mathbb {F} _{q}.}By a different injective map we could then consider the DLP in the additive groupFq{\displaystyle \mathbb {F} _{q}}instead of DLP on the Jacobian. However, DLP in this additive group is trivial to solve, as can easily be seen. So also these curves, called anomalous curves, are not to be used in DLP.
Hence, in order to choose a good curve and a good underlying finite field, it is important to know the order of the Jacobian. Consider a hyperelliptic curveC{\textstyle C}of genusg{\textstyle g}over the fieldFq{\textstyle \mathbb {F} _{q}}whereq{\textstyle q}is the power of a prime number and defineCk{\textstyle C_{k}}asC{\textstyle C}but now over the fieldFqk{\textstyle \mathbb {F} _{q^{k}}}. It can be shown that the order of the Jacobian ofCk{\textstyle C_{k}}lies in the interval[(qk−1)2g,(qk+1)2g]{\textstyle [({\sqrt {q}}^{k}-1)^{2g},({\sqrt {q}}^{k}+1)^{2g}]}, called the Hasse-Weil interval.[6]
But there is more, we can compute the order using the zeta-function on hyperelliptic curves. LetAk{\textstyle A_{k}}be the number of points onCk{\textstyle C_{k}}. Then we define the zeta-function ofC=C1{\textstyle C=C_{1}}asZC(t)=exp(∑i=1∞Aitii){\textstyle Z_{C}(t)=\exp(\sum _{i=1}^{\infty }{A_{i}{\frac {t^{i}}{i}}})}. For this zeta-function it can be shown thatZC(t)=P(t)(1−t)(1−qt){\textstyle Z_{C}(t)={\frac {P(t)}{(1-t)(1-qt)}}}whereP(t){\textstyle P(t)}is a polynomial of degree2g{\textstyle 2g}with coefficients inZ{\textstyle \mathbb {Z} }.[7]FurthermoreP(t){\textstyle P(t)}factors asP(t)=∏i=1g(1−ait)(1−ai¯t){\textstyle P(t)=\prod _{i=1}^{g}{(1-a_{i}t)(1-{\bar {a_{i}}}t)}}whereai∈C{\textstyle a_{i}\in \mathbb {C} }for alli=1,...,g{\textstyle i=1,...,g}. Herea¯{\textstyle {\bar {a}}}denotes thecomplex conjugateofa{\displaystyle a}. Finally we have that the order ofJ(Ck){\textstyle J(C_{k})}equals∏i=1g|1−aik|2{\textstyle \prod _{i=1}^{g}{|1-a_{i}^{k}|^{2}}}. Hence orders of Jacobians can be found by computing the roots ofP(t){\textstyle P(t)}.
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Pairing-based cryptographyis the use of apairingbetween elements of two cryptographicgroupsto a third group with a mappinge:G1×G2→GT{\displaystyle e:G_{1}\times G_{2}\to G_{T}}to construct or analyzecryptographicsystems.
The following definition is commonly used in most academic papers.[1]
LetFq{\displaystyle \mathbb {F} _{q}}be afinite fieldover primeq{\displaystyle q},G1,G2{\displaystyle G_{1},G_{2}}two additivecyclic groupsof prime orderq{\displaystyle q}andGT{\displaystyle G_{T}}another cyclic group of orderq{\displaystyle q}written multiplicatively. A pairing is a map:e:G1×G2→GT{\displaystyle e:G_{1}\times G_{2}\rightarrow G_{T}}, which satisfies the following properties:
If the same group is used for the first two groups (i.e.G1=G2{\displaystyle G_{1}=G_{2}}), the pairing is calledsymmetricand is amappingfrom two elements of one group to an element from a second group.
Some researchers classify pairing instantiations into three (or more) basic types:
If symmetric, pairings can be used to reduce a hard problem in one group to a different, usually easier problem in another group.
For example, in groups equipped with abilinear mappingsuch as theWeil pairingorTate pairing, generalizations of thecomputational Diffie–Hellman problemare believed to be infeasible while the simplerdecisional Diffie–Hellman problemcan be easily solved using the pairing function. The first group is sometimes referred to as aGap Groupbecause of the assumed difference in difficulty between these two problems in the group.[3]
Lete{\displaystyle e}be a non-degenerate, efficiently computable, bilinear pairing. Letg{\displaystyle g}be a generator ofG{\displaystyle G}. Consider an instance of theCDH problem,g{\displaystyle g},gx{\displaystyle g^{x}},gy{\displaystyle g^{y}}. Intuitively, the pairing functione{\displaystyle e}does not help us computegxy{\displaystyle g^{xy}}, the solution to the CDH problem. It is conjectured that this instance of the CDH problem is intractable. Givengz{\displaystyle g^{z}}, we may check to see ifgz=gxy{\displaystyle g^{z}=g^{xy}}without knowledge ofx{\displaystyle x},y{\displaystyle y}, andz{\displaystyle z}, by testing whethere(gx,gy)=e(g,gz){\displaystyle e(g^{x},g^{y})=e(g,g^{z})}holds.
By using the bilinear propertyx+y+z{\displaystyle x+y+z}times, we see that ife(gx,gy)=e(g,g)xy=e(g,g)z=e(g,gz){\displaystyle e(g^{x},g^{y})=e(g,g)^{xy}=e(g,g)^{z}=e(g,g^{z})}, then, sinceGT{\displaystyle G_{T}}is a prime order group,xy=z{\displaystyle xy=z}.
While first used forcryptanalysis,[4]pairings have also been used to construct many cryptographic systems for which no other efficient implementation is known, such asidentity-based encryptionorattribute-based encryptionschemes. Thus, the security level of some pairing friendly elliptic curves have been later reduced.
Pairing-based cryptography is used in theKZG cryptographic commitment scheme.
A contemporary example of using bilinear pairings is exemplified in theBLS digital signaturescheme.[3]
Pairing-based cryptography relies on hardness assumptions separate from e.g. theelliptic-curve cryptography, which is older and has been studied for a longer time.
In June 2012 theNational Institute of Information and Communications Technology(NICT),Kyushu University, andFujitsu Laboratories Limitedimproved the previous bound for successfully computing a discrete logarithm on asupersingular elliptic curvefrom 676 bits to 923 bits.[5]
In 2016, the Extended Tower Number Field Sieve algorithm[6]allowed to reduce the complexity of finding discrete logarithm in some resulting groups of pairings. There are several variants of the multiple and extended tower number field sieve algorithm expanding the applicability and improving the complexity of the algorithm. A unified description of all such algorithms with further improvements was published in 2019.[7]In view of these advances, several works[8][9]provided revised concrete estimates on the key sizes of secure pairing-based cryptosystems.
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https://en.wikipedia.org/wiki/Pairing-based_cryptography
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Quantum cryptographyis the science of exploitingquantum mechanicalproperties to performcryptographictasks.[1][2]The best known example of quantum cryptography isquantum key distribution, which offers aninformation-theoretically securesolution to thekey exchangeproblem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it isimpossible to copydata encoded in aquantum state. If one attempts to read the encoded data, the quantum state will be changed due towave function collapse(no-cloning theorem). This could be used to detect eavesdropping inquantum key distribution(QKD).
In the early 1970s,Stephen Wiesner, then at Columbia University in New York, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by theIEEE Information Theory Societybut was eventually published in 1983 inSIGACT News.[3]In this paper he showed how to store or transmit two messages by encoding them in two "conjugateobservables", such as linear and circularpolarizationofphotons,[4]so that either, but not both, properties may be received and decoded. It was not untilCharles H. Bennett, of the IBM'sThomas J. Watson Research Center, andGilles Brassardmet in 1979 at the 20th IEEE Symposium on the Foundations of Computer Science, held in Puerto Rico, that they discovered how to incorporate Wiesner's findings. "The main breakthrough came when we realized that photons were never meant to store information, but rather to transmit it."[3]In 1984, building upon this work, Bennett and Brassard proposed a method forsecure communication, which is now calledBB84, the first Quantum Key Distribution system.[5][6]Independently, in 1991Artur Ekertproposed to use Bell's inequalities to achieve secure key distribution.[7]Ekert's protocol for the key distribution, as it was subsequently shown byDominic MayersandAndrew Yao, offers device-independent quantum key distribution.
Companies that manufacture quantum cryptography systems includeMagiQ Technologies, Inc.(Boston),ID Quantique(Geneva),QuintessenceLabs(Canberra, Australia),Toshiba(Tokyo),QNu Labs(India) and SeQureNet (Paris).
Cryptography is the strongest link in the chain ofdata security.[8]However, interested parties cannot assume that cryptographic keys will remain secure indefinitely.[9]Quantum cryptography[2]has the potential to encrypt data for longer periods than classical cryptography.[9]Using classical cryptography, scientists cannot guarantee encryption beyond approximately 30 years, but some stakeholders could use longer periods of protection.[9]Take, for example, the healthcare industry. As of 2017, 85.9% of office-based physicians are using electronic medical record systems to store and transmit patient data.[10]Under the Health Insurance Portability and Accountability Act, medical records must be kept secret.[11]Quantum key distribution can protect electronic records for periods of up to 100 years.[9]Also, quantum cryptography has useful applications for governments and militaries as, historically, governments have kept military data secret for periods of over 60 years.[9]There also has been proof that quantum key distribution can travel through a noisy channel over a long distance and be secure. It can be reduced from a noisy quantum scheme to a classical noiseless scheme. This can be solved with classical probability theory.[12]This process of having consistent protection over a noisy channel can be possible through the implementation of quantum repeaters. Quantum repeaters have the ability to resolve quantum communication errors in an efficient way. Quantum repeaters, which are quantum computers, can be stationed as segments over the noisy channel to ensure the security of communication. Quantum repeaters do this by purifying the segments of the channel before connecting them creating a secure line of communication. Sub-par quantum repeaters can provide an efficient amount of security through the noisy channel over a long distance.[12]
Quantum cryptography is a general subject that covers a broad range of cryptographic practices and protocols. Some of the most notable applications and protocols are discussed below.
The best-known and developed application of quantum cryptography isQKD, which is the process of using quantum communication to establish a shared key between two parties (Alice and Bob, for example) without a third party (Eve) learning anything about that key, even if Eve can eavesdrop on all communication between Alice and Bob. If Eve tries to learn information about the key being established, discrepancies will arise causing Alice and Bob to notice. Once the key is established, it is then typically used forencryptedcommunication using classical techniques. For instance, the exchanged key could be used forsymmetric cryptography(e.g.one-time pad).
The security of quantum key distribution can be proven mathematically without imposing any restrictions on the abilities of an eavesdropper, something not possible with classical key distribution. This is usually described as "unconditional security", although there are some minimal assumptions required, including that the laws of quantum mechanics apply and that Alice and Bob are able to authenticate each other, i.e. Eve should not be able to impersonate Alice or Bob as otherwise aman-in-the-middle attackwould be possible.
While QKD is secure, its practical application faces some challenges. There are in fact limitations for the key generation rate at increasing transmission distances.[13][14][15]Recent studies have allowed important advancements in this regard. In 2018, the protocol of twin-field QKD[16]was proposed as a mechanism to overcome the limits of lossy communication. The rate of the twin field protocol was shown to overcome the secret key-agreement capacity of the lossy communication channel, known as repeater-less PLOB bound,[15]at 340 km of optical fiber; its ideal rate surpasses this bound already at 200 km and follows the rate-loss scaling of the higher repeater-assisted secret key-agreement capacity[17](see figure 1 of[16]and figure 11 of[2]for more details). The protocol suggests that optimal key rates are achievable on "550 kilometers of standardoptical fibre", which is already commonly used in communications today. The theoretical result was confirmed in the first experimental demonstration of QKD beyond the PLOB bound which has been characterized as the firsteffectivequantum repeater.[18]Notable developments in terms of achieving high rates at long distances are the sending-not-sending (SNS) version of the TF-QKD protocol.[19][20]and the no-phase-postselected twin-field scheme.[21]
In mistrustful cryptography the participating parties do not trust each other. For example, Alice and Bob collaborate to perform some computation where both parties enter some private inputs. But Alice does not trust Bob and Bob does not trust Alice. Thus, a secure implementation of a cryptographic task requires that after completing the computation, Alice can be guaranteed that Bob has not cheated and Bob can be guaranteed that Alice has not cheated either. Examples of tasks in mistrustful cryptography arecommitment schemesandsecure computations, the latter including the further examples of coin flipping andoblivious transfer.Key distributiondoes not belong to the area of mistrustful cryptography. Mistrustful quantum cryptography studies the area of mistrustful cryptography usingquantum systems.
In contrast toquantum key distributionwhere unconditional security can be achieved based only on the laws ofquantum physics, in the case of various tasks in mistrustful cryptography there are no-go theorems showing that it is impossible to achieve unconditionally secure protocols based only on the laws ofquantum physics. However, some of these tasks can be implemented with unconditional security if the protocols not only exploitquantum mechanicsbut alsospecial relativity. For example, unconditionally secure quantum bit commitment was shown impossible by Mayers[22]and by Lo and Chau.[23]Unconditionally secure ideal quantum coin flipping was shown impossible by Lo and Chau.[24]Moreover, Lo showed that there cannot be unconditionally secure quantum protocols for one-out-of-two oblivious transfer and other secure two-party computations.[25]However, unconditionally secure relativistic protocols for coin flipping and bit-commitment have been shown by Kent.[26][27]
Unlike quantum key distribution,quantum coin flippingis a protocol that is used between two participants who do not trust each other.[28]The participants communicate via a quantum channel and exchange information through the transmission ofqubits.[29]But because Alice and Bob do not trust each other, each expects the other to cheat. Therefore, more effort must be spent on ensuring that neither Alice nor Bob can gain a significant advantage over the other to produce a desired outcome. An ability to influence a particular outcome is referred to as a bias, and there is a significant focus on developing protocols to reduce the bias of a dishonest player,[30][31]otherwise known as cheating. Quantum communication protocols, including quantum coin flipping, have been shown to provide significant security advantages over classical communication, though they may be considered difficult to realize in the practical world.[32]
A coin flip protocol generally occurs like this:[33]
Cheating occurs when one player attempts to influence, or increase the probability of a particular outcome. The protocol discourages some forms of cheating; for example, Alice could cheat at step 4 by claiming that Bob incorrectly guessed her initial basis when he guessed correctly, but Alice would then need to generate a new string of qubits that perfectly correlates with what Bob measured in the opposite table.[33]Her chance of generating a matching string of qubits will decrease exponentially with the number of qubits sent, and if Bob notes a mismatch, he will know she was lying. Alice could also generate a string of photons using a mixture of states, but Bob would easily see that her string will correlate partially (but not fully) with both sides of the table, and know she cheated in the process.[33]There is also an inherent flaw that comes with current quantum devices. Errors and lost qubits will affect Bob's measurements, resulting in holes in Bob's measurement table. Significant losses in measurement will affect Bob's ability to verify Alice's qubit sequence in step 5.
One theoretically surefire way for Alice to cheat is to utilize the Einstein-Podolsky-Rosen (EPR) paradox. Two photons in an EPR pair are anticorrelated; that is, they will always be found to have opposite polarizations, provided that they are measured in the same basis. Alice could generate a string of EPR pairs, sending one photon per pair to Bob and storing the other herself. When Bob states his guess, she could measure her EPR pair photons in the opposite basis and obtain a perfect correlation to Bob's opposite table.[33]Bob would never know she cheated. However, this requires capabilities that quantum technology currently does not possess, making it impossible to do in practice. To successfully execute this, Alice would need to be able to store all the photons for a significant amount of time as well as measure them with near perfect efficiency. This is because any photon lost in storage or in measurement would result in a hole in her string that she would have to fill by guessing. The more guesses she has to make, the more she risks detection by Bob for cheating.
In addition to quantum coin-flipping, quantum commitment protocols are implemented when distrustful parties are involved. Acommitment schemeallows a party Alice to fix a certain value (to "commit") in such a way that Alice cannot change that value while at the same time ensuring that the recipient Bob cannot learn anything about that value until Alice reveals it. Such commitment schemes are commonly used in cryptographic protocols (e.g.Quantum coin flipping,Zero-knowledge proof,secure two-party computation, andOblivious transfer).
In the quantum setting, they would be particularly useful: Crépeau and Kilian showed that from a commitment and a quantum channel, one can construct an unconditionally secure protocol for performing so-calledoblivious transfer.[34]Oblivious transfer, on the other hand, had been shown by Kilian to allow implementation of almost any distributed computation in a secure way (so-calledsecure multi-party computation).[35](Note: The results by Crépeau and Kilian[34][35]together do not directly imply that given a commitment and a quantum channel one can perform secure multi-party computation. This is because the results do not guarantee "composability", that is, when plugging them together, one might lose security.)
