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ASIM cardorSIM(subscriber identity module) is anintegrated circuit(IC) intended to securely store aninternational mobile subscriber identity(IMSI) number and its related key, which are used to identify and authenticate subscribers onmobile telephonedevices (such asmobile phones,tablets, andlaptops). SIMs are also able ... | https://en.wikipedia.org/wiki/SIM_card |
Inprobability theory, thebirthday problemasks for the probability that, in a set ofnrandomlychosen people, at least two will share the samebirthday. Thebirthday paradoxis the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.
The birthday paradox is averidical paradox: it seems wr... | https://en.wikipedia.org/wiki/Birthday_problem |
Abirthday attackis a bruteforcecollision attackthat exploits the mathematics behind thebirthday probleminprobability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of pe... | https://en.wikipedia.org/wiki/Birthday_attack |
Incomputer science,brute-force searchorexhaustive search, also known asgenerate and test, is a very generalproblem-solvingtechnique andalgorithmic paradigmthat consists ofsystematically checkingall possible candidates for whether or not each candidate satisfies the problem's statement.
A brute-force algorithm that fin... | https://en.wikipedia.org/wiki/Brute-force_search |
Theone-time pad(OTP) is anencryptiontechnique that cannot becrackedincryptography. It requires the use of a single-usepre-shared keythat is larger than or equal to the size of the message being sent. In this technique, aplaintextis paired with a random secretkey(also referred to as aone-time pad). Then, each bit or cha... | https://en.wikipedia.org/wiki/Vernam_cipher |
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–Hellman |
Inmathematics,integer factorizationis the decomposition of apositive integerinto aproductof integers. Every positive integer greater than 1 is either the product of two or more integerfactorsgreater than 1, in which case it is acomposite number, or it is not, in which case it is aprime number. For example,15is a compos... | https://en.wikipedia.org/wiki/Factoring_problem |
Bluetoothis a short-rangewirelesstechnology standard that is used for exchanging data between fixed and mobile devices over short distances and buildingpersonal area networks(PANs). In the most widely used mode, transmission power is limited to 2.5milliwatts, giving it a very short range of up to 10 metres (33 ft). It ... | https://en.wikipedia.org/wiki/Bluetooth#Bluetooth_2.1 |
Abiometric passport(also known as anelectronic passport,e-passportor adigital passport) is apassportthat has an embedded electronicmicroprocessorchip, which containsbiometricinformation that can be used to authenticate the identity of the passport holder. It usescontactless smart cardtechnology, including a microproces... | https://en.wikipedia.org/wiki/E-passport |
Achosen-ciphertext attack(CCA) is anattack modelforcryptanalysiswhere the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the secret key used for decryption.
For formal definitions of security against chosen-c... | https://en.wikipedia.org/wiki/Chosen-ciphertext_attack |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Inmathematics, especially in the field ofalgebra, apolynomial ringorpolynomial algebrais aringformed from thesetofpolynomialsin one or moreindeterminates(traditionall... | https://en.wikipedia.org/wiki/Polynomial_ring |
Inmathematics, the concept of aninverse elementgeneralises the concepts ofopposite(−x) andreciprocal(1/x) of numbers.
Given anoperationdenoted here∗, and anidentity elementdenotede, ifx∗y=e, one says thatxis aleft inverseofy, and thatyis aright inverseofx. (An identity element is an element such thatx*e=xande*y=yfor a... | https://en.wikipedia.org/wiki/Invertible_element#Definition_of_invertible_elements_in_modular_arithmetic |
Innumber theory, twointegersaandbarecoprime,relatively primeormutually primeif the only positive integer that is adivisorof both of them is 1.[1]Consequently, anyprime numberthat dividesadoes not divideb, and vice versa. This is equivalent to theirgreatest common divisor(GCD) being 1.[2]One says alsoais prime toborais ... | https://en.wikipedia.org/wiki/Coprime_integers |
Incryptographyandcomputer security, aman-in-the-middle[a](MITM)attack, oron-path attack, is acyberattackwhere the attacker secretly relays and possibly alters thecommunicationsbetween two parties who believe that they are directly communicating with each other, where in actuality the attacker has inserted themselves be... | https://en.wikipedia.org/wiki/Man-in-the-middle_attack |
Incryptography,key sizeorkey lengthrefers to the number ofbitsin akeyused by acryptographicalgorithm (such as acipher).
