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Innumber theory,Fermat's little theoremstates that ifpis aprime number, then for anyintegera, the numberap−ais an integer multiple ofp. In the notation ofmodular arithmetic, this is expressed asap≡a(modp).{\displaystyle a^{p}\equiv a{\pmod {p}}.}
For example, ifa= 2andp= 7, then27= 128, and128 − 2 = 126 = 7 × 18is an ... | https://en.wikipedia.org/wiki/Fermat%27s_little_theorem |
Inmathematics, apermutationof asetcan mean one of two different things:
An example of the first meaning is the six permutations (orderings) of the set {1, 2, 3}: written astuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).Anagramsof a word whose letters are all different are also pe... | https://en.wikipedia.org/wiki/Permutation |
Inmathematics,Stirling numbersarise in a variety ofanalyticandcombinatorialproblems. They are named afterJames Stirling, who introduced them in a purely algebraic setting in his bookMethodus differentialis(1730).[1]They were rediscovered and given a combinatorial meaning by Masanobu Saka in his 1782Sanpō-Gakkai(The Sea... | https://en.wikipedia.org/wiki/Stirling_numbers |
Inmathematics,Stirling's approximation(orStirling's formula) is anasymptoticapproximation forfactorials. It is a good approximation, leading to accurate results even for small values ofn{\displaystyle n}. It is named afterJames Stirling, though a related but less precise result was first stated byAbraham de Moivre.[1][... | https://en.wikipedia.org/wiki/Stirling_approximation |
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/IDEA_(cipher) |
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/Global_System_for_Mobile_Communications |
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#Security |
3Grefers to the third-generation ofcellular networktechnology. These networks were rolled out beginning in the early 2000s and represented a significant advancement over the second-generation (2G), particularly in terms of data transfer speeds andmobile internetcapabilities. The major 3G standards areUMTS(developed by3... | https://en.wikipedia.org/wiki/3G#Security |
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#Security |
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#Authentication |
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 |
TheRSA(Rivest–Shamir–Adleman)cryptosystemis apublic-key cryptosystem, one of the oldest widely used for secure data transmission. Theinitialism"RSA" comes from the surnames ofRon Rivest,Adi ShamirandLeonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 atGove... | https://en.wikipedia.org/wiki/RSA_(cryptosystem) |
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/One-time_pad |
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/Commitment_scheme |
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 |
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 |
Diffie–Hellman(DH)key exchange[nb 1]is a mathematicalmethodof securely generating a symmetriccryptographic keyover a public channel and was one of the firstpublic-key protocolsas conceived byRalph Merkleand named afterWhitfield DiffieandMartin Hellman.[1][2]DH is one of the earliest practical examples of public key exc... | https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange |
TheRabin cryptosystemis a family ofpublic-key encryptionschemes
based on atrapdoor functionwhose security, like that ofRSA, is related to the difficulty ofinteger factorization.[1][2]
The Rabin trapdoor function has the advantage that inverting it has beenmathematicallyproven to be as hard as factoring integers, while... | https://en.wikipedia.org/wiki/Rabin_cryptosystem |
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/Complexity_of_algorithms |
Incryptography, theElGamal encryption systemis anasymmetric key encryption algorithmforpublic-key cryptographywhich is based on the Diffie–Hellman key exchange. It was described byTaher Elgamalin 1985.[1]ElGamal encryption is used in the freeGNU Privacy Guardsoftware, recent versions ofPGP, and othercryptosystems. TheD... | https://en.wikipedia.org/wiki/ElGamal_encryption |
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#Modes_of_operation |
Astream cipheris asymmetric keycipherwhere plaintext digits are combined with apseudorandomcipher digit stream (keystream). In a stream cipher, eachplaintextdigitis encrypted one at a time with the corresponding digit of the keystream, to give a digit of theciphertextstream. Since encryption of each digit is dependent ... | https://en.wikipedia.org/wiki/Stream_cipher |
Inmathematics, for givenreal numbersa{\displaystyle a}andb{\displaystyle b}, thelogarithmlogb(a){\displaystyle \log _{b}(a)}is a numberx{\displaystyle x}such thatbx=a{\displaystyle b^{x}=a}. Analogously, in anygroupG{\displaystyle G}, powersbk{\displaystyle b^{k}}can be defined for allintegersk{\displaystyle k}, and t... | https://en.wikipedia.org/wiki/Discrete_logarithm |
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#Link_keys_and_encryption_keys |
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#Pairing |
