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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 appl... | https://en.wikipedia.org/wiki/GSM_03.48 |
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 ... | https://en.wikipedia.org/wiki/Intelligent_Network |
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 delibe... | https://en.wikipedia.org/wiki/Parlay_X |
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 911requirement... | https://en.wikipedia.org/wiki/RRLP |
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 supportGP... | https://en.wikipedia.org/wiki/Um_interface |
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 th... | https://en.wikipedia.org/wiki/Visitors_Location_Register |
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 mob... | https://en.wikipedia.org/wiki/List_of_mobile_phone_generations |
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 u... | https://en.wikipedia.org/wiki/Mobile_radio_telephone |
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 generatio... | https://en.wikipedia.org/wiki/Mobile_broadband |
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... | https://en.wikipedia.org/wiki/Wireless_device_radiation_and_health |
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 retroact... | https://en.wikipedia.org/wiki/1G |
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 device... | https://en.wikipedia.org/wiki/2G |
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 conside... | https://en.wikipedia.org/wiki/4G |
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 s... | https://en.wikipedia.org/wiki/5G |
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 object... | https://en.wikipedia.org/wiki/6G |
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, f... | https://en.wikipedia.org/wiki/ANT_(network) |
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 implementati... | https://en.wikipedia.org/wiki/Bluetooth_stack |
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 C... | https://en.wikipedia.org/wiki/List_of_Bluetooth_profiles |
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 video... | https://en.wikipedia.org/wiki/Bluesniping |
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 need... | https://en.wikipedia.org/wiki/BlueSoleil |
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 proxi... | https://en.wikipedia.org/wiki/Bluetooth_Low_Energy_beacon |
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 ac... | https://en.wikipedia.org/wiki/Types_of_beacons#AltBeacon_(Radius_Networks) |
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. ... | https://en.wikipedia.org/wiki/IBeacon |
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-... | https://en.wikipedia.org/wiki/Eddystone_(Google) |
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 co... | https://en.wikipedia.org/wiki/Bluetooth_mesh_networking |
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 andHI... | https://en.wikipedia.org/wiki/Continua_Health_Alliance |
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,AES12... | https://en.wikipedia.org/wiki/DASH7 |
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 com... | https://en.wikipedia.org/wiki/Audio_headset |
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 typic... | https://en.wikipedia.org/wiki/Wi-Fi_hotspot |
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 St... | https://en.wikipedia.org/wiki/Java_APIs_for_Bluetooth |
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 tab... | https://en.wikipedia.org/wiki/Key_finder |
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 thevisib... | https://en.wikipedia.org/wiki/Li-Fi |
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 Bluet... | https://en.wikipedia.org/wiki/List_of_Bluetooth_protocols |
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... | https://en.wikipedia.org/wiki/MyriaNed |
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 cardtec... | https://en.wikipedia.org/wiki/Near-field_communication |
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 includeautomo... | https://en.wikipedia.org/wiki/NearLink |
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 net... | https://en.wikipedia.org/wiki/RuBee |
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),Blue... | https://en.wikipedia.org/wiki/Tethering |
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, ... | https://en.wikipedia.org/wiki/Thread_(network_protocol) |
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 ... | https://en.wikipedia.org/wiki/IEEE_802.11ah |
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 c... | https://en.wikipedia.org/wiki/Zigbee |
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.... | https://en.wikipedia.org/wiki/ISM_band |
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... | https://en.wikipedia.org/wiki/IEEE_802.15.4 |
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 ... | https://en.wikipedia.org/wiki/Stream_cipher_attacks |
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 ... | https://en.wikipedia.org/wiki/Wireless_security |
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 stora... | https://en.wikipedia.org/wiki/Disk_encryption |
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 authenticatio... | https://en.wikipedia.org/wiki/Authenticated_encryption |
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 conven... | https://en.wikipedia.org/wiki/One-way_compression_function |
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 eth... | https://en.wikipedia.org/wiki/Agrippa_(A_Book_of_the_Dead) |
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 wit... | https://en.wikipedia.org/wiki/Information_theoretic_security |
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 keyi... | https://en.wikipedia.org/wiki/Numbers_station |