Key length defines the upper-bound on an algorithm'ssecurity(i.e. a logarithmic measure of the fastest known attack against an algorithm), because the security of all algorithms can be violated bybru... | https://en.wikipedia.org/wiki/Key_size#Key_sizes_and_security |
Symmetric-key algorithms[a]arealgorithmsforcryptographythat use the samecryptographic keysfor both the encryption ofplaintextand the decryption ofciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys.[1]The keys, in practice, represent ashared secretbetween two or mor... | https://en.wikipedia.org/wiki/Symmetric-key_algorithm#Key_length |
Wired Equivalent Privacy(WEP) is an obsolete, severely flawedsecurityalgorithm for 802.11wireless networks. Introduced as part of the originalIEEE 802.11standard ratified in 1997, its intention was to provide security/privacy comparable to that of a traditional wirednetwork.[1]WEP, recognizable by its key of 10 or 26he... | https://en.wikipedia.org/wiki/Wired_Equivalent_Privacy |
Incomputingandmathematics, themodulo operationreturns theremainderor signed remainder of adivision, after one number is divided by another, the latter being called themodulusof the operation.
Given two positive numbersaandn,amodulon(often abbreviated asamodn) is the remainder of theEuclidean divisionofabyn, whereais t... | https://en.wikipedia.org/wiki/Modulo_operation |
Inmathematics,modular arithmeticis a system ofarithmeticoperations forintegers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called themodulus. The modern approach to modular arithmetic was developed byCarl Friedrich Gaussin his bookDisquisitiones Arit... | https://en.wikipedia.org/wiki/Integers_modulo_n |
Inmathematics,modular arithmeticis a system ofarithmeticoperations forintegers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called themodulus. The modern approach to modular arithmetic was developed byCarl Friedrich Gaussin his bookDisquisitiones Arit... | https://en.wikipedia.org/wiki/Modular_arithmetic |
48(forty-eight) is thenatural numberfollowing47and preceding49. It is one third of agross, or fourdozens.
48 is ahighly composite number, and aStørmer number.[1]
By a classical result ofHonsberger, the number ofincongruentinteger-sidedtrianglesofperimeterm{\displaystyle m}is given by the equationsm248{\displaystyle ... | https://en.wikipedia.org/wiki/48_(number) |
Incryptography,Triple DES(3DESorTDES), officially theTriple Data Encryption Algorithm(TDEAorTriple DEA), is asymmetric-keyblock cipher, which applies theDEScipher algorithm three times to each data block. The 56-bit key of the Data Encryption Standard (DES) is no longer considered adequate in the face of modern cryptan... | https://en.wikipedia.org/wiki/Double_DES |
Incryptography, theInternational Data Encryption Algorithm(IDEA), originally calledImproved Proposed Encryption Standard(IPES), is asymmetric-keyblock cipherdesigned byJames MasseyofETH ZurichandXuejia Laiand was first described in 1991. The algorithm was intended as a replacement for theData Encryption Standard(DES). ... | https://en.wikipedia.org/wiki/International_Data_Encryption_Algorithm |
SHA-3(Secure Hash Algorithm 3) is the latest[4]member of theSecure Hash Algorithmfamily of standards, released byNISTon August 5, 2015.[5][6][7]Although part of the same series of standards, SHA-3 is internally different from theMD5-likestructureofSHA-1andSHA-2.