Innumber theory,Euler's totient functioncounts the positive integers up to a given integernthat arerelatively primeton. It is written using the Greek letterphiasφ(n){\displaystyle \varphi (n)}orϕ(n){\displaystyle \phi (n)}, and may also be calledEuler's phi function. In other words, it is the number of integerskin the ... | https://en.wikipedia.org/wiki/Euler%27s_totient_function |
Aprime number(or aprime) is anatural numbergreater than 1 that is not aproductof two smaller natural numbers. A natural number greater than 1 that is not prime is called acomposite number. For example, 5 is prime because the only ways of writing it as a product,1 × 5or5 × 1, involve 5 itself. However, 4 is composite be... | https://en.wikipedia.org/wiki/Prime_number |
Acomposite numberis apositive integerthat can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least onedivisorother than 1 and itself.[1][2]Every positive integer is composite,prime, or theunit1, so the composite numbers are exactly the numbers that are not prime... | https://en.wikipedia.org/wiki/Composite_number |
Moore's lawis the observation that the number oftransistorsin anintegrated circuit(IC) doubles about every two years. Moore's law is anobservationandprojectionof a historical trend. Rather than alaw of physics, it is anempirical relationship. It is anexperience-curve law, a type of law quantifying efficiency gains from... | https://en.wikipedia.org/wiki/Moore%27s_law |
Intel Corporation[note 1]is an Americanmultinational corporationandtechnology companyheadquartered inSanta Clara, California, andincorporated in Delaware.[3]Intel designs, manufactures, and sells computer components such asCPUsand related products for business and consumer markets. It is considered one of the world'sla... | https://en.wikipedia.org/wiki/Intel |
Inmodular arithmetic, theintegerscoprime(relatively prime) tonfrom the set{0,1,…,n−1}{\displaystyle \{0,1,\dots ,n-1\}}ofnnon-negative integers form agroupunder multiplicationmodulon, called themultiplicative group of integers modulon. Equivalently, the elements of this group can be thought of as thecongruence classes... | https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n |
Inmathematics, theChinese remainder theoremstates that if one knows theremainders of the Euclidean divisionof anintegernby several integers, then one can determine uniquely the remainder of the division ofnby the product of these integers, under the condition that thedivisorsarepairwise coprime(no two divisors share a ... | https://en.wikipedia.org/wiki/Chinese_remainder_theorem |
Inmathematics, anisomorphismis a structure-preservingmappingormorphismbetween twostructuresof the same type that can be reversed by aninverse mapping. Two mathematical structures areisomorphicif an isomorphism exists between them. The word is derived fromAncient Greekἴσος(isos)'equal'andμορφή(morphe)'form, shape'.
The... | https://en.wikipedia.org/wiki/Isomorphism |
Incryptography, asaltisrandomdata fed as an additional input to aone-way functionthathashesdata, apasswordorpassphrase.[1]Salting helps defend against attacks that use precomputed tables (e.g.rainbow tables), by vastly growing the size of table needed for a successful attack.[2][3][4]It also helps protect passwords tha... | https://en.wikipedia.org/wiki/Salt_(cryptography) |
Incryptography, akey derivation function(KDF) is a cryptographic algorithm that derives one or moresecret keysfrom a secret value such as a master key, apassword, or apassphraseusing apseudorandom function(which typically uses acryptographic hash functionorblock cipher).[1][2][3]KDFs can be used to stretch keys into lo... | https://en.wikipedia.org/wiki/Password_hashing#Salting |
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_paradox |
Ahash functionis anyfunctionthat can be used to mapdataof arbitrary size to fixed-size values, though there are some hash functions that support variable-length output.[1]The values returned by a hash function are calledhash values,hash codes, (hash/message)digests,[2]or simplyhashes. The values are usually used to in... | https://en.wikipedia.org/wiki/Hash_function |
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/Triple_DES |
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 |
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#WPA-TKIP |
Incryptography, theMerkle–Damgård constructionorMerkle–Damgård hash functionis a method of buildingcollision-resistantcryptographic hash functionsfrom collision-resistantone-way compression functions.[1]: 145This construction was used in the design of many popular hash algorithms such asMD5,SHA-1, andSHA-2.
The Merkle... | https://en.wikipedia.org/wiki/Merkle%E2%80%93Damg%C3%A5rd_construction |
Innumber theory, aCarmichael numberis acomposite numbern{\displaystyle n}which inmodular arithmeticsatisfies thecongruence relation:
for all integersb{\displaystyle b}.[1]The relation may also be expressed[2]in the form:
for all integersb{\displaystyle b}that arerelatively primeton{\displaystyle n}. They areinf... | https://en.wikipedia.org/wiki/Carmichael_number |
Inmathematics, agroupis asetwith abinary operationthat satisfies the following constraints: the operation isassociative, it has anidentity element, and every element of the set has aninverse element.