Early quantum commitment protocols[36]were shown to be flawed. In fact, Mayers showed that (unconditionally secure) quantum commitment is impossible: a computationally unlimited attacker can break any quantum commitment protocol.[22]
Yet, the result by Mayers does not preclude the possibility of constructing quantum commitment protocols (and thus secure multi-party computation protocols) under assumptions that are much weaker than the assumptions needed for commitment protocols that do not use quantum communication. The bounded quantum storage model described below is an example for a setting in which quantum communication can be used to construct commitment protocols. A breakthrough in November 2013 offers "unconditional" security of information by harnessing quantum theory and relativity, which has been successfully demonstrated on a global scale for the first time.[37]More recently, Wang et al., proposed another commitment scheme in which the "unconditional hiding" is perfect.[38]
Physical unclonable functionscan be also exploited for the construction of cryptographic commitments.[39]
One possibility to construct unconditionally secure quantumcommitmentand quantumoblivious transfer(OT) protocols is to use the bounded quantum storage model (BQSM). In this model, it is assumed that the amount of quantum data that an adversary can store is limited by some known constant Q. However, no limit is imposed on the amount of classical (i.e., non-quantum) data the adversary may store.
In the BQSM, one can construct commitment and oblivious transfer protocols.[40]The underlying idea is the following: The protocol parties exchange more than Q quantum bits (qubits). Since even a dishonest party cannot store all that information (the quantum memory of the adversary is limited to Q qubits), a large part of the data will have to be either measured or discarded. Forcing dishonest parties to measure a large part of the data allows the protocol to circumvent the impossibility result, commitment and oblivious transfer protocols can now be implemented.[22]
The protocols in the BQSM presented by Damgård, Fehr, Salvail, and Schaffner[40]do not assume that honest protocol participants store any quantum information; the technical requirements are similar to those inquantum key distributionprotocols. These protocols can thus, at least in principle, be realized with today's technology. The communication complexity is only a constant factor larger than the bound Q on the adversary's quantum memory.
The advantage of the BQSM is that the assumption that the adversary's quantum memory is limited is quite realistic. With today's technology, storing even a single qubit reliably over a sufficiently long time is difficult. (What "sufficiently long" means depends on the protocol details. By introducing an artificial pause in the protocol, the amount of time over which the adversary needs to store quantum data can be made arbitrarily large.)
An extension of the BQSM is thenoisy-storage modelintroduced by Wehner, Schaffner and Terhal.[41]Instead of considering an upper bound on the physical size of the adversary's quantum memory, an adversary is allowed to use imperfect quantum storage devices of arbitrary size. The level of imperfection is modelled by noisy quantum channels. For high enough noise levels, the same primitives as in the BQSM can be achieved[42]and the BQSM forms a special case of the noisy-storage model.
In the classical setting, similar results can be achieved when assuming a bound on the amount of classical (non-quantum) data that the adversary can store.[43]It was proven, however, that in this model also the honest parties have to use a large amount of memory (namely the square-root of the adversary's memory bound).[44]This makes these protocols impractical for realistic memory bounds. (Note that with today's technology such as hard disks, an adversary can cheaply store large amounts of classical data.)
The goal of position-based quantum cryptography is to use thegeographical locationof a player as its (only) credential. For example, one wants to send a message to a player at a specified position with the guarantee that it can only be read if the receiving party is located at that particular position. In the basic task ofposition-verification, a player, Alice, wants to convince the (honest) verifiers that she is located at a particular point. It has been shown by Chandranet al.that position-verification using classical protocols is impossible against colluding adversaries (who control all positions except the prover's claimed position).[45]Under various restrictions on the adversaries, schemes are possible.
Under the name of 'quantum tagging', the first position-based quantum schemes have been investigated in 2002 by Kent. A US-patent[46]was granted in 2006. The notion of using quantum effects for location verification first appeared in the scientific literature in 2010.[47][48]After several other quantum protocols for position verification have been suggested in 2010,[49][50]Buhrman et al. claimed a general impossibility result:[51]using an enormous amount ofquantum entanglement(they use a doubly exponential number ofEPR pairs, in the number of qubits the honest player operates on), colluding adversaries are always able to make it look to the verifiers as if they were at the claimed position. However, this result does not exclude the possibility of practical schemes in the bounded- or noisy-quantum-storage model (see above). Later Beigi and König improved the amount of EPR pairs needed in the general attack against position-verification protocols to exponential. They also showed that a particular protocol remains secure against adversaries who controls only a linear amount of EPR pairs.[52]It is argued in[53]that due to time-energy coupling the possibility of formal unconditional location verification via quantum effects remains an open problem. The study of position-based quantum cryptography also has connections with the protocol of port-based quantum teleportation, which is a more advanced version of quantum teleportation, where many EPR pairs are simultaneously used as ports.
A quantum cryptographic protocol isdevice-independentif its security does not rely on trusting that the quantum devices used are truthful. Thus the security analysis of such a protocol needs to consider scenarios of imperfect or even malicious devices.[54]Mayers and Yao[55]proposed the idea of designing quantum protocols using "self-testing" quantum apparatus, the internal operations of which can be uniquely determined by their input-output statistics. Subsequently, Roger Colbeck in his Thesis[56]proposed the use ofBell testsfor checking the honesty of the devices. Since then, several problems have been shown to admit unconditional secure and device-independent protocols, even when the actual devices performing the Bell test are substantially "noisy", i.e., far from being ideal. These problems includequantum key distribution,[57][58]randomness expansion,[58][59]andrandomness amplification.[60]
In 2018, theoretical studies performed by Arnon- Friedman et al. suggest that exploiting a property of entropy that is later referred to as "Entropy Accumulation Theorem (EAT)", an extension ofAsymptotic equipartition property, can guarantee the security of a device independent protocol.[61]
Quantum computersmay become a technological reality; it is therefore important to study cryptographic schemes used against adversaries with access to a quantum computer. The study of such schemes is often referred to aspost-quantum cryptography. The need for post-quantum cryptography arises from the fact that many popular encryption and signature schemes (schemes based onECCandRSA) can be broken usingShor's algorithmforfactoringand computingdiscrete logarithmson a quantum computer. Examples for schemes that are, as of today's knowledge, secure against quantum adversaries areMcElieceandlattice-basedschemes, as well as mostsymmetric-key algorithms.[62][63]Surveys of post-quantum cryptography are available.[64][65]
There is also research into how existing cryptographic techniques have to be modified to be able to cope with quantum adversaries. For example, when trying to developzero-knowledge proof systemsthat are secure against quantum adversaries, new techniques need to be used: In a classical setting, the analysis of a zero-knowledge proof system usually involves "rewinding", a technique that makes it necessary to copy the internal state of the adversary. In a quantum setting, copying a state is not always possible (no-cloning theorem); a variant of the rewinding technique has to be used.[66]
Post quantum algorithms are also called "quantum resistant", because – unlike quantum key distribution – it is not known or provable that there will not be potential future quantum attacks against them. Even though they may possibly be vulnerable to quantum attacks in the future, the NSA is announcing plans to transition to quantum resistant algorithms.[67]The National Institute of Standards and Technology (NIST) believes that it is time to think of quantum-safe primitives.[68]
So far, quantum cryptography has been mainly identified with the development of quantum key distribution protocols. Symmetric cryptosystems with keys that have been distributed by means of quantum key distribution become inefficient for large networks (many users), because of the necessity for the establishment and the manipulation of many pairwise secret keys (the so-called "key-management problem"). Moreover, this distribution alone does not address many other cryptographic tasks and functions, which are of vital importance in everyday life. Kak's three-stage protocol has been proposed as a method for secure communication that is entirely quantum unlike quantum key distribution, in which the cryptographic transformation uses classical algorithms[69]
Besides quantum commitment and oblivious transfer (discussed above), research on quantum cryptography beyond key distribution revolves around quantum message authentication,[70]quantum digital signatures,[71][72]quantum one-way functions and public-key encryption,[73][74][75][76][77][78][79]quantum key-exchange,[80]quantum fingerprinting[81]and entity authentication[82][83][84](for example, seeQuantum readout of PUFs), etc.
H. P. Yuen presented Y-00 as a stream cipher using quantum noise around 2000 and applied it for the U.S. Defense Advanced Research Projects Agency (DARPA) High-Speed and High-Capacity Quantum Cryptography Project as an alternative to quantum key distribution.[85][86]The review paper summarizes it well.[87]
Unlike quantum key distribution protocols, the main purpose of Y-00 is to transmit a message without eavesdrop-monitoring, not to distribute a key. Therefore,privacy amplificationmay be used only for key distributions.[88]Currently, research is being conducted mainly in Japan and China: e.g.[89][90]
The principle of operation is as follows. First, legitimate users share a key and change it to a pseudo-random keystream using the same pseudo-random number generator. Then, the legitimate parties can perform conventional optical communications based on the shared key by transforming it appropriately. For attackers who do not share the key, the wire-tap channel model ofAaron D. Wyneris implemented. The legitimate users' advantage based on the shared key is called "advantage creation". The goal is to achieve longer covert communication than theinformation-theoretic securitylimit (one-time pad) set by Shannon.[91]The source of the noise in the above wire-tap channel is the uncertainty principle of the electromagnetic field itself, which is a theoretical consequence of the theory of laser described byRoy J. GlauberandE. C. George Sudarshan(coherent state).[92][93][94]Therefore, existing optical communication technologies are sufficient for implementation that some reviews describes: e.g.[87]Furthermore, since it uses ordinary communication laser light, it is compatible with existing communication infrastructure and can be used for high-speed
and long-distance communication and routing.[95][96][97][98][99]
Although the main purpose of the protocol is to transmit the message, key distribution is possible by simply replacing the message with a key.[100][88]Since it is a symmetric key cipher, it must share the initial key previously; however, a method of the initial key agreement was also proposed.[101]
On the other hand, it is currently unclear what implementation realizesinformation-theoretic security, and security of this protocol has long been a matter of debate.[102][103][104][105][106][107][108][109][110][111]
In theory, quantum cryptography seems to be a successful turning point in theinformation securitysector. However, no cryptographic method can ever be absolutely secure.[112]In practice, quantum cryptography is only conditionally secure, dependent on a key set of assumptions.[113]
The theoretical basis for quantum key distribution assumes the use of single-photon sources. However, such sources are difficult to construct, and most real-world quantum cryptography systems use faint laser sources as a medium for information transfer.[113]These multi-photon sources open the possibility for eavesdropper attacks, particularly a photon splitting attack.[114]An eavesdropper, Eve, can split the multi-photon source and retain one copy for herself.[114]The other photons are then transmitted to Bob without any measurement or trace that Eve captured a copy of the data.[114]Scientists believe they can retain security with a multi-photon source by using decoy states that test for the presence of an eavesdropper.[114]However, in 2016, scientists developed a near perfect single photon source and estimate that one could be developed in the near future.[115]
In practice, multiple single-photon detectors are used in quantum key distribution devices, one for Alice and one for Bob.[113]These photodetectors are tuned to detect an incoming photon during a short window of only a few nanoseconds.[116]Due to manufacturing differences between the two detectors, their respective detection windows will be shifted by some finite amount.[116]An eavesdropper, Eve, can take advantage of this detector inefficiency by measuring Alice's qubit and sending a "fake state" to Bob.[116]Eve first captures the photon sent by Alice and then generates another photon to send to Bob.[116]Eve manipulates the phase and timing of the "faked" photon in a way that prevents Bob from detecting the presence of an eavesdropper.[116]The only way to eliminate this vulnerability is to eliminate differences in photodetector efficiency, which is difficult to do given finite manufacturing tolerances that cause optical path length differences, wire length differences, and other defects.[116]
Because of the practical problems with quantum key distribution, some governmental organizations recommend the use of post-quantum cryptography (quantum resistant cryptography) instead. For example, the USNational Security Agency,[117]European Union Agency for Cybersecurityof EU (ENISA),[118]UK'sNational Cyber Security Centre,[119]French Secretariat for Defense and Security (ANSSI),[120]and German Federal Office for Information Security (BSI)[121]recommend post-quantum cryptography.
For example, the US National Security Agency addresses five issues:[117]
In response to problem 1 above, attempts to deliver authentication keys using post-quantum cryptography (or quantum-resistant cryptography) have been proposed worldwide. On the other hand, quantum-resistant cryptography is cryptography belonging to the class of computational security. In 2015, a research result was already published that "sufficient care must be taken in implementation to achieve information-theoretic security for the system as a whole when authentication keys that are not information-theoretic secure are used" (if the authentication key is not information-theoretically secure, an attacker can break it to bring all classical and quantum communications under control and relay them to launch aman-in-the-middle attack).[123]Ericsson, a private company, also cites and points out the above problems and then presents a report that it may not be able to support thezero trust security model, which is a recent trend in network security technology.[124]
Quantum cryptography, specifically the BB84 protocol, has become an important topic in physics and computer science education. The challenge of teaching quantum cryptography lies in the technical requirements and the conceptual complexity of quantum mechanics. However, simplified experimental setups for educational purposes are becoming more common,[125]allowing undergraduate students to engage with the core principles of quantum key distribution (QKD) without requiring advanced quantum technology.
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Supersingular isogeny Diffie–Hellman key exchange(SIDHorSIKE) is an insecure proposal for apost-quantumcryptographic algorithmto establish a secret key between two parties over an untrusted communications channel. It is analogous to theDiffie–Hellman key exchange, but is based on walks in asupersingular isogeny graphand was designed to resistcryptanalytic attackby an adversary in possession of aquantum computer. Before it was broken, SIDH boasted one of the smallest key sizes of all post-quantum key exchanges; with compression, SIDH used 2688-bit[1]public keys at a 128-bit quantumsecurity level. SIDH also distinguishes itself[disputed–discuss]from similar systems such asNTRUandRing-LWE[citation needed]by supportingperfect forward secrecy, a property that prevents compromised long-term keys from compromising the confidentiality of old communication sessions. These properties seemed to make SIDH a natural candidate to replaceDiffie–Hellman(DHE) andelliptic curve Diffie–Hellman(ECDHE), which are widely used in Internet communication. However, SIDH is vulnerable to a devastatingkey-recovery attackpublished in July 2022 and is therefore insecure. The attack does not require a quantum computer.[2][3]
For certain classes of problems, algorithms running onquantum computersare naturally capable of achieving lowertime complexitythan on classical computers. That is,quantum algorithmscan solve certain problems faster than the most efficient algorithm running on a traditional computer. For example,Shor's algorithmcan factor an integerNinpolynomial time, while the best-known factoring classic algorithm, thegeneral number field sieve, operates insub-exponential time. This is significant topublic key cryptographybecause the security ofRSAis dependent on the infeasibility of factoring integers, theinteger factorization problem. Shor's algorithm can also efficiently solve thediscrete logarithm problem, which is the basis for the security ofDiffie–Hellman,elliptic curve Diffie–Hellman,elliptic curve DSA,Curve25519,ed25519, andElGamal. Although quantum computers are currently in their infancy, the ongoing development of quantum computers and their theoretical ability to compromise modern cryptographic protocols (such asTLS/SSL) has prompted the development of post-quantum cryptography.[4]
SIDH was created in 2011 by De Feo, Jao, and Plut.[5]It uses conventionalelliptic curveoperations and is not patented. SIDH providesperfect forward secrecyand thus does not rely on the security of long-term private keys. Forward secrecy improves the long-term security of encrypted communications, helps defend againstmass surveillance, and reduces the impact of vulnerabilities likeHeartbleed.[6][7]
Thej-invariantof an elliptic curve given by theWeierstrass equationy2=x3+ax+b{\displaystyle y^{2}=x^{3}+ax+b}is given by the formula:
Isomorphiccurves have the same j-invariant; over an algebraically closed field, two curves with the same j-invariant are isomorphic.
The supersingular isogeny Diffie-Hellman protocol (SIDH) works with the graph whose vertices are (isomorphism classes of)supersingular elliptic curvesand whose edges are isogenies between those curves. Anisogenyϕ:E→E′{\displaystyle \phi :E\to E'}between elliptic curvesE{\displaystyle E}andE′{\displaystyle E'}is arational mapwhich is also a group homomorphism. Ifseparable,ϕ{\displaystyle \phi }is determined by itskernelup to an isomorphism of target curveE′{\displaystyle E'}.
The setup for SIDH is a prime of the formp=lAeA⋅lBeB⋅f∓1{\displaystyle p=l_{A}^{e_{A}}\cdot l_{B}^{e_{B}}\cdot f\mp 1}, for different (small) primeslA{\displaystyle l_{A}}andlB{\displaystyle l_{B}}, (large) exponentseA{\displaystyle e_{A}}andeB{\displaystyle e_{B}}, and small cofactorf{\displaystyle f}, together with a supersingular elliptic curveE{\displaystyle E}defined overFp2{\displaystyle \mathbb {F} _{p^{2}}}. Such a curve has two large torsion subgroups,E[lAeA]{\displaystyle E[l_{A}^{e_{A}}]}andE[lBeB]{\displaystyle E[l_{B}^{e_{B}}]}, which are assigned to Alice and Bob, respectively, as indicated by the subscripts. Each party starts the protocol by selecting a (secret) random cyclic subgroup of their respective torsion subgroup and computing the corresponding (secret) isogeny. They then publish, or otherwise provide the other party with, the equation for the target curve of their isogeny along with information about the image of the other party's torsion subgroup under that isogeny. This allows them both to privately compute new isogenies fromE{\displaystyle E}whose kernels are jointly generated by the two secret cyclic subgroups. Since the kernels of these two new isogenies agree, their target curves are isomorphic. The common j-invariant of these target curves may then be taken as the required shared secret.
Since the security of the scheme depends on the smaller torsion subgroup, it is recommended to chooselAeA≈lBeB{\displaystyle l_{A}^{e_{A}}\approx l_{B}^{e_{B}}}.