SHA-3 is a subset of the broader cryptographic primitive... | https://en.wikipedia.org/wiki/Keccak |
Aspace–time trade-off, also known astime–memory trade-offorthe algorithmic space-time continuumincomputer scienceis a case where analgorithmorprogramtradesincreased space usage with decreased time. Here,spacerefers to thedata storageconsumed in performing a given task (RAM,HDD, etc.), andtimerefers to the time consumed... | https://en.wikipedia.org/wiki/Time-memory_tradeoff |
Incryptography, apreimage attackoncryptographic hash functionstries to find amessagethat has a specific hash value. A cryptographic hash function should resist attacks on itspreimage(set of possible inputs).
In the context of attack, there are two types of preimage resistance:
These can be compared with acollision re... | https://en.wikipedia.org/wiki/Preimage_attack |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Inmathematics, aring homomorphismis a structure-preservingfunctionbetween tworings. More explicitly, ifRandSare rings, then a ring homomorphism is a functionf:R→Sthat... | https://en.wikipedia.org/wiki/Ring_isomorphism |
TheFermat primality testis aprobabilistictest to determine whether a number is aprobable prime.
Fermat's little theoremstates that ifpis prime andais not divisible byp, then
If one wants to test whetherpis prime, then we can pick random integersanot divisible bypand see whether the congruence holds. If it does not ho... | https://en.wikipedia.org/wiki/Fermat_primality_test |
TheMiller–Rabin primality testorRabin–Miller primality testis a probabilisticprimality test: analgorithmwhich determines whether a given number islikely to be prime, similar to theFermat primality testand theSolovay–Strassen primality test.
It is of historical significance in the search for apolynomial-timedeterminist... | https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test |
Wi-Fi Protected Access(WPA) (Wireless Protected Access),Wi-Fi Protected Access 2(WPA2), andWi-Fi Protected Access 3(WPA3) are the three security certification programs developed after 2000 by theWi-Fi Allianceto secure wireless computer networks. The Alliance defined these in response to serious weaknesses researchers... | https://en.wikipedia.org/wiki/Wi-Fi_Protected_Access#WPA2 |
Inmathematics, afieldis aseton whichaddition,subtraction,multiplication, anddivisionare defined and behave as the corresponding operations onrationalandreal numbers. A field is thus a fundamentalalgebraic structurewhich is widely used inalgebra,number theory, and many other areas of mathematics.
The best known fields ... | https://en.wikipedia.org/wiki/Field_(mathematics) |
Inmathematics, aprime poweris apositive integerwhich is a positive integerpowerof a singleprime number.
For example:7 = 71,9 = 32and64 = 26are prime powers, while6 = 2 × 3,12 = 22× 3and36 = 62= 22× 32are not.
The sequence of prime powers begins:
2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41,... | https://en.wikipedia.org/wiki/Prime_power |
Information securityis the practice of protectinginformationby mitigating information risks. It is part of information risk management.[1]It typically involves preventing or reducing the probability of unauthorized or inappropriate access todataor the unlawful use,disclosure, disruption, deletion, corruption, modificat... | https://en.wikipedia.org/wiki/Information_security |
Acyclic redundancy check(CRC) is anerror-detecting codecommonly used in digitalnetworksand storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a shortcheck valueattached, based on the remainder of apolynomial divisionof their contents. On retrieval, the calculation is... | https://en.wikipedia.org/wiki/Cyclic_redundancy_check |
TheData Encryption Standard(DES/ˌdiːˌiːˈɛs,dɛz/) is asymmetric-key algorithmfor theencryptionof digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement ofcryptography.
Developed in the early 1970s atIBMand based on an earli... | https://en.wikipedia.org/wiki/Data_Encryption_Standard#Key_schedule |
Inabstract algebra,group theorystudies thealgebraic structuresknown asgroups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such asrings,fields, andvector spaces, can all be seen as groups endowed with additionaloperationsandaxioms. Groups recur throughout mathematics, ... | https://en.wikipedia.org/wiki/Group_theory#Finite_groups |
Incomputer science,brute-force searchorexhaustive search, also known asgenerate and test, is a very generalproblem-solvingtechnique andalgorithmic paradigmthat consists ofsystematically checkingall possible candidates for whether or not each candidate satisfies the problem's statement.