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(KE... | https://en.wikipedia.org/wiki/Session_key |
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... | https://en.wikipedia.org/wiki/Steganography |
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 ... | https://en.wikipedia.org/wiki/Tradecraft |
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 det... | https://en.wikipedia.org/wiki/Unicity_distance |
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 ... | https://en.wikipedia.org/wiki/No-hiding_theorem |
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 ... | https://en.wikipedia.org/wiki/Oblivious_transfer |
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 definit... | https://en.wikipedia.org/wiki/Accumulator_(cryptography) |
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 t... | https://en.wikipedia.org/wiki/Key_signing_party |
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 acerti... | https://en.wikipedia.org/wiki/Web_of_trust |
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 proto... | https://en.wikipedia.org/wiki/Zerocoin |
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... | https://en.wikipedia.org/wiki/Anagram#Establishment_of_priority |
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 propert... | https://en.wikipedia.org/wiki/Arithmetic_dynamics |
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... | https://en.wikipedia.org/wiki/Elliptic_algebra |
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 cho... | https://en.wikipedia.org/wiki/Elliptic_surface |
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 graph... | https://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems |
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 isoge... | https://en.wikipedia.org/wiki/Isogeny |
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 clo... | https://en.wikipedia.org/wiki/J-line |
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... | https://en.wikipedia.org/wiki/Level_structure_(algebraic_geometry) |
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 f... | https://en.wikipedia.org/wiki/Modularity_theorem |
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... | https://en.wikipedia.org/wiki/Moduli_stack_of_elliptic_curves |
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 t... | https://en.wikipedia.org/wiki/Nagell%E2%80%93Lutz_theorem |
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 ... | https://en.wikipedia.org/wiki/Riemann%E2%80%93Hurwitz_formula |
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 u... | https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem |
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... | https://en.wikipedia.org/wiki/Cryptocurrency |
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 implem... | https://en.wikipedia.org/wiki/Curve25519 |
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 sourc... | https://en.wikipedia.org/wiki/FourQ |
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 ident... | https://en.wikipedia.org/wiki/DNSCurve |
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, 2... | https://en.wikipedia.org/wiki/ECC_patents |
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 use... | https://en.wikipedia.org/wiki/Elliptic-curve_Diffie%E2%80%93Hellman |
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. Bern... | https://en.wikipedia.org/wiki/EdDSA |
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... | https://en.wikipedia.org/wiki/ECMQV |
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 opera... | https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication |
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 outpu... | https://en.wikipedia.org/wiki/Homomorphic_signatures_for_network_coding |
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}i... | https://en.wikipedia.org/wiki/Hyperelliptic_curve_cryptography |
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... | https://en.wikipedia.org/wiki/Pairing-based_cryptography |
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 ... | https://en.wikipedia.org/wiki/Quantum_cryptography |
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 graphan... | https://en.wikipedia.org/wiki/Supersingular_isogeny_key_exchange |
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... | https://en.wikipedia.org/wiki/BLS_digital_signature |
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: mathema... | https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_problem |
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 machin... | https://en.wikipedia.org/wiki/Denial-of-service_attack |
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 u... | https://en.wikipedia.org/wiki/Post-Quantum_Extended_Diffie%E2%80%93Hellman |
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, and... | https://en.wikipedia.org/wiki/Topics_in_cryptography |
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; th... | https://en.wikipedia.org/wiki/Blum_Blum_Shub |
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 co... | https://en.wikipedia.org/wiki/Shanks%E2%80%93Tonelli_algorithm |
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 messag... | https://en.wikipedia.org/wiki/Schmidt%E2%80%93Samoa_cryptosystem |
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... | https://en.wikipedia.org/wiki/Blum%E2%80%93Goldwasser_cryptosystem |
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 th... | https://en.wikipedia.org/wiki/Computational_complexity |
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 st... | https://en.wikipedia.org/wiki/Descriptive_complexity_theory |
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... | https://en.wikipedia.org/wiki/Game_complexity |
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