An excellent reference for this subject is De Feo's article "Mathematics of Isogeny Based Cryptography."[8]
The most straightforward way to attack SIDH is to solve the problem of finding an isogeny between two supersingular elliptic curves with the same number of points. At the time of the original publication due to De Feo, Jao and Plût, the best attack known against SIDH was based on solving the relatedclaw-finding problem, which led to a complexity ofO(p1/4)for classical computers andO(p1/6)forquantum computers. This suggested that SIDH with a 768-bit prime (p) would have a 128-bit security level.[5]A 2014 study of the isogeny problem by Delfs and Galbraith confirmed theO(p1/4)security analysis for classical computers.[9]The classical securityO(p1/4)remained unaffected by related cryptanalytic work of Biasse, Jao and Sankar as well as Galbraith, Petit, Shani and Yan.[10][11]
A more intricate attack strategy is based on exploiting the auxiliary elliptic-curve points present in SIDH public keys, which in principle reveal a lot of additional information about the secret isogenies, but this information did not seem computationally useful for attackers at first. Petit in 2017 first demonstrated a technique making use of these points to attack some rather peculiar SIDH variants.[12]Despite follow-up work extending the attack to much more realistic SIDH instantiations, the attack strategy still failed to break "standard" SIDH as employed by theNIST PQCsubmission SIKE.
In July 2022, Castryck and Decru published an efficient key-recovery attack on SIKE that exploits the auxiliary points. Using a single-core computer, SIKEp434 was broken within approximately an hour, SIKEp503 within approximately 2 hours, SIKEp610 within approximately 8 hours and SIKEp751 within approximately 21 hours.[2][13]The attack relies on gluing together multiple of the elliptic curves appearing in the SIDH construction, giving anabelian surface(more generally, anabelian variety), and computing a specially crafted isogeny defined by the given auxiliary points on that higher-dimensional object.
It should be stressed that the attack crucially relies on the auxiliary points given in SIDH, and there is no known way to apply similar techniques to the general isogeny problem.
During a key exchange, entities A and B will each transmit information of 2 coefficients modulop2defining an elliptic curve and 2 elliptic curve points. Each elliptic curve coefficient requireslog2p2bits. Each elliptic curve point can be transmitted in1 + log2p2bits; hence, the transmission is4 + 4 log2p2bits. This is 6144 bits for a 768-bit modulusp(128-bit security). However, this can be reduced by over half to 2640 bits (330 bytes) using key-compression techniques, the latest of which appears in recent work by authors Costello, Jao, Longa, Naehrig, Renes and Urbanik.[14]With these compression techniques, SIDH has a similar bandwidth requirement to traditional 3072-bit RSA signatures or Diffie-Hellman key exchanges. This small space requirement makes SIDH applicable to context that have a strict space requirement, such asBitcoinorTor. Tor's data cells must be less than 517 bytes in length, so they can hold 330-byte SIDH keys. By contrast, NTRUEncrypt must exchange approximately 600 bytes to achieve a 128-bit security and cannot be used within Tor without increasing the cell size.[15]
In 2014, researchers at the University of Waterloo developed a software implementation of SIDH. They ran their partially optimized code on an x86-64 processor running at 2.4 GHz. For a 768-bit modulus they were able to complete the key exchange computations in 200 milliseconds thus demonstrating that the SIDH is computationally practical.[16]
In 2016, researchers from Microsoft posted software for the SIDH which runs in constant time (thus protecting against timing attacks) and is the most efficient implementation to date. They write: "The size of public keys is only 564 bytes, which is significantly smaller than most of the popular post-quantum key exchange alternatives. Ultimately, the size and speed of our software illustrates the strong potential of SIDH as a post-quantum key exchange candidate and we hope that these results encourage a wider cryptanalytic effort."[17]The code is open source (MIT) and is available on GitHub:https://github.com/microsoft/PQCrypto-SIDH.
In 2016, researchers from Florida Atlantic University developed efficient ARM implementations of SIDH and provided a comparison of affine and projective coordinates.[18][19]In 2017, researchers from Florida Atlantic University developed the first FPGA implementations of SIDH.[20]
While several steps of SIDH involve complex isogeny calculations, the overall flow of SIDH for parties A and B is straightforward for those familiar with a Diffie-Hellman key exchange or its elliptic curve variant.
These are public parameters that can be shared by everyone in the network, or they can be negotiated by parties A and B at the beginning of a session.
In the key exchange, parties A and B will each create an isogeny from a common elliptic curve E. They each will do this by creating a random point in what will be the kernel of their isogeny. The kernel of their isogeny will be spanned byRA{\displaystyle R_{A}}andRB{\displaystyle R_{B}}respectively. The different pairs of points used ensure that parties A and B create different, non-commuting, isogenies. A random point (RA{\displaystyle R_{A}}, orRB{\displaystyle R_{B}}) in the kernel of the isogenies is created as a random linear combination of the pointsPA{\displaystyle P_{A}},QA{\displaystyle Q_{A}}andPB{\displaystyle P_{B}},QB{\displaystyle Q_{B}}.
UsingRA{\displaystyle R_{A}}, orRB{\displaystyle R_{B}}, parties A and B then use Velu's formulas for creating isogeniesϕA{\displaystyle \phi _{A}}andϕB{\displaystyle \phi _{B}}respectively. From this they compute the image of the pairs of pointsPA{\displaystyle P_{A}},QA{\displaystyle Q_{A}}orPB{\displaystyle P_{B}},QB{\displaystyle Q_{B}}under theϕB{\displaystyle \phi _{B}}andϕA{\displaystyle \phi _{A}}isogenies respectively.
As a result, A and B will now have two pairs of pointsϕA(PB){\displaystyle \phi _{A}(P_{B})},ϕA(QB){\displaystyle \phi _{A}(Q_{B})}andϕB(PA){\displaystyle \phi _{B}(P_{A})},ϕB(QA){\displaystyle \phi _{B}(Q_{A})}respectively. A and B now exchange these pairs of points over a communications channel.
A and B now use the pair of points they receive as the basis for the kernel of a new isogeny. They use the same linear coefficients they used above with the points they received to form a point in the kernel of an isogeny that they will create. They each compute pointsSBA{\displaystyle S_{BA}}andSAB{\displaystyle S_{AB}}and useVelu's formulasto construct new isogenies.
To complete the key exchange, A and B compute the coefficients of two new elliptic curves under these two new isogenies. They then compute the j-invariant of these curves. Unless there were errors in transmission, the j-invariant of the curve created by A will equal to the j-invariant of the curve created by B.
Notationally, the SIDH key exchange between parties A and B works as follows:
1A. A generates two random integersmA,nA<(wA)eA.{\displaystyle m_{A},n_{A}<(w_{A})^{e_{A}}.}
2A. A generatesRA:=mA⋅(PA)+nA⋅(QA).{\displaystyle R_{A}:=m_{A}\cdot (P_{A})+n_{A}\cdot (Q_{A}).}
3A. A uses the pointRA{\displaystyle R_{A}}to create an isogeny mappingϕA:E→EA{\displaystyle \phi _{A}:E\rightarrow E_{A}}and curveEA{\displaystyle E_{A}}isogenous toE.{\displaystyle E.}
4A. A appliesϕA{\displaystyle \phi _{A}}toPB{\displaystyle P_{B}}andQB{\displaystyle Q_{B}}to form two points onEA:ϕA(PB){\displaystyle E_{A}:\phi _{A}(P_{B})}andϕA(QB).{\displaystyle \phi _{A}(Q_{B}).}
5A. A sends to BEA,ϕA(PB){\displaystyle E_{A},\phi _{A}(P_{B})}, andϕA(QB).{\displaystyle \phi _{A}(Q_{B}).}
1B - 4B: Same as A1 through A4, but with A and B subscripts swapped.
5B. B sends to AEB,ϕB(PA){\displaystyle E_{B},\phi _{B}(P_{A})}, andϕB(QA).{\displaystyle \phi _{B}(Q_{A}).}
6A. A hasmA,nA,ϕB(PA){\displaystyle m_{A},n_{A},\phi _{B}(P_{A})}, andϕB(QA){\displaystyle \phi _{B}(Q_{A})}and formsSBA:=mA(ϕB(PA))+nA(ϕB(QA)).{\displaystyle S_{BA}:=m_{A}(\phi _{B}(P_{A}))+n_{A}(\phi _{B}(Q_{A})).}
7A. A usesSBA{\displaystyle S_{BA}}to create an isogeny mappingψBA{\displaystyle \psi _{BA}}.
8A. A usesψBA{\displaystyle \psi _{BA}}to create an elliptic curveEBA{\displaystyle E_{BA}}which is isogenous toE{\displaystyle E}.
9A. A computesK:=j-invariant(EBA){\displaystyle K:={\text{ j-invariant }}(E_{BA})}of the curveEBA{\displaystyle E_{BA}}.
6B. Similarly, B hasmB,nB,ϕA(PB){\displaystyle m_{B},n_{B},\phi _{A}(P_{B})}, andϕA(QB){\displaystyle \phi _{A}(Q_{B})}and formsSAB=mB(ϕA(PB))+nB(ϕA(QB)){\displaystyle S_{AB}=m_{B}(\phi _{A}(P_{B}))+n_{B}(\phi _{A}(Q_{B}))}.
7B. B usesSAB{\displaystyle S_{AB}}to create an isogeny mappingψAB{\displaystyle \psi _{AB}}.
8B. B usesψAB{\displaystyle \psi _{AB}}to create an elliptic curveEAB{\displaystyle E_{AB}}which is isogenous toE{\displaystyle E}.
9B. B computesK:=j-invariant(EAB){\displaystyle K:={\text{ j-invariant }}(E_{AB})}of the curveEAB{\displaystyle E_{AB}}.
The curvesEAB{\displaystyle E_{AB}}andEBA{\displaystyle E_{BA}}are guaranteed to have the same j-invariant. A function ofK{\displaystyle K}is used as the shared key.[5]
The following parameters were taken as an example by De Feo et al.:[5]
The prime for the key exchange was selected withwA= 2,wB= 3,eA= 63,eB= 41andf= 11, so thatp= 263· 341· 11 − 1.
The starting curveE0wasy2=x3+x.
Luca De Feo, one of the authors of the paper defining the key exchange, has posted software that implements the key exchange for these and other parameters.[21]
A predecessor to the SIDH was published in 2006 by Rostovtsev and Stolbunov. They created the first Diffie-Hellman replacement based on elliptic curve isogenies. Unlike the method of De Feo, Jao, and Plut, the method of Rostovtsev and Stolbunov used ordinary elliptic curves[22]and was found to have a subexponential quantum attack.[23]
In March 2014, researchers at the Chinese State Key Lab for Integrated Service Networks and Xidian University extended the security of the SIDH to a form of digital signature with strong designated verifier.[24]In October 2014, Jao and Soukharev from the University of Waterloo presented an alternative method of creating undeniable signatures with designated verifier using elliptic curve isogenies.[25][importance?]
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ABLS digital signature,also known asBoneh–Lynn–Shacham[1](BLS), is acryptographicsignature schemewhich allows a user to verify that a signer isauthentic.
The scheme uses abilinear pairinge:G1×G2→GT{\displaystyle e:G_{1}\times G_{2}\to G_{T}}, whereG1,G2,{\displaystyle G_{1},G_{2},}andGT{\displaystyle G_{T}}areelliptic curvegroups of prime orderq{\displaystyle q}, and a hash functionH{\displaystyle H}from the message space intoG1{\displaystyle G_{1}}. Signature are elements ofG1{\displaystyle G_{1}}, public keys are elements ofG2{\displaystyle G_{2}}, and the secret key is an integer in[0,q−1]{\displaystyle [0,q-1]}. Working in an elliptic curve group provides some defense againstindex calculusattacks (with the caveat that such attacks are still possible in the target groupGT{\displaystyle G_{T}}of the pairing), allowing shorter signatures thanFDHsignatures for a similarlevel of security.
Signatures produced by the BLS signature scheme are often referred to asshort signatures,BLS short signatures, or simplyBLS signatures.[2]The signature scheme isprovably secure(the scheme isexistentially unforgeableunderadaptive chosen-message attacks) in therandom oraclemodel assuming the intractability of thecomputational Diffie–Hellman problemin a gap Diffie–Hellman group.[1]
Asignature schemeconsists of three functions:generate,sign, andverify.[1]
The key generation algorithm selects the private key by picking a random integerx∈[0,q−1]{\displaystyle x\in [0,q-1]}. The holder of the private key publishes the public key,g2x{\displaystyle g_{2}^{x}}, whereg2{\displaystyle g_{2}}is a generator ofG2{\displaystyle G_{2}}.
Given the private keyx{\displaystyle x}, and some messagem{\displaystyle m}, we compute the signature by hashing the bitstringm{\displaystyle m}, ash=H(m){\displaystyle h=H(m)}, and we output the signatureσ=hx{\displaystyle \sigma =h^{x}}.
Given a signatureσ{\displaystyle \sigma }for messagem{\displaystyle m}and public keyg2x{\displaystyle g_{2}^{x}}, we verify thate(σ,g2)=e(H(m),g2x){\displaystyle e(\sigma ,g_{2})=e(H(m),g_{2}^{x})}.
BLS12-381 is part of a family of elliptic curves named after Barreto, Lynn, and Scott[7](a different BLS trio, except for the L). It was designed by Sean Bowe in early 2017 as the foundation for an upgrade to theZcashprotocol. It is both pairing-friendly, making it efficient for digital signatures, and effective for constructingzkSnarks.[8]The planned usage[clarification needed]of BLS12-381 for BLS signatures is detailed in the June 2022IETFinternet draft.[9]
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TheDiffie–Hellman problem(DHP) is a mathematical problem first proposed byWhitfield DiffieandMartin Hellman[1]in the context ofcryptographyand serves as the theoretical basis of theDiffie–Hellman key exchangeand its derivatives. The motivation for this problem is that many security systems useone-way functions: mathematical operations that are fast to compute, but hard to reverse. For example, they enable encrypting a message, but reversing the encryption is difficult. If solving the DHP were easy, these systems would be easily broken.
The Diffie–Hellman problem is stated informally as follows:
Formally,g{\displaystyle g}is ageneratorof somegroup(typically themultiplicative groupof afinite fieldor anelliptic curvegroup) andx{\displaystyle x}andy{\displaystyle y}are randomly chosen integers.
For example, in the Diffie–Hellman key exchange, an eavesdropper observesgx{\displaystyle g^{x}}andgy{\displaystyle g^{y}}exchanged as part of the protocol, and the two parties both compute the shared keygxy{\displaystyle g^{xy}}. A fast means of solving the DHP would allow an eavesdropper to violate the privacy of the Diffie–Hellman key exchange and many of its variants, includingElGamal encryption.
Incryptography, for certain groups, it isassumedthat the DHP is hard, and this is often called theDiffie–Hellman assumption. The problem has survived scrutiny for a few decades and no "easy" solution has yet been publicized.
As of 2006, the most efficient means known to solve the DHP is to solve thediscrete logarithm problem(DLP), which is to findxgivengandgx. In fact, significant progress (by den Boer,Maurer, Wolf,BonehandLipton) has been made towards showing that over many groups the DHP is almost as hard as the DLP. There is no proof to date that either the DHP or the DLP is a hard problem, except in generic groups (by Nechaev and Shoup). A proof that either problem is hard implies thatP≠NP.[clarification needed]
Many variants of the Diffie–Hellman problem have been considered. The most significant variant is thedecisional Diffie–Hellman problem(DDHP), which is to distinguishgxyfrom a random group element, giveng,gx, andgy. Sometimes the DHP is called thecomputational Diffie–Hellman problem(CDHP) to more clearly distinguish it from the DDHP. Recently groups withpairingshave become popular, and in these groups the DDHP is easy, yet the CDHP is still assumed to be hard. For less significant variants of the DHP see the references.
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https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_problem
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Incomputing, adenial-of-service attack(DoS attack) is acyberattackin which the perpetrator seeks to make a machine or network resource unavailable to its intendedusersby temporarily or indefinitely disruptingservicesof ahostconnected to anetwork. Denial of service is typically accomplished byfloodingthe targeted machine or resource with superfluous requests in an attempt to overload systems and prevent some or all legitimate requests from being fulfilled.[1]The range of attacks varies widely, spanning from inundating a server with millions of requests to slow its performance, overwhelming a server with a substantial amount of invalid data, to submitting requests with an illegitimateIP address.[2]
In adistributed denial-of-service attack(DDoS attack), the incoming traffic flooding the victim originates from many different sources. More sophisticated strategies are required to mitigate this type of attack; simply attempting to block a single source is insufficient as there are multiple sources.[3][4]A DDoS attack is analogous to a group of people crowding the entry door of a shop, making it hard for legitimate customers to enter, thus disrupting trade and losing the business money. Criminal perpetrators of DDoS attacks often target sites or services hosted on high-profileweb serverssuch asbanksorcredit cardpayment gateways.Revengeandblackmail,[5][6][7]as well ashacktivism,[8]can motivate these attacks.