A brute-force algorithm that fin... | https://en.wikipedia.org/wiki/Exhaustive_search |
Intheoretical computer scienceand mathematics,computational complexity theoryfocuses on classifyingcomputational problemsaccording to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanica... | https://en.wikipedia.org/wiki/Computational_complexity_theory |
Jacobi symbol(k/n)for variousk(along top) andn(along left side). Only0 ≤k<nare shown, since due to rule (2) below any otherkcan be reduced modulon.Quadratic residuesare highlighted in yellow — note that no entry with a Jacobi symbol of −1 is a quadratic residue, and ifkis a quadratic residue modulo a coprimen, then(... | https://en.wikipedia.org/wiki/Jacobi_symbol |
Inmathematics,integer factorizationis the decomposition of apositive integerinto aproductof integers. Every positive integer greater than 1 is either the product of two or more integerfactorsgreater than 1, in which case it is acomposite number, or it is not, in which case it is aprime number. For example,15is a compos... | https://en.wikipedia.org/wiki/Integer_factorization |
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/Tonelli%E2%80%93Shanks_algorithm |
Inalgebra, ahomomorphismis astructure-preservingmapbetween twoalgebraic structuresof the same type (such as twogroups, tworings, or twovector spaces). The wordhomomorphismcomes from theAncient Greek language:ὁμός(homos) meaning "same" andμορφή(morphe) meaning "form" or "shape". However, the word was apparently introduc... | https://en.wikipedia.org/wiki/Homomorphism |
Inmathematics, given twogroups, (G,∗) and (H, ·), agroup homomorphismfrom (G,∗) to (H, ·) is afunctionh:G→Hsuch that for alluandvinGit holds that
where the group operation on the left side of the equation is that ofGand on the right side that ofH.
From this property, one can deduce thathmaps theidentity elementeGofGt... | https://en.wikipedia.org/wiki/Group_homomorphism |
In cryptography, ablock cipher mode of operationis an algorithm that uses ablock cipherto provideinformation securitysuch asconfidentialityorauthenticity.[1]A block cipher by itself is only suitable for the secure cryptographic transformation (encryption or decryption) of one fixed-length group ofbitscalled ablock.[2]A... | https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation#Counter_mode |
Ininformation theory, thenoisy-channel coding theorem(sometimesShannon's theoremorShannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digitalinformation) nearly error-free up to a computable maximum rate thro... | https://en.wikipedia.org/wiki/Shannon's_theorem |
Ininformation theory, theentropyof arandom variablequantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities... | https://en.wikipedia.org/wiki/Information_entropy |
TheUniversal Mobile Telecommunications System(UMTS) is a3Gmobile cellular system for networks based on theGSMstandard.[1]UMTS useswideband code-division multiple access(W-CDMA) radio access technology to offer greater spectral efficiency and bandwidth tomobile network operatorscompared to previous2Gsystems likeGPRSandC... | https://en.wikipedia.org/wiki/Universal_Mobile_Telecommunications_System |
A5/1is astream cipherused to provide over-the-air communicationprivacyin theGSMcellular telephonestandard. It is one of several implementations of the A5 security protocol. It was initially kept secret, but became public knowledge through leaks andreverse engineering. A number of serious weaknesses in the cipher have b... | https://en.wikipedia.org/wiki/A5/1 |
Inarithmeticandcomputer programming, theextended Euclidean algorithmis an extension to theEuclidean algorithm, and computes, in addition to thegreatest common divisor(gcd) of integersaandb, also the coefficients ofBézout's identity, which are integersxandysuch that
This is acertifying algorithm, because the gcd is th... | https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm |
Incryptography, apublic key certificate, also known as adigital certificateoridentity certificate, is anelectronic documentused to prove the validity of apublic key.[1][2]The certificate includes the public key and information about it, information about the identity of its owner (called the subject), and thedigital si... | https://en.wikipedia.org/wiki/Digital_certificate |
Apublic key infrastructure(PKI) is a set of roles, policies, hardware, software and procedures needed to create, manage, distribute, use, store and revokedigital certificatesand managepublic-key encryption.