Manymathematical structuresare groups endowed with other properties. For example, theintegerswith theaddition operation... | https://en.wikipedia.org/wiki/Group_(mathematics) |
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 |
Public-key cryptography, orasymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of apublic keyand a correspondingprivate key.[1][2]Key pairs are generated withcryptographicalgorithmsbased onmathematicalproblems termedone-way functions. Security of public-... | https://en.wikipedia.org/wiki/Public-key_cryptography |
Incryptography,encryption(more specifically,encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the information, known asplaintext, into an alternative form known asciphertext. Despite its goal, encryption... | https://en.wikipedia.org/wiki/Encryption |
Key managementrefers to management ofcryptographic keysin acryptosystem. This includes dealing with the generation, exchange, storage, use,crypto-shredding(destruction) and replacement of keys. It includescryptographic protocoldesign,key servers, user procedures, and other relevant protocols.[1][2]
Key management con... | https://en.wikipedia.org/wiki/Key_management |
Innumber theory,Euler's theorem(also known as theFermat–Euler theoremorEuler's totient theorem) states that, ifnandaarecoprimepositive integers, thenaφ(n){\displaystyle a^{\varphi (n)}}is congruent to1{\displaystyle 1}modulon, whereφ{\displaystyle \varphi }denotesEuler's totient function; that is
In 1736,Leonhard Eule... | https://en.wikipedia.org/wiki/Euler%27s_theorem |
TheRSA(Rivest–Shamir–Adleman)cryptosystemis apublic-key cryptosystem, one of the oldest widely used for secure data transmission. Theinitialism"RSA" comes from the surnames ofRon Rivest,Adi ShamirandLeonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 atGove... | https://en.wikipedia.org/wiki/RSA_algorithm |
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 |
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#In_the_context_of_modular_arithmetic |
Authentication(fromGreek:αὐθεντικόςauthentikos, "real, genuine", from αὐθέντηςauthentes, "author") is the act of proving anassertion, such as theidentityof a computer system user. In contrast withidentification, the act of indicating a person or thing's identity, authentication is the process of verifying that identity... | https://en.wikipedia.org/wiki/Authentication |
S/KEYis aone-time passwordsystem developed forauthenticationtoUnix-likeoperating systems, especially fromdumb terminalsor untrusted public computers on which one does not want to type a long-term password. A user's real password is combined in an offline device with a short set of characters and a decrementing counter ... | https://en.wikipedia.org/wiki/S/Key |
Acryptographic hash function(CHF) is ahash algorithm(amapof an arbitrary binary string to a binary string with a fixed size ofn{\displaystyle n}bits) that has special properties desirable for acryptographicapplication:[1]
Cryptographic hash functions have manyinformation-securityapplications, notably indigital signatu... | https://en.wikipedia.org/wiki/Cryptographic_hash_function |
Aone-time password(OTP), also known as aone-time PIN,one-time passcode,one-time authorization code(OTAC) ordynamic password, is a password that is valid for only one login session or transaction, on a computer system or other digital device. OTPs avoid several shortcomings that are associated with traditional (static) ... | https://en.wikipedia.org/wiki/One-time_password |
Public-key cryptography, orasymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of apublic keyand a correspondingprivate key.[1][2]Key pairs are generated withcryptographicalgorithmsbased onmathematicalproblems termedone-way functions. Security of public-... | https://en.wikipedia.org/wiki/Public_key_cryptography |
Innumber theory, a branch ofmathematics, theCarmichael functionλ(n)of apositive integernis the smallest positive integermsuch that
holds for every integeracoprimeton. In algebraic terms,λ(n)is theexponentof themultiplicative group of integers modulon. As this is afinite abelian group, there must exist an element whose... | https://en.wikipedia.org/wiki/Carmichael_function |
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 |
Inmodular arithmetic, theintegerscoprime(relatively prime) tonfrom the set{0,1,…,n−1}{\displaystyle \{0,1,\dots ,n-1\}}ofnnon-negative integers form agroupunder multiplicationmodulon, called themultiplicative group of integers modulon. Equivalently, the elements of this group can be thought of as thecongruence classes... | https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_mod_n |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Inmathematics, and more specifically inring theory, anidealof aringis a specialsubsetof its elements. Ideals generalize certain subsets of theintegers, such as theeve... | https://en.wikipedia.org/wiki/Ideal_(ring_theory) |
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 |
Inabstract algebra, acyclic groupormonogenous groupis agroup, denoted Cn(also frequentlyZ{\displaystyle \mathbb {Z} }nor Zn, not to be confused with the commutative ring ofp-adic numbers), that isgeneratedby a single element.[1]That is, it is asetofinvertibleelements with a singleassociativebinary operation, and it con... | https://en.wikipedia.org/wiki/Cyclic_group |
Ingeometry,topology, and related branches ofmathematics, aclosed setis asetwhosecomplementis anopen set.[1][2]In atopological space, a closed set can be defined as a set which contains all itslimit points. In acomplete metric space, a closed set is a set which isclosedunder thelimitoperation. This should not be confuse... | https://en.wikipedia.org/wiki/Closed_set |
Anintegeris thenumberzero (0), a positivenatural number(1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...).[1]The negations oradditive inversesof the positive natural numbers are referred to asnegative integers.[2]Thesetof all integers is often denoted by theboldfaceZorblackboard boldZ{\displ... | https://en.wikipedia.org/wiki/Integer |
Incryptography, theElliptic Curve Digital Signature Algorithm(ECDSA) offers a variant of theDigital Signature Algorithm(DSA) which useselliptic-curve cryptography.