Panix, the third-oldestISPin the world, was the target of what is thought to be the first DoS attack. On September 6, 1996, Panix was subject to aSYN floodattack, which brought down its services for several days while hardware vendors, notablyCisco, figured out a proper defense.[9]Another early demonstration of the DoS attack was made by Khan C. Smith in 1997 during aDEF CONevent, disrupting Internet access to theLas Vegas Stripfor over an hour. The release of sample code during the event led to the online attack ofSprint,EarthLink,E-Trade, and other major corporations in the year to follow.[citation needed]The largest DDoS attack to date happened in September 2017, whenGoogle Cloudexperienced an attack with a peak volume of2.54 Tb/s, revealed by Google on October 17, 2020.[10]The record holder was thought to be an attack executed by an unnamed customer of the US-based service providerArbor Networks, reaching a peak of about1.7 Tb/s.[11]
In February 2020,Amazon Web Servicesexperienced an attack with a peak volume of2.3 Tb/s.[12]In July 2021, CDN ProviderCloudflareboasted of protecting its client from a DDoS attack from a globalMirai botnetthat was up to 17.2 million requests per second.[13]Russian DDoS prevention providerYandexsaid it blocked a HTTP pipelining DDoS attack on Sept. 5. 2021 that originated from unpatched Mikrotik networking gear.[14]In the first half of 2022, theRussian invasion of Ukrainesignificantly shaped the cyberthreat landscape, with an increase in cyberattacks attributed to both state-sponsored actors and global hacktivist activities. The most notable event was a DDoS attack in February, the largest Ukraine has encountered, disrupting government and financial sector services. This wave of cyber aggression extended to Western allies like the UK, the US, and Germany. Particularly, the UK's financial sector saw an increase in DDoS attacks fromnation-stateactors and hacktivists, aimed at undermining Ukraine's allies.[15]
In February 2023, Cloudflare faced a 71 million/requests per second attack which Cloudflare claims was the largest HTTP DDoS attack at the time.[16]HTTP DDoS attacks are measured by HTTP requests per second instead of packets per second or bits per second. On July 10, 2023, the fanfiction platformArchive of Our Own(AO3) faced DDoS attacks, disrupting services.Anonymous Sudan, claiming the attack for religious and political reasons, was viewed skeptically by AO3 and experts. Flashpoint, a threat intelligence vendor, noted the group's past activities but doubted their stated motives. AO3, supported by the non-profitOrganization for Transformative Works(OTW) and reliant on donations, is unlikely to meet the $30,000Bitcoinransom.[17][18]In August 2023, the group of hacktivistsNoName057targeted several Italian financial institutions, through the execution ofslow DoS attacks.[19]On 14 January 2024, they executed a DDoS attack on Swiss federal websites, prompted byPresident Zelensky's attendance at theDavos World Economic Forum. Switzerland's National Cyber Security Centre quickly mitigated the attack, ensuring core federal services remained secure, despite temporary accessibility issues on some websites.[20]In October 2023, exploitation of a new vulnerability in theHTTP/2protocol resulted in the record for largest HTTP DDoS attack being broken twice, once with a 201 million requests per second attack observed by Cloudflare,[21]and again with a 398 million requests per second attack observed byGoogle.[22]In August 2024, Global Secure Layer observed and reported on a record-breaking packet DDoS at 3.15 billion packets per second, which targeted an undisclosed number of unofficialMinecraft game servers.[23]In October 2024, theInternet Archivefaced two severe DDoS attacks that brought the site completely offline, immediately following a previous attack that leaked records of over 31 million of the site's users.[24][25]The hacktivist groupSN_Blackmetaclaimed the DDoS attack as retribution for American involvement in theGaza war, despite the Internet Archive being unaffiliated with the United States government; however, their link with the preceding data leak remains unclear.[26]
Denial-of-service attacks are characterized by an explicit attempt by attackers to prevent legitimate use of a service. There are two general forms of DoS attacks: those that crash services and those that flood services. The most serious attacks are distributed.[27]
A distributed denial-of-service (DDoS) attack occurs when multiple systems flood thebandwidthor resources of a targeted system, usually one or more web servers.[27]A DDoS attack uses more than one unique IP address or machines, often from thousands of hosts infected withmalware.[28][29]A distributed denial of service attack typically involves more than around 3–5 nodes on different networks; fewer nodes may qualify as a DoS attack but is not a DDoS attack.[30][31]
Multiple attack machines can generate more attack traffic than a single machine and are harder to disable, and the behavior of each attack machine can be stealthier, making the attack harder to track and shut down. Since the incoming traffic flooding the victim originates from different sources, it may be impossible to stop the attack simply by usingingress filtering. It also makes it difficult to distinguish legitimate user traffic from attack traffic when spread across multiple points of origin. As an alternative or augmentation of a DDoS, attacks may involve forging of IP sender addresses (IP address spoofing) further complicating identifying and defeating the attack. These attacker advantages cause challenges for defense mechanisms. For example, merely purchasing more incoming bandwidth than the current volume of the attack might not help, because the attacker might be able to simply add more attack machines.[citation needed]The scale of DDoS attacks has continued to rise over recent years, by 2016 exceeding aterabit per second.[32][33]Some common examples of DDoS attacks areUDP flooding,SYN floodingandDNS amplification.[34][35]
Ayo-yoattack is a specific type of DoS/DDoS aimed atcloud-hostedapplications which useautoscaling.[36][37][38]The attacker generates a flood of traffic until a cloud-hosted service scales outwards to handle the increase of traffic, then halts the attack, leaving the victim with over-provisioned resources. When the victim scales back down, the attack resumes, causing resources to scale back up again. This can result in a reduced quality of service during the periods of scaling up and down and a financial drain on resources during periods of over-provisioning while operating with a lower cost for an attacker compared to a normal DDoS attack, as it only needs to be generating traffic for a portion of the attack period.
Anapplication layer DDoS attack(sometimes referred to aslayer 7 DDoS attack) is a form of DDoS attack where attackers targetapplication-layerprocesses.[39][30]The attack over-exercises specific functions or features of a website with the intention to disable those functions or features. This application-layer attack is different from an entire network attack, and is often used against financial institutions to distract IT and security personnel from security breaches.[40]In 2013, application-layer DDoS attacks represented 20% of all DDoS attacks.[41]According to research byAkamai Technologies, there have been "51 percent more application layer attacks" from Q4 2013 to Q4 2014 and "16 percent more" from Q3 2014 to Q4 2014.[42]In November 2017; Junade Ali, an engineer at Cloudflare noted that whilst network-level attacks continue to be of high capacity, they were occurring less frequently. Ali further noted that although network-level attacks were becoming less frequent, data from Cloudflare demonstrated that application-layer attacks were still showing no sign of slowing down.[43]
TheOSI model(ISO/IEC 7498-1) is a conceptual model that characterizes and standardizes the internal functions of a communication system by partitioning it intoabstraction layers. The model is a product of theOpen Systems Interconnectionproject at theInternational Organization for Standardization(ISO). The model groups similar communication functions into one of seven logical layers. A layer serves the layer above it and is served by the layer below it. For example, a layer that provides error-free communications across a network provides the communications path needed by applications above it, while it calls the next lower layer to send and receive packets that traverse that path. In the OSI model, the definition of its application layer is narrower in scope than is often implemented. The OSI model defines the application layer as being the user interface. The OSI application layer is responsible for displaying data and images to the user in a human-recognizable format and to interface with thepresentation layerbelow it. In an implementation, the application and presentation layers are frequently combined.
The simplest DoS attack relies primarily on brute force, flooding the target with an overwhelming flux of packets, oversaturating its connection bandwidth or depleting the target's system resources. Bandwidth-saturating floods rely on the attacker's ability to generate the overwhelming flux of packets. A common way of achieving this today is via distributed denial-of-service, employing abotnet. An application layer DDoS attack is done mainly for specific targeted purposes, including disrupting transactions and access to databases. It requires fewer resources than network layer attacks but often accompanies them.[44]An attack may be disguised to look like legitimate traffic, except it targets specific application packets or functions. The attack on the application layer can disrupt services such as the retrieval of information or search functions on a website.[41]
Anadvanced persistent DoS(APDoS) is associated with anadvanced persistent threatand requires specializedDDoS mitigation.[45]These attacks can persist for weeks; the longest continuous period noted so far lasted 38 days. This attack involved approximately 50+ petabits (50,000+ terabits) of malicious traffic.[46]Attackers in this scenario may tactically switch between several targets to create a diversion to evade defensive DDoS countermeasures but all the while eventually concentrating the main thrust of the attack onto a single victim. In this scenario, attackers with continuous access to several very powerful network resources are capable of sustaining a prolonged campaign generating enormous levels of unamplified DDoS traffic. APDoS attacks are characterized by:
Some vendors provide so-calledbooterorstresserservices, which have simple web-based front ends, and accept payment over the web. Marketed and promoted as stress-testing tools, they can be used to perform unauthorized denial-of-service attacks, and allow technically unsophisticated attackers access to sophisticated attack tools.[48]Usually powered by a botnet, the traffic produced by a consumer stresser can range anywhere from 5-50 Gbit/s, which can, in most cases, deny the average home user internet access.[49]
A Markov-modulated denial-of-service attack occurs when the attacker disrupts control packets using ahidden Markov model. A setting in which Markov-model based attacks are prevalent is online gaming as the disruption of the control packet undermines game play and system functionality.[50]
TheUnited States Computer Emergency Readiness Team(US-CERT) has identified symptoms of a denial-of-service attack to include:[51]
In cases such asMyDoomandSlowloris, the tools are embedded inmalwareand launch their attacks without the knowledge of the system owner.Stacheldrahtis a classic example of a DDoS tool. It uses a layered structure where the attacker uses aclient programto connect to handlers which are compromised systems that issue commands to thezombie agentswhich in turn facilitate the DDoS attack. Agents are compromised via the handlers by the attacker using automated routines to exploit vulnerabilities in programs that accept remote connections running on the targeted remote hosts. Each handler can control up to a thousand agents.[52]
In other cases a machine may become part of a DDoS attack with the owner's consent, for example, inOperation Paybackorganized by the groupAnonymous. TheLow Orbit Ion Cannonhas typically been used in this way. Along withHigh Orbit Ion Cannona wide variety of DDoS tools are available today, including paid and free versions, with different features available. There is an underground market for these in hacker-related forums and IRC channels.
Application-layer attacks employ DoS-causingexploitsand can cause server-running software to fill the disk space or consume all available memory orCPU time. Attacks may use specific packet types or connection requests to saturate finite resources by, for example, occupying the maximum number of open connections or filling the victim's disk space with logs. An attacker with shell-level access to a victim's computer may slow it until it is unusable or crash it by using afork bomb. Another kind of application-level DoS attack is XDoS (or XML DoS) which can be controlled by modern webapplication firewalls(WAFs). All attacks belonging to the category oftimeout exploiting.[53]
Slow DoS attacksimplement an application-layer attack. Examples of threats are Slowloris, establishing pending connections with the victim, orSlowDroid, an attack running on mobile devices. Another target of DDoS attacks may be to produce added costs for the application operator, when the latter uses resources based oncloud computing. In this case, normally application-used resources are tied to a needed quality of service (QoS) level (e.g. responses should be less than 200 ms) and this rule is usually linked to automated software (e.g. Amazon CloudWatch[54]) to raise more virtual resources from the provider to meet the defined QoS levels for the increased requests. The main incentive behind such attacks may be to drive the application owner to raise the elasticity levels to handle the increased application traffic, to cause financial losses, or force them to become less competitive. Abanana attackis another particular type of DoS. It involves redirecting outgoing messages from the client back onto the client, preventing outside access, as well as flooding the client with the sent packets. ALANDattack is of this type.
Pulsing zombies are compromised computers that are directed to launch intermittent and short-lived floodings of victim websites with the intent of merely slowing it rather than crashing it. This type of attack, referred to asdegradation-of-service, can be more difficult to detect and can disrupt and hamper connection to websites for prolonged periods of time, potentially causing more overall disruption than a denial-of-service attack.[55][56]Exposure of degradation-of-service attacks is complicated further by the matter of discerning whether the server is really being attacked or is experiencing higher than normal legitimate traffic loads.[57]
If an attacker mounts an attack from a single host, it would be classified as a DoS attack. Any attack against availability would be classed as a denial-of-service attack. On the other hand, if an attacker uses many systems to simultaneously launch attacks against a remote host, this would be classified as a DDoS attack.Malwarecan carry DDoS attack mechanisms; one of the better-known examples of this wasMyDoom. Its DoS mechanism was triggered on a specific date and time. This type of DDoS involved hardcoding the targetIP addressbefore releasing the malware and no further interaction was necessary to launch the attack. A system may also be compromised with atrojancontaining azombie agent. Attackers can also break into systems using automated tools that exploit flaws in programs that listen for connections from remote hosts. This scenario primarily concerns systems acting as servers on the web.Stacheldrahtis a classic example of a DDoS tool. It uses a layered structure where the attacker uses aclient programto connect to handlers, which are compromised systems that issue commands to the zombie agents, which in turn facilitate the DDoS attack. Agents are compromised via the handlers by the attacker. Each handler can control up to a thousand agents.[52]In some cases a machine may become part of a DDoS attack with the owner's consent, for example, inOperation Payback, organized by the groupAnonymous. These attacks can use different types of internet packets such as TCP, UDP, ICMP, etc.
These collections of compromised systems are known asbotnets. DDoS tools likeStacheldrahtstill use classic DoS attack methods centered onIP spoofingand amplification likesmurf attacksandfraggle attacks(types of bandwidth consumption attacks).SYN floods(a resource starvation attack) may also be used. Newer tools can use DNS servers for DoS purposes. Unlike MyDoom's DDoS mechanism, botnets can be turned against any IP address.Script kiddiesuse them to deny the availability of well known websites to legitimate users.[58]More sophisticated attackers use DDoS tools for the purposes ofextortion– including against their business rivals.[59]It has been reported that there are new attacks frominternet of things(IoT) devices that have been involved in denial of service attacks.[60]In one noted attack that was made peaked at around 20,000 requests per second which came from around 900 CCTV cameras.[61]UK'sGCHQhas tools built for DDoS, named PREDATORS FACE and ROLLING THUNDER.[62]
Simple attacks such as SYN floods may appear with a wide range of source IP addresses, giving the appearance of a distributed DoS. These flood attacks do not require completion of the TCPthree-way handshakeand attempt to exhaust the destination SYN queue or the server bandwidth. Because the source IP addresses can be trivially spoofed, an attack could come from a limited set of sources, or may even originate from a single host. Stack enhancements such asSYN cookiesmay be effective mitigation against SYN queue flooding but do not address bandwidth exhaustion. In 2022, TCP attacks were the leading method in DDoS incidents, accounting for 63% of all DDoS activity. This includes tactics likeTCP SYN, TCP ACK, and TCP floods. With TCP being the most widespread networking protocol, its attacks are expected to remain prevalent in the DDoS threat scene.[15]
In 2015, DDoS botnets such as DD4BC grew in prominence, taking aim at financial institutions.[63]Cyber-extortionists typically begin with a low-level attack and a warning that a larger attack will be carried out if a ransom is not paid inbitcoin.[64]Security experts recommend targeted websites to not pay the ransom. The attackers tend to get into an extended extortion scheme once they recognize that the target is ready to pay.[65]
First discovered in 2009, the HTTP slow POST attack sends a complete, legitimateHTTP POST header, which includes aContent-Lengthfield to specify the size of the message body to follow. However, the attacker then proceeds to send the actual message body at an extremely slow rate (e.g. 1 byte/110 seconds). Due to the entire message being correct and complete, the target server will attempt to obey theContent-Lengthfield in the header, and wait for the entire body of the message to be transmitted, which can take a very long time. The attacker establishes hundreds or even thousands of such connections until all resources for incoming connections on the victim server are exhausted, making any further connections impossible until all data has been sent. It is notable that unlike many other DDoS or DDoS attacks, which try to subdue the server by overloading its network or CPU, an HTTP slow POST attack targets thelogicalresources of the victim, which means the victim would still have enough network bandwidth and processing power to operate.[66]Combined with the fact that theApache HTTP Serverwill, by default, accept requests up to 2GB in size, this attack can be particularly powerful. HTTP slow POST attacks are difficult to differentiate from legitimate connections and are therefore able to bypass some protection systems.OWASP, anopen sourceweb application security project, released a tool to test the security of servers against this type of attack.[67]
A Challenge Collapsar (CC) attack is an attack where standard HTTP requests are sent to a targeted web server frequently. TheUniform Resource Identifiers(URIs) in the requests require complicated time-consuming algorithms or database operations which may exhaust the resources of the targeted web server.[68][69][70]In 2004, a Chinese hacker nicknamed KiKi invented a hacking tool to send these kinds of requests to attack a NSFOCUS firewall named Collapsar, and thus the hacking tool was known as Challenge Collapsar, orCCfor short. Consequently, this type of attack got the nameCC attack.[71]
Asmurf attackrelies on misconfigured network devices that allow packets to be sent to all computer hosts on a particular network via thebroadcast addressof the network, rather than a specific machine. The attacker will send large numbers ofIPpackets with the source address faked to appear to be the address of the victim.[72]Most devices on a network will, by default, respond to this by sending a reply to the source IP address. If the number of machines on the network that receive and respond to these packets is very large, the victim's computer will be flooded with traffic. This overloads the victim's computer and can even make it unusable during such an attack.[73]
Ping floodis based on sending the victim an overwhelming number ofpingpackets, usually using thepingcommand fromUnix-likehosts.[a]It is very simple to launch, the primary requirement being access to greaterbandwidththan the victim.Ping of deathis based on sending the victim a malformed ping packet, which will lead to a system crash on a vulnerable system. TheBlackNurseattack is an example of an attack taking advantage of the required Destination Port Unreachable ICMP packets.