The purpose of a PKI is to facilitate the secure electronic transfer of information for a range of network activ... | https://en.wikipedia.org/wiki/Public_key_infrastructure |
Inmathematics, afinite fieldorGalois field(so-named in honor ofÉvariste Galois) is afieldthat contains a finite number ofelements. As with any field, a finite field is aseton which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common example... | https://en.wikipedia.org/wiki/Galois_field#Galois_field_of_order_2^n |
Inmathematics, anabelian group, also called acommutative group, is agroupin which the result of applying thegroup operationto two group elements does not depend on the order in which they are written. That is, the group operation iscommutative. With addition as an operation, theintegersand thereal numbersform abelian g... | https://en.wikipedia.org/wiki/Abelian_group |
Inabstract algebra, afinite groupis agroupwhoseunderlying setisfinite. Finite groups often arise when considering symmetry ofmathematicalorphysicalobjects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups includecyclic groupsandpermutation grou... | https://en.wikipedia.org/wiki/Finite_group |
Kerckhoffs's principle(also calledKerckhoffs's desideratum,assumption,axiom,doctrineorlaw) ofcryptographywas stated byDutch-borncryptographerAuguste Kerckhoffsin the 19th century. The principle holds that acryptosystemshould be secure, even if everything about the system, except thekey, is public knowledge. This concep... | https://en.wikipedia.org/wiki/Kerckhoffs%27_principle |
Symmetric-key algorithms[a]arealgorithmsforcryptographythat use the samecryptographic keysfor both the encryption ofplaintextand the decryption ofciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys.[1]The keys, in practice, represent ashared secretbetween two or mor... | https://en.wikipedia.org/wiki/Symmetric-key_algorithm |
Intheoretical computer science,communication complexitystudies the amount of communication required to solve a problem when the input to the problem isdistributedamong two or more parties. The study of communication complexity was first introduced byAndrew Yaoin 1979, while studying the problem of computation distribut... | https://en.wikipedia.org/wiki/Communication_complexity |
Transport Layer Security(TLS) is acryptographic protocoldesigned to provide communications security over a computer network, such as theInternet. Theprotocolis widely used inapplicationssuch asemail,instant messaging, andvoice over IP, but its use in securingHTTPSremains the most publicly visible.
The TLS protocol aim... | https://en.wikipedia.org/wiki/Transport_Layer_Security#TLS_versions |
Apassword, sometimes called apasscode, is secret data, typically a string of characters, usually used to confirm a user's identity. Traditionally, passwords were expected to bememorized,[1]but the large number of password-protected services that a typical individual accesses can make memorization of unique passwords fo... | https://en.wikipedia.org/wiki/Password#Hashing_and_salt |
Incryptography, ablock cipheris adeterministic algorithmthat operates on fixed-length groups ofbits, calledblocks. Block ciphers are the elementarybuilding blocksof manycryptographic protocols. They are ubiquitous in the storage and exchange of data, where such data is secured and authenticated viaencryption.
A block ... | https://en.wikipedia.org/wiki/Block_cipher |
Inmathematics, theassociative property[1]is a property of somebinary operationsthat rearranging theparenthesesin an expression will not change the result. Inpropositional logic,associativityis avalidrule of replacementforexpressionsinlogical proofs.