As with elliptic-curve cryptography in general, the bitsizeof theprivate keybelieved to be needed for ECDSA is about twice the size of thesecurity level, i... | https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm |
RSAmay refer to: | https://en.wikipedia.org/wiki/RSA#Signature_generation_and_verification |
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 |
Incryptography,RC4(Rivest Cipher 4, also known asARC4orARCFOUR, meaning Alleged RC4, see below) is astream cipher. While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, rendering it insecure.[3][4]It is especially vulnerable when the beginning of the outp... | https://en.wikipedia.org/wiki/RC4 |
Incryptography,SHA-1(Secure Hash Algorithm 1) is ahash functionwhich takes an input and produces a 160-bit(20-byte) hash value known as amessage digest– typically rendered as 40hexadecimaldigits. It was designed by the United StatesNational Security Agency, and is a U.S.Federal Information Processing Standard.[3]The al... | https://en.wikipedia.org/wiki/SHA-1 |
TheMD5 message-digest algorithmis a widely usedhash functionproducing a 128-bithash value. MD5 was designed byRonald Rivestin 1991 to replace an earlier hash functionMD4,[3]and was specified in 1992 as RFC 1321.
MD5 can be used as achecksumto verifydata integrityagainst unintentional corruption. Historically it was wi... | https://en.wikipedia.org/wiki/MD5 |
TheMD4 Message-Digest Algorithmis acryptographic hash functiondeveloped byRonald Rivestin 1990.[3]The digest length is 128 bits. The algorithm has influenced later designs, such as theMD5,SHA-1andRIPEMDalgorithms. The initialism "MD" stands for "Message Digest".
The security of MD4 has been severely compromised. The f... | https://en.wikipedia.org/wiki/MD4 |
Incryptanalysisandcomputer security, adictionary attackis an attack using a restricted subset of a keyspace to defeat acipheror authentication mechanism by trying to determine its decryption key orpassphrase, sometimes trying thousands or millions of likely possibilities[1]often obtained from lists of past security bre... | https://en.wikipedia.org/wiki/Dictionary_attack |
Password strengthis a measure of the effectiveness of apasswordagainst guessing orbrute-force attacks. In its usual form, it estimates how many trials an attacker who does not have direct access to the password would need, on average, to guess it correctly. The strength of a password is a function of length, complexity... | https://en.wikipedia.org/wiki/Password_strength#Dictionary_attack |
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/Unit_(ring_theory) |
Radio-frequency identification(RFID) useselectromagnetic fieldsto automaticallyidentifyandtracktags attached to objects. An RFID system consists of a tiny radiotranspondercalled a tag, aradio receiver, and atransmitter. When triggered by an electromagnetic interrogation pulse from a nearby RFID reader device, the tag t... | https://en.wikipedia.org/wiki/Radio-frequency_identification |
AESmost often refers to:
AESmay also refer to: | https://en.wikipedia.org/wiki/AES |
For AES-128, the key can be recovered with acomputational complexityof 2126.1using thebiclique attack. For biclique attacks on AES-192 and AES-256, the computational complexities of 2189.7and 2254.4respectively apply.Related-key attackscan break AES-256 and AES-192 with complexities 299.5and 2176in both time and data, ... | https://en.wikipedia.org/wiki/Rijndael |
Confidentialityinvolves a set of rules or a promise sometimes executed throughconfidentiality agreementsthat limits the access to or places restrictions on the distribution of certain types ofinformation.