A nuke is an old-fashioned denial-of-service attack againstcomputer networksconsisting of fragmented or otherwise invalidICMPpackets sent to the target, achieved by using a modifiedpingutility to repeatedly send thiscorrupt data, thus slowing down the affected computer until it comes to a complete stop.[74]A specific example of a nuke attack that gained some prominence is theWinNuke, which exploited the vulnerability in theNetBIOShandler inWindows 95. A string of out-of-band data was sent toTCPport 139 of the victim's machine, causing it to lock up and display aBlue Screen of Death.[74]
Attackers have found a way to exploit a number of bugs inpeer-to-peerservers to initiate DDoS attacks. The most aggressive of these peer-to-peer-DDoS attacks exploitsDC++.[citation needed][ambiguous]With peer-to-peer there is no botnet and the attacker does not have to communicate with the clients it subverts. Instead, the attacker acts as apuppet master, instructing clients of largepeer-to-peer file sharinghubs to disconnect from their peer-to-peer network and to connect to the victim's website instead.[75][76][77]
Permanent denial-of-service (PDoS), also known loosely as phlashing,[78]is an attack that damages a system so badly that it requires replacement or reinstallation of hardware.[79]Unlike the distributed denial-of-service attack, a PDoS attack exploits security flaws which allow remote administration on the management interfaces of the victim's hardware, such asrouters, printers, or othernetworking hardware. The attacker uses thesevulnerabilitiesto replace a device'sfirmwarewith a modified, corrupt, or defective firmware image—a process which when done legitimately is known asflashing.The intent is tobrickthe device, rendering it unusable for its original purpose until it can be repaired or replaced. The PDoS is a pure hardware-targeted attack that can be much faster and requires fewer resources than using a botnet in a DDoS attack. Because of these features, and the potential and high probability of security exploits on network-enabled embedded devices, this technique has come to the attention of numerous hacking communities.BrickerBot, a piece of malware that targeted IoT devices, used PDoS attacks to disable its targets.[80]PhlashDance is a tool created by Rich Smith (an employee ofHewlett-Packard's Systems Security Lab) used to detect and demonstrate PDoS vulnerabilities at the 2008 EUSecWest Applied Security Conference in London, UK.[81]
A distributed denial-of-service attack may involve sending forged requests of some type to a very large number of computers that will reply to the requests. UsingInternet Protocol address spoofing, the source address is set to that of the targeted victim, which means all the replies will go to (and flood) the target. This reflected attack form is sometimes called adistributed reflective denial-of-service(DRDoS) attack.[82]ICMP echo requestattacks (Smurf attacks) can be considered one form of reflected attack, as the flooding hosts send Echo Requests to the broadcast addresses of mis-configured networks, thereby enticing hosts to send Echo Reply packets to the victim. Some early DDoS programs implemented a distributed form of this attack.
Amplification attacks are used to magnify the bandwidth that is sent to a victim. Many services can be exploited to act as reflectors, some harder to block than others.[83]US-CERT have observed that different services may result in different amplification factors, as tabulated below:[84]
DNSamplification attacks involves an attacker sending a DNS name lookup request to one or more public DNS servers, spoofing the source IP address of the targeted victim. The attacker tries to request as much information as possible, thus amplifying the DNS response that is sent to the targeted victim. Since the size of the request is significantly smaller than the response, the attacker is easily able to increase the amount of traffic directed at the target.[90][91]
Simple Network Management Protocol(SNMP) andNetwork Time Protocol(NTP) can also be exploited as reflectors in an amplification attack. An example of an amplified DDoS attack through the NTP is through a command called monlist, which sends the details of the last 600 hosts that have requested the time from the NTP server back to the requester. A small request to this time server can be sent using a spoofed source IP address of some victim, which results in a response 556.9 times the size of the request being sent to the victim. This becomes amplified when using botnets that all send requests with the same spoofed IP source, which will result in a massive amount of data being sent back to the victim. It is very difficult to defend against these types of attacks because the response data is coming from legitimate servers. These attack requests are also sent through UDP, which does not require a connection to the server. This means that the source IP is not verified when a request is received by the server. To bring awareness of these vulnerabilities, campaigns have been started that are dedicated to finding amplification vectors which have led to people fixing their resolvers or having the resolvers shut down completely.[citation needed]
TheMirai botnetworks by using acomputer wormto infect hundreds of thousands of IoT devices across the internet. The worm propagates through networks and systems taking control of poorly protected IoT devices such as thermostats, Wi-Fi-enabled clocks, and washing machines.[92]The owner or user will usually have no immediate indication of when the device becomes infected. The IoT device itself is not the direct target of the attack, it is used as a part of a larger attack.[93]Once the hacker has enslaved the desired number of devices, they instruct the devices to try to contact an ISP. In October 2016, a Mirai botnetattacked Dynwhich is the ISP for sites such asTwitter,Netflix, etc.[92]As soon as this occurred, these websites were all unreachable for several hours.
RUDY attack targets web applications by starvation of available sessions on the web server. Much like Slowloris, RUDY keeps sessions at halt using never-ending POST transmissions and sending an arbitrarily large content-length header value.[94]
Manipulatingmaximum segment sizeandselective acknowledgement(SACK) may be used by a remote peer to cause a denial of service by aninteger overflowin the Linux kernel, potentially causing akernel panic.[95]Jonathan Looney discoveredCVE-2019-11477, CVE-2019-11478, CVE-2019-11479on June 17, 2019.[96]
The shrew attack is a denial-of-service attack on theTransmission Control Protocolwhere the attacker employsman-in-the-middle techniques. It exploits a weakness in TCP's re-transmission timeout mechanism, using short synchronized bursts of traffic to disrupt TCP connections on the same link.[97]
A slow read attack sends legitimate application layer requests, but reads responses very slowly, keeping connections open longer hoping to exhaust the server's connection pool. The slow read is achieved by advertising a very small number for the TCP Receive Window size, and at the same time emptying clients' TCP receive buffer slowly, which causes a very low data flow rate.[98]
A sophisticated low-bandwidth DDoS attack is a form of DoS that uses less traffic and increases its effectiveness by aiming at a weak point in the victim's system design, i.e., the attacker sends traffic consisting of complicated requests to the system.[99]Essentially, a sophisticated DDoS attack is lower in cost due to its use of less traffic, is smaller in size making it more difficult to identify, and it has the ability to hurt systems which are protected by flow control mechanisms.[99][100]
ASYN floodoccurs when a host sends a flood of TCP/SYN packets, often with a forged sender address. Each of these packets is handled like a connection request, causing the server to spawn ahalf-open connection, send back a TCP/SYN-ACK packet, and wait for a packet in response from the sender address. However, because the sender's address is forged, the response never comes. These half-open connections exhaust the available connections the server can make, keeping it from responding to legitimate requests until after the attack ends.[101]
Ateardrop attackinvolves sendingmangledIP fragmentswith overlapping, oversized payloads to the target machine. This can crash various operating systems because of a bug in theirTCP/IPfragmentation re-assemblycode.[102]Windows 3.1x,Windows 95andWindows NToperating systems, as well as versions ofLinuxprior to versions 2.0.32 and 2.1.63 are vulnerable to this attack.[b]One of the fields in anIP headeris thefragment offsetfield, indicating the starting position, or offset, of the data contained in a fragmented packet relative to the data in the original packet. If the sum of the offset and size of one fragmented packet differs from that of the next fragmented packet, the packets overlap. When this happens, a server vulnerable to teardrop attacks is unable to reassemble the packets resulting in a denial-of-service condition.[105]
Voice over IPhas made abusive origination of large numbers oftelephonevoice calls inexpensive and easily automated while permitting call origins to be misrepresented throughcaller ID spoofing. According to the USFederal Bureau of Investigation, telephony denial-of-service (TDoS) has appeared as part of various fraudulent schemes:
TDoS can exist even withoutInternet telephony. In the2002 New Hampshire Senate election phone jamming scandal,telemarketerswere used to flood political opponents with spurious calls to jam phone banks on election day. Widespread publication of a number can also flood it with enough calls to render it unusable, as happened by accident in 1981 with multiple +1-area code-867-5309 subscribers inundated by hundreds of calls daily in response to the song "867-5309/Jenny". TDoS differs from othertelephone harassment(such asprank callsandobscene phone calls) by the number of calls originated. By occupying lines continuously with repeated automated calls, the victim is prevented from making or receiving both routine and emergency telephone calls. Related exploits include SMS flooding attacks andblack faxor continuous fax transmission by using a loop of paper at the sender.
It takes more router resources to drop a packet with aTTLvalue of 1 or less than it does to forward a packet with a higher TTL value. When a packet is dropped due to TTL expiry, the router CPU must generate and send anICMP time exceededresponse. Generating many of these responses can overload the router's CPU.[108]
A UPnP attack uses an existing vulnerability inUniversal Plug and Play(UPnP) protocol to get past network security and flood a target's network and servers. The attack is based on a DNS amplification technique, but the attack mechanism is a UPnP router that forwards requests from one outer source to another. The UPnP router returns the data on an unexpected UDP port from a bogus IP address, making it harder to take simple action to shut down the traffic flood. According to theImpervaresearchers, the most effective way to stop this attack is for companies to lock down UPnP routers.[109][110]
In 2014, it was discovered thatSimple Service Discovery Protocol(SSDP) was being used inDDoSattacks known as anSSDP reflection attackwith amplification. Many devices, including some residential routers, have a vulnerability in the UPnP software that allows an attacker to get replies fromUDP port 1900to a destination address of their choice. With abotnetof thousands of devices, the attackers can generate sufficient packet rates and occupy bandwidth to saturate links, causing the denial of services.[111][112][113]Because of this weakness, the network companyCloudflarehas described SSDP as the "Stupidly Simple DDoS Protocol".[113]
ARP spoofingis a common DoS attack that involves a vulnerability in the ARP protocol that allows an attacker to associate theirMAC addressto the IP address of another computer orgateway, causing traffic intended for the original authentic IP to be re-routed to that of the attacker, causing a denial of service.
Defensive responses to denial-of-service attacks typically involve the use of a combination of attack detection, traffic classification and response tools, aiming to block traffic the tools identify as illegitimate and allow traffic that they identify as legitimate.[114]A list of response tools include the following.
All traffic destined to the victim is diverted to pass through acleaning centeror ascrubbing centervia various methods such as: changing the victim IP address in the DNS system, tunneling methods (GRE/VRF, MPLS, SDN),[115]proxies, digital cross connects, or even direct circuits. The cleaning center separatesbadtraffic (DDoS and also other common internet attacks) and only passes good legitimate traffic to the victim server.[116]The victim needs central connectivity to the Internet to use this kind of service unless they happen to be located within the same facility as the cleaning center. DDoS attacks can overwhelm any type of hardware firewall, and passing malicious traffic through large and mature networks becomes more and more effective and economically sustainable against DDoS.[117]
Application front-end hardware is intelligent hardware placed on the network before traffic reaches the servers. It can be used on networks in conjunction with routers andswitchesand as part ofbandwidth management. Application front-end hardware analyzes data packets as they enter the network, and identifies and drops dangerous or suspicious flows.
Approaches to detection of DDoS attacks against cloud-based applications may be based on an application layer analysis, indicating whether incoming bulk traffic is legitimate.[118]These approaches mainly rely on an identified path of value inside the application and monitor the progress of requests on this path, through markers calledkey completion indicators.[119]In essence, these techniques are statistical methods of assessing the behavior of incoming requests to detect if something unusual or abnormal is going on. An analogy is to a brick-and-mortar department store where customers spend, on average, a known percentage of their time on different activities such as picking up items and examining them, putting them back, filling a basket, waiting to pay, paying, and leaving. If a mob of customers arrived in the store and spent all their time picking up items and putting them back, but never made any purchases, this could be flagged as unusual behavior.
Withblackhole routing, all the traffic to the attacked DNS or IP address is sent to ablack hole(null interface or a non-existent server). To be more efficient and avoid affecting network connectivity, it can be managed by the ISP.[120]ADNS sinkholeroutes traffic to a valid IP address which analyzes traffic and rejects bad packets. Sinkholing may not be efficient for severe attacks.
Intrusion prevention systems(IPS) are effective if the attacks have signatures associated with them. However, the trend among attacks is to have legitimate content but bad intent. Intrusion-prevention systems that work on content recognition cannot block behavior-based DoS attacks.[45]AnASICbased IPS may detect and block denial-of-service attacks because they have theprocessing powerand the granularity to analyze the attacks and act like acircuit breakerin an automated way.[45]
More focused on the problem than IPS, a DoS defense system (DDS) can block connection-based DoS attacks and those with legitimate content but bad intent. A DDS can also address both protocol attacks (such as teardrop and ping of death) and rate-based attacks (such as ICMP floods and SYN floods). DDS has a purpose-built system that can easily identify and obstruct denial of service attacks at a greater speed than a software-based system.[121]
In the case of a simple attack, afirewallcan be adjusted to deny all incoming traffic from the attackers, based on protocols, ports, or the originating IP addresses. More complex attacks will however be hard to block with simple rules: for example, if there is an ongoing attack on port 80 (web service), it is not possible to drop all incoming traffic on this port because doing so will prevent the server from receiving and serving legitimate traffic.[122]Additionally, firewalls may be too deep in the network hierarchy, with routers being adversely affected before the traffic gets to the firewall. Also, many security tools still do not support IPv6 or may not be configured properly, so the firewalls may be bypassed during the attacks.[123]
Similar to switches, routers have somerate-limitingandACLcapabilities. They, too, are manually set. Most routers can be easily overwhelmed under a DoS attack. Nokia SR-OS using FP4 or FP5 processors offers DDoS protection.[124]Nokia SR-OS also uses big data analytics-based Nokia Deepfield Defender for DDoS protection.[125]Cisco IOShas optional features that can reduce the impact of flooding.[126]
Most switches have some rate-limiting andACLcapability. Some switches provide automatic or system-widerate limiting,traffic shaping,delayed binding(TCP splicing),deep packet inspectionandbogon filtering(bogus IP filtering) to detect and remediate DoS attacks through automatic rate filtering and WAN Link failover and balancing. These schemes will work as long as the DoS attacks can be prevented by using them. For example, SYN flood can be prevented using delayed binding or TCP splicing. Similarly, content-based DoS may be prevented using deep packet inspection. Attacks usingMartian packetscan be prevented using bogon filtering. Automatic rate filtering can work as long as set rate thresholds have been set correctly. WAN-link failover will work as long as both links have a DoS prevention mechanism.[45]
Threats may be associated with specific TCP or UDP port numbers. Blocking these ports at the firewall can mitigate an attack. For example, in an SSDP reflection attack, the key mitigation is to block incoming UDP traffic on port 1900.[127]
An unintentional denial-of-service can occur when a system ends up denied, not due to a deliberate attack by a single individual or group of individuals, but simply due to a sudden enormous spike in popularity. This can happen when an extremely popular website posts a prominent link to a second, less well-prepared site, for example, as part of a news story. The result is that a significant proportion of the primary site's regular users – potentially hundreds of thousands of people – click that link in the space of a few hours, having the same effect on the target website as a DDoS attack. A VIPDoS is the same, but specifically when the link was posted by a celebrity. WhenMichael Jackson diedin 2009, websites such as Google and Twitter slowed down or even crashed.[128]Many sites' servers thought the requests were from a virus or spyware trying to cause a denial-of-service attack, warning users that their queries looked like "automated requests from acomputer virusor spyware application".[129]
News sites and link sites – sites whose primary function is to provide links to interesting content elsewhere on the Internet – are most likely to cause this phenomenon. The canonical example is theSlashdot effectwhen receiving traffic fromSlashdot. It is also known as "theReddithug of death"[130]and "theDiggeffect".[131]
Similar unintentional denial-of-service can also occur via other media, e.g. when a URL is mentioned on television. In March 2014, afterMalaysia Airlines Flight 370went missing,DigitalGlobelaunched acrowdsourcingservice on which users could help search for the missing jet in satellite images. The response overwhelmed the company's servers.[132]An unintentional denial-of-service may also result from a prescheduled event created by the website itself, as was the case of theCensus in Australiain 2016.[133]
Legal action has been taken in at least one such case. In 2006,Universal Tube & Rollform Equipment CorporationsuedYouTube: massive numbers of would-be YouTube.com users accidentally typed the tube company's URL, utube.com. As a result, the tube company ended up having to spend large amounts of money on upgrading its bandwidth.[134]The company appears to have taken advantage of the situation, with utube.com now containing ads and receiving advertisement revenue.
Routers have also been known to create unintentional DoS attacks, as bothD-LinkandNetgearrouters haveoverloaded NTP serversby flooding them without respecting the restrictions of client types or geographical limitations.