Within an expression containing two or more occurrences in a row of t... | https://en.wikipedia.org/wiki/Associative_property |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Anon-associative algebra[1](ordistributive algebra) is analgebra over a fieldwhere thebinary multiplication operationis not assumed to beassociative. That is, analgeb... | https://en.wikipedia.org/wiki/Non-associative_algebra |
Intheoretical computer scienceand mathematics,computational complexity theoryfocuses on classifyingcomputational problemsaccording to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanica... | https://en.wikipedia.org/wiki/Computational_intractability |
Bluetoothis a short-rangewirelesstechnology standard that is used for exchanging data between fixed and mobile devices over short distances and buildingpersonal area networks(PANs). In the most widely used mode, transmission power is limited to 2.5milliwatts, giving it a very short range of up to 10 metres (33 ft). It ... | https://en.wikipedia.org/wiki/Bluetooth#Bluetooth_security |
Inmathematics, asquare rootof a numberxis a numberysuch thaty2=x{\displaystyle y^{2}=x}; in other words, a numberywhosesquare(the result of multiplying the number by itself, ory⋅y{\displaystyle y\cdot y}) isx.[1]For example, 4 and −4 are square roots of 16 because42=(−4)2=16{\displaystyle 4^{2}=(-4)^{2}=16}.
Everynonn... | https://en.wikipedia.org/wiki/Square_root#Modular_square_root |
TheGlobal System for Mobile Communications(GSM) is a family of standards to describe the protocols for second-generation (2G) digitalcellular networks,[2]as used by mobile devices such asmobile phonesandmobile broadband modems. GSM is also atrade markowned by theGSM Association.[3]"GSM" may also refer to the voice code... | https://en.wikipedia.org/wiki/GSM#Encryption |
Modular exponentiationisexponentiationperformed over amodulus. It is useful incomputer science, especially in the field ofpublic-key cryptography, where it is used in bothDiffie–Hellman key exchangeandRSA public/private keys.
Modular exponentiation is the remainder when an integerb(the base) is raised to the powere(th... | https://en.wikipedia.org/wiki/Modular_exponentiation |
Cryptography, orcryptology(fromAncient Greek:κρυπτός,romanized:kryptós"hidden, secret"; andγράφεινgraphein, "to write", or-λογία-logia, "study", respectively[1]), is the practice and study of techniques forsecure communicationin the presence ofadversarialbehavior.[2]More generally, cryptography is about constructing an... | https://en.wikipedia.org/wiki/Cryptography#Kerckhoffs%27_principle |
Inmathematics, amultiplicative inverseorreciprocalfor anumberx, denoted by 1/xorx−1, is a number which whenmultipliedbyxyields themultiplicative identity, 1. The multiplicative inverse of afractiona/bisb/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one ... | https://en.wikipedia.org/wiki/Multiplicative_inverse |
Multiplicationis one of the four elementary mathematical operations ofarithmetic, with the other ones beingaddition,subtraction, anddivision. The result of a multiplication operation is called aproduct. Multiplication is often denoted by the cross symbol,×, by the mid-line dot operator,·, by juxtaposition, or, on compu... | https://en.wikipedia.org/wiki/Integer_multiplication#Time_complexity_of_integer_multiplication_algorithms |
Elliptic-curve cryptography(ECC) is an approach topublic-key cryptographybased on thealgebraic structureofelliptic curvesoverfinite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation inGalois fields, such as theRSA cryptosystemandElGamal cryptosyste... | https://en.wikipedia.org/wiki/Elliptic-curve_cryptography |
Achosen-plaintext attack(CPA) is anattack modelforcryptanalysiswhich presumes that the attacker can obtain theciphertextsfor arbitraryplaintexts.[1]The goal of the attack is to gain information that reduces the security of theencryptionscheme.[2]
Modern ciphers aim to provide semantic security, also known asciphertext... | https://en.wikipedia.org/wiki/Chosen_plaintext_attack |
Aquantum computeris acomputerthat exploitsquantum mechanicalphenomena. On small scales, physical matter exhibits properties ofboth particles and waves, and quantum computing takes advantage of this behavior using specialized hardware.Classical physicscannot explain the operation of these quantum devices, and a scalable... | https://en.wikipedia.org/wiki/Quantum_computing |
Inmathematics, anelliptic curveis asmooth,projective,algebraic curveofgenusone, on which there is a specified pointO. An elliptic curve is defined over afieldKand describes points inK2, theCartesian productofKwith itself. If the field'scharacteristicis different from 2 and 3, then the curve can be described as aplane a... | https://en.wikipedia.org/wiki/Elliptic_curve#Group_structure |
Wi-Fi Protected Access(WPA) (Wireless Protected Access),Wi-Fi Protected Access 2(WPA2), andWi-Fi Protected Access 3(WPA3) are the three security certification programs developed after 2000 by theWi-Fi Allianceto secure wireless computer networks. The Alliance defined these in response to serious weaknesses researchers... | https://en.wikipedia.org/wiki/Wi-Fi_Protected_Access |
Digital Enhanced Cordless Telecommunications(DECT) is acordless telephonystandard maintained byETSI. It originated inEurope, where it is the common standard, replacing earlier standards, such asCT1andCT2.[1]Since the DECT-2020 standard onwards, it also includesIoTcommunication.
