About: Non-commutative cryptography

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Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups, groups and rings which are non-commutative. One of the earliest applications of a non-commutative algebraic structure for cryptographic purposes was the use of braid groups to develop cryptographic protocols. Later several other non-commutative structures like Thompson groups, polycyclic groups, Grigorchuk groups, and matrix groups have been identified as potential candidates for cryptographic applications. In contrast to non-commutative cryptography, the currently widely used public-key cryptosystems like RSA cryptosystem, Diffie–Hellman key exchange and elliptic curve cryptography are based on number theory and hence depend on c

Attributes	Values
rdf:type	place
rdfs:label	Non-commutative cryptography (en) Некоммутативная криптография (ru)
rdfs:comment	Некоммутативная криптография — область криптологии, в которой шифровальные примитивы, методы и системы основаны на некоммутативных алгебраических структурах. В основе некоммутативной криптографии лежат операции над некоммутативной группой 𝐺 из (𝐺, ∗), состоящей из групп, полугрупп или колец, в которой существуют хотя бы два элемента группы 𝑎 и 𝑏 из 𝐺 для которых верно неравенство 𝑎∗𝑏 ≠ 𝑏∗𝑎. Использующие данную структуру протоколы были развиты для решения различных проблем шифрования.Примером могут послужить задачи аутентификации, шифрования-дешифрования и установления сеанса обмена ключами. (ru) Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups, groups and rings which are non-commutative. One of the earliest applications of a non-commutative algebraic structure for cryptographic purposes was the use of braid groups to develop cryptographic protocols. Later several other non-commutative structures like Thompson groups, polycyclic groups, Grigorchuk groups, and matrix groups have been identified as potential candidates for cryptographic applications. In contrast to non-commutative cryptography, the currently widely used public-key cryptosystems like RSA cryptosystem, Diffie–Hellman key exchange and elliptic curve cryptography are based on number theory and hence depend on c (en)
dcterms:subject	Public-key cryptography Cryptography
Wikipage page ID	42983810 (xsd:integer)
Wikipage revision ID	1116709901 (xsd:integer)
Link from a Wikipage to another Wikipage	Rooted tree Encryption Binary tree Braid group Decryption Algebraic structure Alice and Bob Public-key cryptography Elliptic curve cryptography Cryptography Non-abelian group One-way function Conjugacy problem Cryptographic primitive Key exchange Polycyclic group Subgroup Authentication Cryptology Hash function Semigroup Finite field Non-commutative Diffie–Hellman key exchange Ring (mathematics) Group-based cryptography Group (mathematics) Invertible matrix Matrix group Thompson groups Word (group theory) Word problem for groups Grigorchuk group RSA (cryptosystem) Finite group Public-key cryptosystem XOR Secret key
sameAs	Non-commutative cryptography Non-commutative cryptography Non-commutative cryptography Non-commutative cryptography Non-commutative cryptography
dbp:wikiPageUsesTemplate	dbt:Cite_arXiv dbt:Cite_book dbt:Main dbt:Refbegin dbt:Refend dbt:Reflist dbt:GBurl dbt:Cryptography_navbox
has abstract	Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups, groups and rings which are non-commutative. One of the earliest applications of a non-commutative algebraic structure for cryptographic purposes was the use of braid groups to develop cryptographic protocols. Later several other non-commutative structures like Thompson groups, polycyclic groups, Grigorchuk groups, and matrix groups have been identified as potential candidates for cryptographic applications. In contrast to non-commutative cryptography, the currently widely used public-key cryptosystems like RSA cryptosystem, Diffie–Hellman key exchange and elliptic curve cryptography are based on number theory and hence depend on commutative algebraic structures. Non-commutative cryptographic protocols have been developed for solving various cryptographic problems like key exchange, encryption-decryption, and authentication. These protocols are very similar to the corresponding protocols in the commutative case. (en) Некоммутативная криптография — область криптологии, в которой шифровальные примитивы, методы и системы основаны на некоммутативных алгебраических структурах. В основе некоммутативной криптографии лежат операции над некоммутативной группой 𝐺 из (𝐺, ∗), состоящей из групп, полугрупп или колец, в которой существуют хотя бы два элемента группы 𝑎 и 𝑏 из 𝐺 для которых верно неравенство 𝑎∗𝑏 ≠ 𝑏∗𝑎. Использующие данную структуру протоколы были развиты для решения различных проблем шифрования.Примером могут послужить задачи аутентификации, шифрования-дешифрования и установления сеанса обмена ключами. (ru)
gold:hypernym	Area
prov:wasDerivedFrom	wikipedia-en:Non-commutative_cryptography?oldid=1116709901&ns=0
page length (characters) of wiki page	12619 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Non-commutative_cryptography
is Link from a Wikipage to another Wikipage of	Non-abelian cryptography Nonabelian cryptography Noncommutative cryptography Braid group Algebraic Eraser Boaz Tsaban Cayley–Purser algorithm Group-based cryptography Thompson groups Artin–Tits group Grigorchuk group
is Wikipage redirect of	Non-abelian cryptography Nonabelian cryptography Noncommutative cryptography
is foaf:primaryTopic of	wikipedia-en:Non-commutative_cryptography

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