In computer network security, backscatter is a side-effect of a spoofed denial-of-service attack. In this kind of attack, the attacker spoofs the source address inIP packetssent to the victim. In general, the victim machine cannot distinguish between the spoofed packets and legitimate packets, so the victim responds to the spoofed packets as it normally would. These response packets are known as backscatter.[135]
If the attacker is spoofing source addresses randomly, the backscatter response packets from the victim will be sent back to random destinations. This effect can be used bynetwork telescopesas indirect evidence of such attacks. The termbackscatter analysisrefers to observing backscatter packets arriving at a statistically significant portion of the IP address space to determine the characteristics of DoS attacks and victims.
Many jurisdictions have laws under which denial-of-service attacks are illegal.UNCTADhighlights that 156 countries, or 80% globally, have enactedcybercrimelaws to combat its widespread impact. Adoption rates vary by region, with Europe at a 91% rate, and Africa at 72%.[137]
In the US, denial-of-service attacks may be considered a federal crime under theComputer Fraud and Abuse Actwith penalties that include years of imprisonment.[138]TheComputer Crime and Intellectual Property Sectionof theUS Department of Justicehandles cases of DoS and DDoS. In one example, in July 2019, Austin Thompson, akaDerpTrolling, was sentenced to 27 months in prison and $95,000 restitution by a federal court for conducting multiple DDoS attacks on major video gaming companies, disrupting their systems from hours to days.[139][140]
In European countries, committing criminal denial-of-service attacks may, as a minimum, lead to arrest.[141]The United Kingdom is unusual in that it specifically outlawed denial-of-service attacks and set a maximum penalty of 10 years in prison with thePolice and Justice Act 2006, which amended Section 3 of theComputer Misuse Act 1990.[142]
In January 2019,Europolannounced that "actions are currently underway worldwide to track down the users" of Webstresser.org, a former DDoS marketplace that was shut down in April 2018 as part ofOperation PowerOFF.[143]Europol said UK police were conducting a number of "live operations" targeting over 250 users of Webstresser and other DDoS services.[144]
On January 7, 2013,Anonymousposted apetitionon thewhitehouse.govsite asking that DDoS be recognized as a legal form of protest similar to theOccupy movement, the claim being that the similarity in the purpose of both is same.[145]
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Incryptography,Post-Quantum Extended Diffie–Hellman(PQXDH) is aKyber-basedpost-quantum cryptographyupgrade to theDiffie–Hellman key exchange. It is notably being incorporated into theSignal Protocol, anend-to-end encryptionprotocol.
In September 2023, the developers of the Signal Protocol announced that it was being updated to support PQXDH.[1][2][3]
PQXDH is an upgraded version of theX3DHprotocol and uses both the quantum-resistant CRYSTALS-Kyber protocol as well as the old elliptic curveX25519protocol. This ensures that an attacker must break both of the encryption protocols to gain access to sensitive data, mitigating potential security vulnerabilities the new protocol could have. The protocol is designed for asynchronous communication where the clients exchangepublic keysthrough aserverto derive a secureshared keywhich they can use to encrypt sensitive data without needing to constantly sync new keys with each other.[2][3]
In October 2023, the protocol underwentformal verificationwhich managed to "prove all the desired security properties of the protocol" for its second revision.[4]
This cryptography-related article is astub. You can help Wikipedia byexpanding it.
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The followingoutlineis provided as an overview of and topical guide to cryptography:
Cryptography(orcryptology) – practice and study of hidinginformation. Modern cryptography intersects the disciplines ofmathematics,computer science, andengineering. Applications of cryptography includeATM cards,computer passwords, andelectronic commerce.
List of cryptographers
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Blum Blum Shub(B.B.S.) is apseudorandom number generatorproposed in 1986 byLenore Blum,Manuel BlumandMichael Shub[1]that is derived fromMichael O. Rabin's one-way function.
Blum Blum Shub takes the form
whereM=pqis the product of two largeprimespandq. At each step of the algorithm, some output is derived fromxn+1; the output is commonly either thebit parityofxn+1or one or more of the least significant bits ofxn+1.
Theseedx0should be an integer that is co-prime toM(i.e.pandqare not factors ofx0) and not 1 or 0.
The two primes,pandq, should both becongruentto 3 (mod 4) (this guarantees that eachquadratic residuehas onesquare rootwhich is also a quadratic residue), and should besafe primeswith a smallgcd((p-3)/2, (q-3)/2) (this makes the cycle length large).
An interesting characteristic of the Blum Blum Shub generator is the possibility to calculate anyxivalue directly (viaEuler's theorem):
whereλ{\displaystyle \lambda }is theCarmichael function. (Here we haveλ(M)=λ(p⋅q)=lcm(p−1,q−1){\displaystyle \lambda (M)=\lambda (p\cdot q)=\operatorname {lcm} (p-1,q-1)}).
There is a proof reducing its security to thecomputational difficultyof factoring.[1]When the primes are chosen appropriately, andO(loglogM) lower-order bits of eachxnare output, then in the limit asMgrows large, distinguishing the output bits from random should be at least as difficult as solving thequadratic residuosity problemmoduloM.
The performance of the BBS random-number generator depends on the size of the modulusMand the number of bits per iterationj. While loweringMor increasingjmakes the algorithm faster, doing so also reduces the security. A 2005 paper gives concrete, as opposed to asymptotic, security proof of BBS, for a givenMandj. The result can also be used to guide choices of the two numbers by balancing expected security against computational cost.[2]
Letp=11{\displaystyle p=11},q=23{\displaystyle q=23}ands=3{\displaystyle s=3}(wheres{\displaystyle s}is the seed). We can expect to get a large cycle length for those small numbers, becausegcd((p−3)/2,(q−3)/2)=2{\displaystyle {\rm {gcd}}((p-3)/2,(q-3)/2)=2}.
The generator starts to evaluatex0{\displaystyle x_{0}}by usingx−1=s{\displaystyle x_{-1}=s}and creates the sequencex0{\displaystyle x_{0}},x1{\displaystyle x_{1}},x2{\displaystyle x_{2}},…{\displaystyle \ldots }x5{\displaystyle x_{5}}= 9, 81, 236, 36, 31, 202. The following table shows the output (in bits) for the different bit selection methods used to determine the output.
The following is aPythonimplementation that does check for primality.
The followingCommon Lispimplementation provides a simple demonstration of the generator, in particular regarding the three bit selection methods. It is important to note that the requirements imposed upon the parametersp,qands(seed) are not checked.
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TheTonelli–Shanksalgorithm(referred to by Shanks as the RESSOL algorithm) is used inmodular arithmeticto solve forrin a congruence of the formr2≡n(modp), wherepis aprime: that is, to find a square root ofnmodulop.
Tonelli–Shanks cannot be used for composite moduli: finding square roots modulo composite numbers is a computational problem equivalent tointeger factorization.[1]
An equivalent, but slightly more redundant version of this algorithm was developed byAlberto Tonelli[2][3]in 1891. The version discussed here was developed independently byDaniel Shanksin 1973, who explained:
My tardiness in learning of these historical references was because I had lent Volume 1 ofDickson'sHistoryto a friend and it was never returned.[4]
According to Dickson,[3]Tonelli's algorithm can take square roots ofxmodulo prime powerspλapart from primes.
Given a non-zeron{\displaystyle n}and a primep>2{\displaystyle p>2}(which will always be odd),Euler's criteriontells us thatn{\displaystyle n}has a square root (i.e.,n{\displaystyle n}is aquadratic residue) if and only if:
In contrast, if a numberz{\displaystyle z}has no square root (is a non-residue), Euler's criterion tells us that:
It is not hard to find suchz{\displaystyle z}, because half of the integers between 1 andp−1{\displaystyle p-1}have this property. So we assume that we have access to such a non-residue.
By (normally) dividing by 2 repeatedly, we can writep−1{\displaystyle p-1}asQ2S{\displaystyle Q2^{S}}, whereQ{\displaystyle Q}is odd. Note that if we try
thenR2≡nQ+1=(n)(nQ)(modp){\displaystyle R^{2}\equiv n^{Q+1}=(n)(n^{Q}){\pmod {p}}}. Ift≡nQ≡1(modp){\displaystyle t\equiv n^{Q}\equiv 1{\pmod {p}}}, thenR{\displaystyle R}is a square root ofn{\displaystyle n}. Otherwise, forM=S{\displaystyle M=S}, we haveR{\displaystyle R}andt{\displaystyle t}satisfying:
If, given a choice ofR{\displaystyle R}andt{\displaystyle t}for a particularM{\displaystyle M}satisfying the above (whereR{\displaystyle R}is not a square root ofn{\displaystyle n}), we can easily calculate anotherR{\displaystyle R}andt{\displaystyle t}forM−1{\displaystyle M-1}such that the above relations hold, then we can repeat this untilt{\displaystyle t}becomes a20{\displaystyle 2^{0}}-th root of 1, i.e.,t=1{\displaystyle t=1}. At that pointR{\displaystyle R}is a square root ofn{\displaystyle n}.
We can check whethert{\displaystyle t}is a2M−2{\displaystyle 2^{M-2}}-th root of 1 by squaring itM−2{\displaystyle M-2}times and check whether it is 1. If it is, then we do not need to do anything, as the same choice ofR{\displaystyle R}andt{\displaystyle t}works. But if it is not,t2M−2{\displaystyle t^{2^{M-2}}}must be -1 (because squaring it gives 1, and there can only be two square roots 1 and -1 of 1 modulop{\displaystyle p}).
To find a new pair ofR{\displaystyle R}andt{\displaystyle t}, we can multiplyR{\displaystyle R}by a factorb{\displaystyle b}, to be determined. Thent{\displaystyle t}must be multiplied by a factorb2{\displaystyle b^{2}}to keepR2≡nt(modp){\displaystyle R^{2}\equiv nt{\pmod {p}}}. So, whent2M−2{\displaystyle t^{2^{M-2}}}is -1, we need to find a factorb2{\displaystyle b^{2}}so thattb2{\displaystyle tb^{2}}is a2M−2{\displaystyle 2^{M-2}}-th root of 1, or equivalentlyb2{\displaystyle b^{2}}is a2M−2{\displaystyle 2^{M-2}}-th root of -1.
The trick here is to make use ofz{\displaystyle z}, the known non-residue. The Euler's criterion applied toz{\displaystyle z}shown above says thatzQ{\displaystyle z^{Q}}is a2S−1{\displaystyle 2^{S-1}}-th root of -1. So by squaringzQ{\displaystyle z^{Q}}repeatedly, we have access to a sequence of2i{\displaystyle 2^{i}}-th root of -1. We can select the right one to serve asb{\displaystyle b}. With a little bit of variable maintenance and trivial case compression, the algorithm below emerges naturally.
Operations and comparisons on elements of themultiplicative group of integers modulo pZ/pZ{\displaystyle \mathbb {Z} /p\mathbb {Z} }are implicitly modp.
Inputs:
Outputs:
Algorithm:
Once you have solved the congruence withrthe second solution is−r(modp){\displaystyle -r{\pmod {p}}}. If the leastisuch thatt2i=1{\displaystyle t^{2^{i}}=1}isM, then no solution to the congruence exists, i.e.nis not a quadratic residue.
This is most useful whenp≡ 1 (mod 4).
For primes such thatp≡ 3 (mod 4), this problem has possible solutionsr=±np+14(modp){\displaystyle r=\pm n^{\frac {p+1}{4}}{\pmod {p}}}. If these satisfyr2≡n(modp){\displaystyle r^{2}\equiv n{\pmod {p}}}, they are the only solutions. If not,r2≡−n(modp){\displaystyle r^{2}\equiv -n{\pmod {p}}},nis a quadratic non-residue, and there are no solutions.
We can show that at the start of each iteration of the loop the followingloop invariantshold:
Initially:
At each iteration, withM',c',t',R'the new values replacingM,c,t,R:
Fromt2M−1=1{\displaystyle t^{2^{M-1}}=1}and the test againstt= 1 at the start of the loop, we see that we will always find aniin 0 <i<Msuch thatt2i=1{\displaystyle t^{2^{i}}=1}.Mis strictly smaller on each iteration, and thus the algorithm is guaranteed to halt. When we hit the conditiont= 1 and halt, the last loop invariant implies thatR2=n.
We can alternately express the loop invariants using theorderof the elements:
Each step of the algorithm movestinto a smaller subgroup by measuring the exact order oftand multiplying it by an element of the same order.
Solving the congruencer2≡ 5 (mod 41). 41 is prime as required and 41 ≡ 1 (mod 4). 5 is a quadratic residue by Euler's criterion:541−12=520=1{\displaystyle 5^{\frac {41-1}{2}}=5^{20}=1}(as before, operations in(Z/41Z)×{\displaystyle (\mathbb {Z} /41\mathbb {Z} )^{\times }}are implicitly mod 41).
Indeed, 282≡ 5 (mod 41) and (−28)2≡ 132≡ 5 (mod 41). So the algorithm yields the two solutions to our congruence.
The Tonelli–Shanks algorithm requires (on average over all possible input (quadratic residues and quadratic nonresidues))
modular multiplications, wherem{\displaystyle m}is the number of digits in the binary representation ofp{\displaystyle p}andk{\displaystyle k}is the number of ones in the binary representation ofp{\displaystyle p}. If the required quadratic nonresiduez{\displaystyle z}is to be found by checking if a randomly taken numbery{\displaystyle y}is a quadratic nonresidue, it requires (on average)2{\displaystyle 2}computations of theLegendre symbol.[5]The average of two computations of theLegendre symbolare explained as follows:y{\displaystyle y}is a quadratic residue with chancep+12p=1+1p2{\displaystyle {\tfrac {\tfrac {p+1}{2}}{p}}={\tfrac {1+{\tfrac {1}{p}}}{2}}}, which is smaller than1{\displaystyle 1}but≥12{\displaystyle \geq {\tfrac {1}{2}}}, so we will on average need to check if ay{\displaystyle y}is a quadratic residue two times.
This shows essentially that the Tonelli–Shanks algorithm works very well if the modulusp{\displaystyle p}is random, that is, ifS{\displaystyle S}is not particularly large with respect to the number of digits in the binary representation ofp{\displaystyle p}. As written above,Cipolla's algorithmworks better than Tonelli–Shanks if (and only if)S(S−1)>8m+20{\displaystyle S(S-1)>8m+20}.
However, if one instead uses Sutherland's algorithm to perform the discrete logarithm computation in the 2-Sylow subgroup ofFp∗{\displaystyle \mathbb {F} _{p}^{\ast }}, one may replaceS(S−1){\displaystyle S(S-1)}with an expression that is asymptotically bounded byO(SlogS/loglogS){\displaystyle O(S\log S/\log \log S)}.[6]Explicitly, one computese{\displaystyle e}such thatce≡nQ{\displaystyle c^{e}\equiv n^{Q}}and thenR≡c−e/2n(Q+1)/2{\displaystyle R\equiv c^{-e/2}n^{(Q+1)/2}}satisfiesR2≡n{\displaystyle R^{2}\equiv n}(note thate{\displaystyle e}is a multiple of 2 becausen{\displaystyle n}is a quadratic residue).
The algorithm requires us to find a quadratic nonresiduez{\displaystyle z}. There is no known deterministic algorithm that runs in polynomial time for finding such az{\displaystyle z}. However, if thegeneralized Riemann hypothesisis true, there exists a quadratic nonresiduez<2ln2p{\displaystyle z<2\ln ^{2}{p}},[7]making it possible to check everyz{\displaystyle z}up to that limit and find a suitablez{\displaystyle z}withinpolynomial time. Keep in mind, however, that this is a worst-case scenario; in general,z{\displaystyle z}is found in on average 2 trials as stated above.
The Tonelli–Shanks algorithm can (naturally) be used for any process in which square roots modulo a prime are necessary. For example, it can be used for finding points onelliptic curves. It is also useful for the computations in theRabin cryptosystemand in the sieving step of thequadratic sieve.
Tonelli–Shanks can be generalized to any cyclic group (instead of(Z/pZ)×{\displaystyle (\mathbb {Z} /p\mathbb {Z} )^{\times }}) and tokth roots for arbitrary integerk, in particular to taking thekth root of an element of afinite field.[8]
If many square-roots must be done in the same cyclic group and S is not too large, a table of square-roots of the elements of 2-power order can be prepared in advance and the algorithm simplified and sped up as follows.
According to Dickson's "Theory of Numbers"[3]
A. Tonelli[9]gave an explicit formula for the roots ofx2=c(modpλ){\displaystyle x^{2}=c{\pmod {p^{\lambda }}}}[3]
The Dickson reference shows the following formula for the square root ofx2modpλ{\displaystyle x^{2}{\bmod {p^{\lambda }}}}.
Noting that232mod293≡529{\displaystyle 23^{2}{\bmod {29^{3}}}\equiv 529}and noting thatβ=7⋅292{\displaystyle \beta =7\cdot 29^{2}}then
To take another example:23332mod293≡4142{\displaystyle 2333^{2}{\bmod {29^{3}}}\equiv 4142}and
Dickson also attributes the following equation to Tonelli:
Usingp=23{\displaystyle p=23}and using the modulus ofp3{\displaystyle p^{3}}the math follows:
First, find the modular square root modp{\displaystyle p}which can be done by the regular Tonelli algorithm for one or the other roots:
And applying Tonelli's equation (see above):
Dickson's reference[3]clearly shows that Tonelli's algorithm works on moduli ofpλ{\displaystyle p^{\lambda }}.