Beyond Europe, it has been adopted byAus... | https://en.wikipedia.org/wiki/Digital_Enhanced_Cordless_Telecommunications |
Code-division multiple access(CDMA) is achannel access methodused by variousradiocommunication technologies. CDMA is an example ofmultiple access, where several transmitters can send information simultaneously over a single communication channel. This allows several users to share a band of frequencies (seebandwidth).... | https://en.wikipedia.org/wiki/Code_division_multiple_access |
Inmathematics, afinite fieldorGalois field(so-named in honor ofÉvariste Galois) is afieldthat contains a finite number ofelements. As with any field, a finite field is aseton which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common example... | https://en.wikipedia.org/wiki/Finite_field#Field_operations |
In cryptography,security levelis a measure of the strength that acryptographic primitive— such as acipherorhash function— achieves. Security level is usually expressed as a number of "bitsof security" (alsosecurity strength),[1]wheren-bit security means that the attacker would have to perform 2noperations to break it,[... | https://en.wikipedia.org/wiki/Cryptographic_strength |
Wired Equivalent Privacy(WEP) is an obsolete, severely flawedsecurityalgorithm for 802.11wireless networks. Introduced as part of the originalIEEE 802.11standard ratified in 1997, its intention was to provide security/privacy comparable to that of a traditional wirednetwork.[1]WEP, recognizable by its key of 10 or 26he... | https://en.wikipedia.org/wiki/Wired_Equivalent_Privacy#Data_integrity |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Inmathematics, anoncommutative ringis aringwhose multiplication is notcommutative; that is, there existaandbin the ring such thatabandbaare different. Equivalently, a... | https://en.wikipedia.org/wiki/Noncommutative_algebra |
Addition(usually signified by theplus symbol, +) is one of the four basicoperationsofarithmetic, the other three beingsubtraction,multiplication, anddivision. The addition of twowhole numbersresults in the total orsumof those values combined. For example, the adjacent image shows two columns of apples, one with three a... | https://en.wikipedia.org/wiki/Addition |
Subtraction(which is signified by theminus sign, –) is one of the fourarithmetic operationsalong withaddition,multiplicationanddivision. Subtraction is an operation that represents removal of objects from a collection.[1]For example, in the adjacent picture, there are5 − 2peaches—meaning 5 peaches with 2 taken away, re... | https://en.wikipedia.org/wiki/Subtraction |
Multiplicationis one of the four elementary mathematical operations ofarithmetic, with the other ones beingaddition,subtraction, anddivision. The result of a multiplication operation is called aproduct. Multiplication is often denoted by the cross symbol,×, by the mid-line dot operator,·, by juxtaposition, or, on compu... | https://en.wikipedia.org/wiki/Multiplication |
Exclusive or,exclusive disjunction,exclusive alternation,logical non-equivalence, orlogical inequalityis alogical operatorwhose negation is thelogical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of ... | https://en.wikipedia.org/wiki/Exclusive_or |
Incryptography, acipher(orcypher) is analgorithmfor performingencryptionordecryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term isencipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "... | https://en.wikipedia.org/wiki/Cipher#Perfect_secrecy |
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 |
TheVigenère cipher(French pronunciation:[viʒnɛːʁ]) is a method ofencryptingalphabetictext where each letter of theplaintextis encoded with a differentCaesar cipher, whose increment is determined by the corresponding letter of another text, thekey.