By law, lawyers are often required to keep confidential anything on the representation of a client. The duty of co... | https://en.wikipedia.org/wiki/Confidentiality |
Incryptography, abrute-force attackconsists of an attacker submitting manypasswordsorpassphraseswith the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess thekeywhich is typic... | https://en.wikipedia.org/wiki/Brute-force_attack |
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 |
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 |
Incryptography,Galois/Counter Mode(GCM)[1]is amode of operationforsymmetric-keycryptographicblock cipherswhich is widely adopted for its performance. GCM throughput rates for state-of-the-art, high-speed communication channels can be achieved with inexpensive hardware resources.[2]
The GCM algorithm provides both data... | https://en.wikipedia.org/wiki/Galois/Counter_Mode |
Incryptography, anHMAC(sometimes expanded as eitherkeyed-hash message authentication codeorhash-based message authentication code) is a specific type ofmessage authentication code(MAC) involving acryptographic hash functionand a secret cryptographic key. As with any MAC, it may be used to simultaneously verify both the... | https://en.wikipedia.org/wiki/HMAC |
Incryptography, amessage authentication code(MAC), sometimes known as anauthentication tag, is a short piece of information used forauthenticatingandintegrity-checking a message. In other words, it is used to confirm that the message came from the stated sender (its authenticity) and has not been changed (its integrity... | https://en.wikipedia.org/wiki/Message_authentication_code |
Moore's lawis the observation that the number oftransistorsin anintegrated circuit(IC) doubles about every two years. Moore's law is anobservationandprojectionof a historical trend. Rather than alaw of physics, it is anempirical relationship. It is anexperience-curve law, a type of law quantifying efficiency gains from... | https://en.wikipedia.org/wiki/Moore%27s_law#Implications |
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#Overview |
Data communication, includingdata transmissionanddata reception, is the transfer ofdata,transmittedand received over apoint-to-pointorpoint-to-multipointcommunication channel. Examples of such channels arecopper wires,optical fibers,wirelesscommunication usingradio spectrum,storage mediaandcomputer buses. The data are ... | https://en.wikipedia.org/wiki/Data_transmission |
TheEnigma machineis acipherdevice developed and used in the early- to mid-20th century to protectcommercial, diplomatic, and military communication. It was employed extensively byNazi GermanyduringWorld War II, in all branches of theGerman military. The Enigma machine was considered so secure that it was used to enciph... | https://en.wikipedia.org/wiki/Enigma_machine |
Apseudorandom number generator(PRNG), also known as adeterministic random bit generator(DRBG),[1]is analgorithmfor generating a sequence of numbers whose properties approximate the properties of sequences ofrandom numbers. The PRNG-generated sequence is not trulyrandom, because it is completely determined by an initia... | https://en.wikipedia.org/wiki/Pseudorandom_number_generator |
TheElGamal signature schemeis adigital signaturescheme which is based on the difficulty of computingdiscrete logarithms. It was described byTaher Elgamalin 1985.[1]
The ElGamal signature algorithm is rarely used in practice. A variant developed at theNSAand known as theDigital Signature Algorithmis much more widely us... | https://en.wikipedia.org/wiki/ElGamal_signature_scheme |
Incryptography,collision resistanceis a property ofcryptographic hash functions: a hash functionHis collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputsaandbwherea≠bbutH(a) =H(b).[1]: 136Thepigeonhole principlemeans that any hash function with more inputs than outputs w... | https://en.wikipedia.org/wiki/Collision_resistance |
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/Second_preimage_attack |
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#Construction_of_finite_fields |
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%27s_principle |
For AES-128, the key can be recovered with acomputational complexityof 2126.1using thebiclique attack. For biclique attacks on AES-192 and AES-256, the computational complexities of 2189.7and 2254.4respectively apply.Related-key attackscan break AES-256 and AES-192 with complexities 299.5and 2176in both time and data, ... | https://en.wikipedia.org/wiki/Advanced_Encryption_Standard |
Themeet-in-the-middle attack(MITM), a known-plaintext attack,[1]is a genericspace–time tradeoffcryptographic attack against encryption schemes that rely on performing multiple encryption operations in sequence. The MITM attack is the primary reason whyDouble DESis not used and why aTriple DESkey (168-bit) can be brute-... | https://en.wikipedia.org/wiki/Meet-in-the-middle_attack |
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#Round_function |
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#Finite_fields |
Data integrityis the maintenance of, and the assurance of, data accuracy and consistency over its entirelife-cycle.[1]It is a critical aspect to the design, implementation, and usage of any system that stores, processes, or retrieves data. The term is broad in scope and may have widely different meanings depending on t... | https://en.wikipedia.org/wiki/Data_integrity |
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#The_fundamental_trilogy |
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