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TheSchmidt-Samoa cryptosystemis an asymmetriccryptographictechnique, whose security, likeRabindepends on the difficulty of integerfactorization. Unlike Rabin this algorithm does not produce an ambiguity in the decryption at a cost of encryption speed.
NowNis the public key anddis the private key.
To encrypt a messagemwe compute the ciphertext asc=mNmodN.{\displaystyle c=m^{N}\mod N.}
To decrypt a ciphertextcwe compute the plaintext asm=cdmodpq,{\displaystyle m=c^{d}\mod pq,}which like for Rabin andRSAcan be computed with theChinese remainder theorem.
Example:
Now to verify:
The algorithm, like Rabin, is based on the difficulty of factoring the modulusN, which is a distinct advantage over RSA.
That is, it can be shown that if there exists an algorithm that can decrypt arbitrary messages, then this algorithm can be used to factorN.
The algorithm processes decryption as fast as Rabin and RSA, however it has much slower encryption since the sender must compute a full exponentiation.
Since encryption uses a fixed known exponent anaddition chainmay be used to optimize the encryption process. The cost of producing an optimal addition chain can be amortized over the life of the public key, that is, it need only be computed once and cached.
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TheBlum–Goldwasser (BG) cryptosystemis anasymmetric key encryption algorithmproposed byManuel BlumandShafi Goldwasserin 1984. Blum–Goldwasser is aprobabilistic,semantically securecryptosystem with a constant-sizeciphertext expansion. The encryption algorithm implements an XOR-basedstream cipherusing theBlum-Blum-Shub(BBS) pseudo-random number generator to generate thekeystream. Decryption is accomplished by manipulating the final state of the BBS generator using theprivate key, in order to find the initial seed and reconstruct the keystream.
The BG cryptosystem issemantically securebased on the assumed intractability ofinteger factorization; specifically, factoring a composite valueN=pq{\displaystyle N=pq}wherep,q{\displaystyle p,q}are largeprimes. BG has multiple advantages over earlier probabilistic encryption schemes such as theGoldwasser–Micali cryptosystem. First, its semantic security reduces solely to integer factorization, without requiring any additional assumptions (e.g., hardness of thequadratic residuosity problemor theRSA problem). Secondly, BG is efficient in terms of storage, inducing a constant-sizeciphertext expansionregardless of message length. BG is also relatively efficient in terms of computation, and fares well even in comparison with cryptosystems such as RSA (depending on message length and exponent choices). However, BG is highly vulnerable to adaptive chosen ciphertext attacks (see below).
Because encryption is performed using a probabilistic algorithm, a given plaintext may produce very different ciphertexts each time it is encrypted. This has significant advantages, as it prevents an adversary from recognizing intercepted messages by comparing them to a dictionary of known ciphertexts.
The Blum–Goldwasser cryptosystem consists of three algorithms: a probabilistic key generation algorithm which produces a public and a private key, aprobabilistic encryptionalgorithm, and a deterministic decryption algorithm.
The public and private keys are generated as follows:
Thenn{\displaystyle n}is the public key and the pair(p,q){\displaystyle (p,q)}is the private key.
A messageM{\displaystyle M}is encrypted with the public keyn{\displaystyle n}as follows:
The encryption of the messageM{\displaystyle M}is then all theci{\displaystyle c_{i}}values plus the finalxt+1{\displaystyle x_{t+1}}value:(c1,c2,…,ct,xt+1){\displaystyle (c_{1},c_{2},\dots ,c_{t},x_{t+1})}.
An encrypted message(c1,c2,…,ct,x){\displaystyle (c_{1},c_{2},\dots ,c_{t},x)}can be decrypted with the private key(p,q){\displaystyle (p,q)}as follows:
Letp=19{\displaystyle p=19}andq=7{\displaystyle q=7}. Thenn=133{\displaystyle n=133}andh=⌊log2(log2(133))⌋=3{\displaystyle h=\lfloor log_{2}(log_{2}(133))\rfloor =3}.
To encrypt the six-bit message1010012{\displaystyle 101001_{2}}, we break it into two 3-bit blocksm1=1012,m2=0012{\displaystyle m_{1}=101_{2},m_{2}=001_{2}}, sot=2{\displaystyle t=2}. We select a randomr=36{\displaystyle r=36}and computex0=362mod133=99{\displaystyle x_{0}=36^{2}{\bmod {1}}33=99}. Now we compute theci{\displaystyle c_{i}}values as follows:
So the encryption is(c1=0012,c2=1002,x3=43){\displaystyle (c_{1}=001_{2},c_{2}=100_{2},x_{3}=43)}.
To decrypt, we compute
It can be seen thatx0{\displaystyle x_{0}}has the same value as in the encryption algorithm. Decryption therefore proceeds the same as encryption:
We must show that the valuex0{\displaystyle x_{0}}computed in step 6 of the decryption algorithm is equal to the value computed in step 4 of the encryption algorithm.
In the encryption algorithm, by constructionx0{\displaystyle x_{0}}is a quadratic residue modulon{\displaystyle n}. It is therefore also a quadratic residue modulop{\displaystyle p}, as are all the otherxi{\displaystyle x_{i}}values obtained from it by squaring. Therefore, byEuler's criterion,xi(p−1)/2≡1modp{\displaystyle x_{i}^{(p-1)/2}\equiv 1\mod {p}}. Then
Similarly,
Raising the first equation to the power(p+1)/4{\displaystyle (p+1)/4}we get
Repeating thist{\displaystyle t}times, we have
And by a similar argument we can show thatxt+1dq≡uq≡x0modq{\displaystyle x_{t+1}^{d_{q}}\equiv u_{q}\equiv x_{0}\mod {q}}.
Finally, sincerpp+rqq=1{\displaystyle r_{p}p+r_{q}q=1}, we can multiply byx0{\displaystyle x_{0}}and get
from whichuqrpp+uprqq≡x0{\displaystyle u_{q}r_{p}p+u_{p}r_{q}q\equiv x_{0}}, modulo bothp{\displaystyle p}andq{\displaystyle q}, and thereforeuqrpp+uprqq≡x0modn{\displaystyle u_{q}r_{p}p+u_{p}r_{q}q\equiv x_{0}\mod {n}}.
The Blum–Goldwasser scheme issemantically-securebased on the hardness of predicting the keystream bits given only the final BBS statey{\displaystyle y}and the public keyN{\displaystyle N}. However, ciphertexts of the formc→,y{\displaystyle {\vec {c}},y}are vulnerable to anadaptive chosen ciphertext attackin which the adversary requests the decryptionm′{\displaystyle m^{\prime }}of a chosen ciphertexta→,y{\displaystyle {\vec {a}},y}. The decryptionm{\displaystyle m}of the original ciphertext can be computed asa→⊕m′⊕c→{\displaystyle {\vec {a}}\oplus m^{\prime }\oplus {\vec {c}}}.
Depending on plaintext size, BG may be more or less computationally expensive than RSA. Because most RSA deployments use a fixed encryption exponent optimized to minimize encryption time, RSA encryption will typically outperform BG for all but the shortest messages. However, as the RSA decryption exponent is randomly distributed, modular exponentiation may require a comparable number of squarings/multiplications to BG decryption for a ciphertext of the same length. BG has the advantage of scaling more efficiently to longer ciphertexts, where RSA requires multiple separate encryptions. In these cases, BG may be significantly more efficient.
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Incomputer science, thecomputational complexityor simplycomplexityof analgorithmis the amount of resources required to run it.[1]Particular focus is given tocomputation time(generally measured by the number of needed elementary operations) andmemory storagerequirements. The complexity of aproblemis the complexity of the best algorithms that allow solving the problem.
The study of the complexity of explicitly given algorithms is calledanalysis of algorithms, while the study of the complexity of problems is calledcomputational complexity theory. Both areas are highly related, as the complexity of an algorithm is always anupper boundon the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the complexity of the most efficient known algorithms. Therefore, there is a large overlap between analysis of algorithms and complexity theory.
As the amount of resources required to run an algorithm generally varies with the size of the input, the complexity is typically expressed as a functionn→f(n), wherenis the size of the input andf(n)is either theworst-case complexity(the maximum of the amount of resources that are needed over all inputs of sizen) or theaverage-case complexity(the average of the amount of resources over all inputs of sizen).Time complexityis generally expressed as the number of required elementary operations on an input of sizen, where elementary operations are assumed to take a constant amount of time on a given computer and change only by a constant factor when run on a different computer.Space complexityis generally expressed as the amount ofmemoryrequired by an algorithm on an input of sizen.
The resource that is most commonly considered is time. When "complexity" is used without qualification, this generally means time complexity.
The usual units of time (seconds, minutes etc.) are not used incomplexity theorybecause they are too dependent on the choice of a specific computer and on the evolution of technology. For instance, a computer today can execute an algorithm significantly faster than a computer from the 1960s; however, this is not an intrinsic feature of the algorithm but rather a consequence of technological advances incomputer hardware. Complexity theory seeks to quantify the intrinsic time requirements of algorithms, that is, the basic time constraints an algorithm would place onanycomputer. This is achieved by counting the number ofelementary operationsthat are executed during the computation. These operations are assumed to take constant time (that is, not affected by the size of the input) on a given machine, and are often calledsteps.
Formally, thebit complexityrefers to the number of operations onbitsthat are needed for running an algorithm. With mostmodels of computation, it equals the time complexity up to a constant factor. Oncomputers, the number of operations onmachine wordsthat are needed is also proportional to the bit complexity. So, thetime complexityand thebit complexityare equivalent for realistic models of computation.
Another important resource is the size ofcomputer memorythat is needed for running algorithms.
For the class ofdistributed algorithmsthat are commonly executed by multiple, interacting parties, the resource that is of most interest is the communication complexity. It is the necessary amount of communication between the executing parties.
The number ofarithmetic operationsis another resource that is commonly used. In this case, one talks ofarithmetic complexity. If one knows anupper boundon the size of thebinary representationof the numbers that occur during a computation, the time complexity is generally the product of the arithmetic complexity by a constant factor.
For many algorithms the size of the integers that are used during a computation is not bounded, and it is not realistic to consider that arithmetic operations take a constant time. Therefore, the time complexity, generally calledbit complexityin this context, may be much larger than the arithmetic complexity. For example, the arithmetic complexity of the computation of thedeterminantof an×ninteger matrixisO(n3){\displaystyle O(n^{3})}for the usual algorithms (Gaussian elimination). The bit complexity of the same algorithms isexponentialinn, because the size of the coefficients may grow exponentially during the computation. On the other hand, if these algorithms are coupled withmulti-modular arithmetic, the bit complexity may be reduced toO~(n4).
Insortingandsearching, the resource that is generally considered is the number of entry comparisons. This is generally a good measure of the time complexity if data are suitably organized.
It is impossible to count the number of steps of an algorithm on all possible inputs. As the complexity generally increases with the size of the input, the complexity is typically expressed as a function of the sizen(inbits) of the input, and therefore, the complexity is a function ofn. However, the complexity of an algorithm may vary dramatically for different inputs of the same size. Therefore, several complexity functions are commonly used.
Theworst-case complexityis the maximum of the complexity over all inputs of sizen, and theaverage-case complexityis the average of the complexity over all inputs of sizen(this makes sense, as the number of possible inputs of a given size is finite). Generally, when "complexity" is used without being further specified, this is the worst-case time complexity that is considered.
It is generally difficult to compute precisely the worst-case and the average-case complexity. In addition, these exact values provide little practical application, as any change of computer or of model of computation would change the complexity somewhat. Moreover, the resource use is not critical for small values ofn, and this makes that, for smalln, the ease of implementation is generally more interesting than a low complexity.
For these reasons, one generally focuses on the behavior of the complexity for largen, that is on itsasymptotic behaviorwhenntends to the infinity. Therefore, the complexity is generally expressed by usingbig O notation.
For example, the usual algorithm for integermultiplicationhas a complexity ofO(n2),{\displaystyle O(n^{2}),}this means that there is a constantcu{\displaystyle c_{u}}such that the multiplication of two integers of at mostndigits may be done in a time less thancun2.{\displaystyle c_{u}n^{2}.}This bound issharpin the sense that the worst-case complexity and the average-case complexity areΩ(n2),{\displaystyle \Omega (n^{2}),}which means that there is a constantcl{\displaystyle c_{l}}such that these complexities are larger thancln2.{\displaystyle c_{l}n^{2}.}Theradixdoes not appear in these complexity, as changing of radix changes only the constantscu{\displaystyle c_{u}}andcl.{\displaystyle c_{l}.}
The evaluation of the complexity relies on the choice of amodel of computation, which consists in defining the basic operations that are done in a unit of time. When the model of computation is not explicitly specified, it is generally implicitely assumed as being amultitape Turing machine, since several more realistic models of computation, such asrandom-access machinesare asymptotically equivalent for most problems. It is only for very specific and difficult problems, such asinteger multiplicationin timeO(nlogn),{\displaystyle O(n\log n),}that the explicit definition of the model of computation is required for proofs.
Adeterministic modelof computation is a model of computation such that the successive states of the machine and the operations to be performed are completely determined by the preceding state. Historically, the first deterministic models wererecursive functions,lambda calculus, andTuring machines. The model ofrandom-access machines(also called RAM-machines) is also widely used, as a closer counterpart to realcomputers.
When the model of computation is not specified, it is generally assumed to be amultitape Turing machine. For most algorithms, the time complexity is the same on multitape Turing machines as on RAM-machines, although some care may be needed in how data is stored in memory to get this equivalence.
In anon-deterministic model of computation, such asnon-deterministic Turing machines, some choices may be done at some steps of the computation. In complexity theory, one considers all possible choices simultaneously, and the non-deterministic time complexity is the time needed, when the best choices are always done. In other words, one considers that the computation is done simultaneously on as many (identical) processors as needed, and the non-deterministic computation time is the time spent by the first processor that finishes the computation. This parallelism is partly amenable toquantum computingvia superposedentangled statesin running specificquantum algorithms, like e.g.Shor's factorizationof yet only small integers (as of March 2018[update]: 21 = 3 × 7).
Even when such a computation model is not realistic yet, it has theoretical importance, mostly related to theP = NPproblem, which questions the identity of the complexity classes formed by taking "polynomial time" and "non-deterministic polynomial time" as least upper bounds. Simulating an NP-algorithm on a deterministic computer usually takes "exponential time". A problem is in the complexity classNP, if it may be solved inpolynomial timeon a non-deterministic machine. A problem isNP-completeif, roughly speaking, it is in NP and is not easier than any other NP problem. Manycombinatorialproblems, such as theKnapsack problem, thetravelling salesman problem, and theBoolean satisfiability problemare NP-complete. For all these problems, the best known algorithm has exponential complexity. If any one of these problems could be solved in polynomial time on a deterministic machine, then all NP problems could also be solved in polynomial time, and one would have P = NP. As of 2017[update]it is generally conjectured thatP ≠ NP,with the practical implication that the worst cases of NP problems are intrinsically difficult to solve, i.e., take longer than any reasonable time span (decades!) for interesting lengths of input.
Parallel and distributed computing consist of splitting computation on several processors, which work simultaneously. The difference between the different model lies mainly in the way of transmitting information between processors. Typically, in parallel computing the data transmission between processors is very fast, while, in distributed computing, the data transmission is done through anetworkand is therefore much slower.
The time needed for a computation onNprocessors is at least the quotient byNof the time needed by a single processor. In fact this theoretically optimal bound can never be reached, because some subtasks cannot be parallelized, and some processors may have to wait a result from another processor.
The main complexity problem is thus to design algorithms such that the product of the computation time by the number of processors is as close as possible to the time needed for the same computation on a single processor.
Aquantum computeris a computer whose model of computation is based onquantum mechanics. TheChurch–Turing thesisapplies to quantum computers; that is, every problem that can be solved by a quantum computer can also be solved by a Turing machine. However, some problems may theoretically be solved with a much lowertime complexityusing a quantum computer rather than a classical computer. This is, for the moment, purely theoretical, as no one knows how to build an efficient quantum computer.
Quantum complexity theoryhas been developed to study thecomplexity classesof problems solved using quantum computers. It is used inpost-quantum cryptography, which consists of designingcryptographic protocolsthat are resistant to attacks by quantum computers.
The complexity of a problem is theinfimumof the complexities of the algorithms that may solve the problem[citation needed], including unknown algorithms. Thus the complexity of a problem is not greater than the complexity of any algorithm that solves the problems.
It follows that every complexity of an algorithm, that is expressed withbig O notation, is also an upper bound on the complexity of the corresponding problem.
On the other hand, it is generally hard to obtain nontrivial lower bounds for problem complexity, and there are few methods for obtaining such lower bounds.
For solving most problems, it is required to read all input data, which, normally, needs a time proportional to the size of the data. Thus, such problems have a complexity that is at leastlinear, that is, usingbig omega notation, a complexityΩ(n).{\displaystyle \Omega (n).}
The solution of some problems, typically incomputer algebraandcomputational algebraic geometry, may be very large. In such a case, the complexity is lower bounded by the maximal size of the output, since the output must be written. For example, asystem ofnpolynomial equations of degreedinnindeterminatesmay have up todn{\displaystyle d^{n}}complexsolutions, if the number of solutions is finite (this isBézout's theorem). As these solutions must be written down, the complexity of this problem isΩ(dn).{\displaystyle \Omega (d^{n}).}For this problem, an algorithm of complexitydO(n){\displaystyle d^{O(n)}}is known, which may thus be considered as asymptotically quasi-optimal.