For example, if the plaintext isattacking tonightand the key isoculorhi... | https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher |
Adigital signatureis a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient.[1][2]
Digital signatures are a standard element of mostcryptographic protocolsuites... | https://en.wikipedia.org/wiki/Digital_signature |
Public Key Cryptography Standards(PKCS) are a group ofpublic-key cryptographystandards devised and published byRSA SecurityLLC, starting in the early 1990s. The company published the standards to promote the use of the cryptography techniques for which they hadpatents, such as theRSA algorithm, theSchnorr signaturealg... | https://en.wikipedia.org/wiki/PKCS#1 |
Incryptography,forward secrecy(FS), also known asperfect forward secrecy(PFS), is a feature of specifickey-agreement protocolsthat gives assurances thatsession keyswill not be compromised even if long-term secrets used in the session key exchange are compromised, limiting damage.[1][2][3]ForTLS, the long-term secret is... | https://en.wikipedia.org/wiki/Forward_secrecy |
Incryptography, asubstitution cipheris a method ofencryptingin which units ofplaintextare replaced with theciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the ... | https://en.wikipedia.org/wiki/Substitution_cipher |
Incryptanalysis,frequency analysis(also known ascounting letters) is the study of thefrequency of lettersor groups of letters in aciphertext. The method is used as an aid to breakingclassical ciphers.
Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinatio... | https://en.wikipedia.org/wiki/Frequency_analysis |
Noncemay refer to: | https://en.wikipedia.org/wiki/Nonce |
Inalgebra, aunitorinvertible element[a]of aringis aninvertible elementfor the multiplication of the ring. That is, an elementuof a ringRis a unit if there existsvinRsuch thatvu=uv=1,{\displaystyle vu=uv=1,}where1is themultiplicative identity; the elementvis unique for this property and is called themultiplicative inver... | https://en.wikipedia.org/wiki/Group_of_units#Finite_groups_of_units |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Inmathematics, aringis analgebraic structureconsisting of a set with twobinary operationscalledadditionandmultiplication, which obey the same basic laws asadditionand... | https://en.wikipedia.org/wiki/Ring_(mathematics) |
Acommitment schemeis acryptographic primitivethat allows one to commit to a chosen value (or chosen statement) while keeping it hidden to others, with the ability to reveal the committed value later.[1]Commitment schemes are designed so that a party cannot change the value or statement after they have committed to it: ... | https://en.wikipedia.org/wiki/Pedersen_commitment |
TheDigital Signature Algorithm(DSA) is apublic-key cryptosystemandFederal Information Processing Standardfordigital signatures, based on the mathematical concept ofmodular exponentiationand thediscrete logarithm problem. In a public-key cryptosystem, a pair of private and public keys are created: data encrypted with ei... | https://en.wikipedia.org/wiki/Digital_Signature_Algorithm |
Morse codeis atelecommunicationsmethod whichencodestextcharacters as standardized sequences of two different signal durations, calleddotsanddashes, orditsanddahs.[3][4]Morse code is named afterSamuel Morse, one of the early developers of the system adopted forelectrical telegraphy.
International Morse codeencodes the ... | https://en.wikipedia.org/wiki/Morse_code |
Cryptographic primitivesare well-established, low-levelcryptographicalgorithmsthat are frequently used to buildcryptographic protocolsfor computer security systems.[1]These routines include, but are not limited to,one-way hash functionsandencryption functions.
When creatingcryptographic systems,designersuse cryptograp... | https://en.wikipedia.org/wiki/Cryptographic_primitive#Message_authentication_codes |
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