A nonlinear lower bound ofΩ(nlogn){\displaystyle \Omega (n\log n)}is known for the number of comparisons needed for asorting algorithm. Thus the best sorting algorithms are optimal, as their complexity isO(nlogn).{\displaystyle O(n\log n).}This lower bound results from the fact that there aren!ways of orderingnobjects. As each comparison splits in two parts this set ofn!orders, the number ofNof comparisons that are needed for distinguishing all orders must verify2N>n!,{\displaystyle 2^{N}>n!,}which impliesN=Ω(nlogn),{\displaystyle N=\Omega (n\log n),}byStirling's formula.
A standard method for getting lower bounds of complexity consists ofreducinga problem to another problem. More precisely, suppose that one may encode a problemAof sizeninto a subproblem of sizef(n)of a problemB, and that the complexity ofAisΩ(g(n)).{\displaystyle \Omega (g(n)).}Without loss of generality, one may suppose that the functionfincreases withnand has aninverse functionh. Then the complexity of the problemBisΩ(g(h(n))).{\displaystyle \Omega (g(h(n))).}This is the method that is used to prove that, ifP ≠ NP(an unsolved conjecture), the complexity of everyNP-complete problemisΩ(nk),{\displaystyle \Omega (n^{k}),}for every positive integerk.
Evaluating the complexity of an algorithm is an important part ofalgorithm design, as this gives useful information on the performance that may be expected.
It is a common misconception that the evaluation of the complexity of algorithms will become less important as a result ofMoore's law, which posits theexponential growthof the power of moderncomputers. This is wrong because this power increase allows working with large input data (big data). For example, when one wants to sort alphabetically a list of a few hundreds of entries, such as thebibliographyof a book, any algorithm should work well in less than a second. On the other hand, for a list of a million of entries (the phone numbers of a large town, for example), the elementary algorithms that requireO(n2){\displaystyle O(n^{2})}comparisons would have to do a trillion of comparisons, which would need around three hours at the speed of 10 million of comparisons per second. On the other hand, thequicksortandmerge sortrequire onlynlog2n{\displaystyle n\log _{2}n}comparisons (as average-case complexity for the former, as worst-case complexity for the latter). Forn= 1,000,000, this gives approximately 30,000,000 comparisons, which would only take 3 seconds at 10 million comparisons per second.
Thus the evaluation of the complexity may allow eliminating many inefficient algorithms before any implementation. This may also be used for tuning complex algorithms without testing all variants. By determining the most costly steps of a complex algorithm, the study of complexity allows also focusing on these steps the effort for improving the efficiency of an implementation.
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Descriptive complexityis a branch ofcomputational complexity theoryand offinite model theorythat characterizescomplexity classesby the type oflogicneeded to express thelanguagesin them. For example,PH, the union of all complexity classes in the polynomial hierarchy, is precisely the class of languages expressible by statements ofsecond-order logic. This connection between complexity and the logic of finite structures allows results to be transferred easily from one area to the other, facilitating new proof methods and providing additional evidence that the main complexity classes are somehow "natural" and not tied to the specificabstract machinesused to define them.
Specifically, eachlogical systemproduces a set ofqueriesexpressible in it. The queries – when restricted to finite structures – correspond to thecomputational problemsof traditional complexity theory.
The first main result of descriptive complexity wasFagin's theorem, shown byRonald Faginin 1974. It established thatNPis precisely the set of languages expressible by sentences of existentialsecond-order logic; that is, second-order logic excludinguniversal quantificationoverrelations,functions, andsubsets. Many other classes were later characterized in such a manner.
When we use the logic formalism to describe a computational problem, the input is a finite structure, and the elements of that structure are thedomain of discourse. Usually the input is either a string (of bits or over an alphabet) and the elements of the logical structure represent positions of the string, or the input is a graph and the elements of the logical structure represent its vertices. The length of the input will be measured by the size of the respective structure.
Whatever the structure is, we can assume that there are relations that can be tested, for example "E(x,y){\displaystyle E(x,y)}is true if and only if there is an edge fromxtoy" (in case of the structure being a graph), or "P(n){\displaystyle P(n)}is true if and only if thenth letter of the string is 1." These relations are the predicates for the first-order logic system. We also have constants, which are special elements of the respective structure, for example if we want to check reachability in a graph, we will have to choose two constantss(start) andt(terminal).
In descriptive complexity theory we often assume that there is a total order over the elements and that we can check equality between elements. This lets us consider elements as numbers: the elementxrepresents the numbernif and only if there are(n−1){\displaystyle (n-1)}elementsywithy<x{\displaystyle y<x}. Thanks to this we also may have the primitive predicate "bit", wherebit(x,k){\displaystyle bit(x,k)}is true if only thekth bit of the binary expansion ofxis 1. (We can replace addition and multiplication by ternary relations such thatplus(x,y,z){\displaystyle plus(x,y,z)}is true if and only ifx+y=z{\displaystyle x+y=z}andtimes(x,y,z){\displaystyle times(x,y,z)}is true if and only ifx∗y=z{\displaystyle x*y=z}).
If we restrict ourselves to ordered structures with a successor relation and basic arithmetical predicates, then we get the following characterisations:
Incircuit complexity, first-order logic with arbitrary predicates can be shown to be equal toAC0, the first class in theAChierarchy. Indeed, there is a natural translation from FO's symbols to nodes of circuits, with∀,∃{\displaystyle \forall ,\exists }being∧{\displaystyle \land }and∨{\displaystyle \lor }of sizen. First-order logic in a signature with arithmetical predicates characterises the restriction of the AC0family of circuits to those constructible inalternating logarithmic time.[1]First-order logic in a signature with only the order relation corresponds to the set ofstar-free languages.[8][9]
First-order logic gains substantially in expressive power when it is augmented with an operator that computes the transitive closure of a binary relation. The resultingtransitive closure logicis known to characterisenon-deterministic logarithmic space (NL)on ordered structures. This was used byImmermanto show that NL is closed under complement (i. e. that NL = co-NL).[10]
When restricting the transitive closure operator todeterministic transitive closure, the resulting logic exactly characteriseslogarithmic spaceon ordered structures.
On structures that have a successor function, NL can also be characterised by second-orderKrom formulae.
SO-Krom is the set of Boolean queries definable with second-order formulae inconjunctive normal formsuch that the first-order quantifiers are universal and the quantifier-free part of the formula is in Krom form, which means that the first-order formula is a conjunction of disjunctions, and in each "disjunction" there are at most two variables. Every second-order Krom formula is equivalent to an existential second-order Krom formula.
SO-Krom characterises NL on structures with a successor function.[11]
On ordered structures, first-orderleast fixed-point logiccapturesPTIME:
FO[LFP] is the extension of first-order logic by a least fixed-point operator, which expresses the fixed-point of a monotone expression. This augments first-order logic with the ability to express recursion. The Immerman–Vardi theorem, shown independently byImmermanandVardi, shows that FO[LFP] characterises PTIME on ordered structures.[12][13]
As of 2022, it is still open whether there is a natural logic characterising PTIME on unordered structures.
TheAbiteboul–Vianu theoremstates that FO[LFP]=FO[PFP] on all structures if and only if FO[LFP]=FO[PFP]; hence if and only if P=PSPACE. This result has been extended to other fixpoints.[14]
In the presence of a successor function, PTIME can also be characterised by second-order Horn formulae.
SO-Horn is the set of Boolean queries definable with SO formulae indisjunctive normal formsuch that the first-order quantifiers are all universal and the quantifier-free part of the formula is inHornform, which means that it is a big AND of OR, and in each "OR" every variable except possibly one are negated.
This class is equal toPon structures with a successor function.[15]
Those formulae can be transformed to prenex formulas in existential second-order Horn logic.[11]
Ronald Fagin's 1974 proof that the complexity class NP was characterised exactly by those classes of structures axiomatizable in existential second-order logic was the starting point of descriptive complexity theory.[4][16]
Since the complement of an existential formula is a universal formula, it follows immediately that co-NP is characterized by universal second-order logic.[4]
SO, unrestricted second-order logic, is equal to thePolynomial hierarchy PH. More precisely, we have the following generalisation of Fagin's theorem: The set of formulae in prenex normal form where existential and universal quantifiers of second order alternatektimes characterise thekth level of the polynomial hierarchy.[17]
Unlike most other characterisations of complexity classes, Fagin's theorem and its generalisation do not presuppose a total ordering on the structures. This is because existential second-order logic is itself sufficiently expressive to refer to the possible total orders on a structure using second-order variables.[18]
The class of all problems computable in polynomial space,PSPACE, can be characterised by augmenting first-order logic with a more expressive partial fixed-point operator.
Partial fixed-point logic, FO[PFP], is the extension of first-order logic with a partial fixed-point operator, which expresses the fixed-point of a formula if there is one and returns 'false' otherwise.
Partial fixed-point logic characterisesPSPACEon ordered structures.[19]
Second-order logic can be extended by a transitive closure operator in the same way as first-order logic, resulting in SO[TC]. The TC operator can now also take second-order variables as argument. SO[TC] characterisesPSPACE. Since ordering can be referenced in second-order logic, this characterisation does not presuppose ordered structures.[20]
Thetime complexityclassELEMENTARYof elementary functions can be characterised byHO, thecomplexity classof structures that can be recognized by formulas ofhigher-order logic. Higher-order logic is an extension offirst-order logicandsecond-order logicwith higher-order quantifiers. There is a relation between thei{\displaystyle i}th order and non-deterministic algorithms the time of which is bounded byi−1{\displaystyle i-1}levels of exponentials.[21]
We define higher-order variables. A variable of orderi>1{\displaystyle i>1}has an arityk{\displaystyle k}and represents any set ofk{\displaystyle k}-tuplesof elements of orderi−1{\displaystyle i-1}. They are usually written in upper-case and with a natural number as exponent to indicate the order. Higher-order logic is the set of first-order formulae where we add quantification over higher-order variables; hence we will use the terms defined in theFOarticle without defining them again.
HOi{\displaystyle ^{i}}is the set of formulae with variables of order at mosti{\displaystyle i}. HOji{\displaystyle _{j}^{i}}is the subset of formulae of the formϕ=∃X1i¯∀X2i¯…QXji¯ψ{\displaystyle \phi =\exists {\overline {X_{1}^{i}}}\forall {\overline {X_{2}^{i}}}\dots Q{\overline {X_{j}^{i}}}\psi }, whereQ{\displaystyle Q}is a quantifier andQXi¯{\displaystyle Q{\overline {X^{i}}}}means thatXi¯{\displaystyle {\overline {X^{i}}}}is a tuple of variable of orderi{\displaystyle i}with the same quantification. So HOji{\displaystyle _{j}^{i}}is the set of formulae withj{\displaystyle j}alternations of quantifiers of orderi{\displaystyle i}, beginning with∃{\displaystyle \exists }, followed by a formula of orderi−1{\displaystyle i-1}.
Using the standard notation of thetetration,exp20(x)=x{\displaystyle \exp _{2}^{0}(x)=x}andexp2i+1(x)=2exp2i(x){\displaystyle \exp _{2}^{i+1}(x)=2^{\exp _{2}^{i}(x)}}.exp2i+1(x)=2222…2x{\displaystyle \exp _{2}^{i+1}(x)=2^{2^{2^{2^{\dots ^{2^{x}}}}}}}withi{\displaystyle i}times2{\displaystyle 2}
Every formula of orderi{\displaystyle i}th is equivalent to a formula in prenex normal form, where we first write quantification over variable ofi{\displaystyle i}th order and then a formula of orderi−1{\displaystyle i-1}in normal form.
HO is equal to the classELEMENTARYof elementary functions. To be more precise,HO0i=NTIME(exp2i−2(nO(1))){\displaystyle {\mathsf {HO}}_{0}^{i}={\mathsf {NTIME}}(\exp _{2}^{i-2}(n^{O(1)}))}, meaning a tower of(i−2){\displaystyle (i-2)}2s, ending withnc{\displaystyle n^{c}}, wherec{\displaystyle c}is a constant. A special case of this is that∃SO=HO02=NTIME(nO(1))=NP{\displaystyle \exists {\mathsf {SO}}={\mathsf {HO}}_{0}^{2}={\mathsf {NTIME}}(n^{O(1)})={\color {Blue}{\mathsf {NP}}}}, which is exactlyFagin's theorem. Usingoracle machinesin thepolynomial hierarchy,HOji=NTIME(exp2i−2(nO(1))ΣjP){\displaystyle {\mathsf {HO}}_{j}^{i}={\color {Blue}{\mathsf {NTIME}}}(\exp _{2}^{i-2}(n^{O(1)})^{\Sigma _{j}^{\mathsf {P}}})}
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Combinatorial game theorymeasuresgame complexityin several ways:
These measures involve understanding the game positions, possible outcomes, andcomputational complexityof various game scenarios.
Thestate-space complexityof a game is the number of legal game positions reachable from the initial position of the game.[1]
When this is too hard to calculate, anupper boundcan often be computed by also counting (some) illegal positions (positions that can never arise in the course of a game).
Thegame tree sizeis the total number of possible games that can be played. This is the number ofleaf nodesin thegame treerooted at the game's initial position.
The game tree is typically vastly larger than the state-space because the same positions can occur in many games by making moves in a different order (for example, in atic-tac-toegame with two X and one O on the board, this position could have been reached in two different ways depending on where the first X was placed). An upper bound for the size of the game tree can sometimes be computed by simplifying the game in a way that only increases the size of the game tree (for example, by allowing illegal moves) until it becomes tractable.
For games where the number of moves is not limited (for example by the size of the board, or by a rule about repetition of position) the game tree is generally infinite.
Adecision treeis a subtree of the game tree, with each position labelled "player A wins", "player B wins", or "draw" if that position can be proved to have that value (assuming best play by both sides) by examining only other positions in the graph. Terminal positions can be labelled directly—with player A to move, a position can be labelled "player A wins" if any successor position is a win for A; "player B wins" if all successor positions are wins for B; or "draw" if all successor positions are either drawn or wins for B. (With player B to move, corresponding positions are marked similarly.)
The following two methods of measuring game complexity use decision trees:
Decision complexityof a game is the number of leaf nodes in the smallest decision tree that establishes the value of the initial position.
Game-tree complexityof a game is the number of leaf nodes in the smallestfull-widthdecision tree that establishes the value of the initial position.[1]A full-width tree includes all nodes at each depth. This is an estimate of the number of positions one would have to evaluate in aminimaxsearch to determine the value of the initial position.
It is hard even to estimate the game-tree complexity, but for some games an approximation can be given byGTC≥bd{\displaystyle GTC\geq b^{d}}, wherebis the game's averagebranching factoranddis the number ofpliesin an average game.
Thecomputational complexityof a game describes theasymptoticdifficulty of a game as it grows arbitrarily large, expressed inbig O notationor as membership in acomplexity class. This concept doesn't apply to particular games, but rather to games that have beengeneralizedso they can be made arbitrarily large, typically by playing them on ann-by-nboard. (From the point of view of computational complexity, a game on a fixed size of board is a finite problem that can be solved in O(1), for example by a look-up table from positions to the best move in each position.)
The asymptotic complexity is defined by the most efficient algorithm for solving the game (in terms of whatevercomputational resourceone is considering). The most common complexity measure,computation time, is always lower-bounded by the logarithm of the asymptotic state-space complexity, since a solution algorithm must work for every possible state of the game. It will be upper-bounded by the complexity of any particular algorithm that works for the family of games. Similar remarks apply to the second-most commonly used complexity measure, the amount ofspaceorcomputer memoryused by the computation. It is not obvious that there is any lower bound on the space complexity for a typical game, because the algorithm need not store game states; however many games of interest are known to bePSPACE-hard, and it follows that their space complexity will be lower-bounded by the logarithm of the asymptotic state-space complexity as well (technically the bound is only a polynomial in this quantity; but it is usually known to be linear).
Fortic-tac-toe, a simple upper bound for the size of the state space is 39= 19,683. (There are three states for each of the nine cells.) This count includes many illegal positions, such as a position with five crosses and no noughts, or a position in which both players have a row of three. A more careful count, removing these illegal positions, gives 5,478.[2][3]And when rotations and reflections of positions are considered identical, there are only 765 essentially different positions.
To bound the game tree, there are 9 possible initial moves, 8 possible responses, and so on, so that there are at most 9! or 362,880 total games. However, games may take less than 9 moves to resolve, and an exact enumeration gives 255,168 possible games. When rotations and reflections of positions are considered the same, there are only 26,830 possible games.
The computational complexity of tic-tac-toe depends on how it isgeneralized. A natural generalization is tom,n,k-games: played on anmbynboard with winner being the first player to getkin a row. This game can be solved inDSPACE(mn) by searching the entire game tree. This places it in the important complexity classPSPACE; with more work, it can be shown to bePSPACE-complete.[4]
Due to the large size of game complexities, this table gives the ceiling of theirlogarithmto base 10. (In other words, the number of digits). All of the following numbers should be considered with caution: seemingly minor changes to the rules of a game can change the numbers (which are often rough estimates anyway) by tremendous factors, which might easily be much greater than the numbers shown.
(positions)
(aslogto base 10)
(aslogto base 10)
(plies)
[49]
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