Some Homomorphic Cryptosystems Based on Nonassociative Structures

Gribov, Alexey

doi:10.1007/s10958-017-3367-7

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…According to [10] quasi-group (Ω, * ) is a CP-groupoid. Some medial quasi-groups have already been used in [8] to create encryption system for homomorphic quasi-group operations * .…”

Section: Basic Definitionsmentioning

confidence: 99%

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Application of non-associative structures for construction of homomorphic cryptosystems

Katyshev

Zyazin

Baryshnikov

2020

Матем. вопр. криптогр.

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Гомоморфное шифрование позволяет выполнять некоторые математические преобразования с шифрованным текстом, в результате которых получается шифрованный текст, соответствующий результату выполнения заданного преобразования открытого текста. Известны так называемые полностью гомоморфные и частично гомоморфные шифрсистемы, различающиеся количеством допустимых для выполнения преобразований. Для построения подобных шифрсистем необходимо иметь гомоморфизм относительно хотя бы одной из выполняемых операций. В работе с использованием неассоциативных операций и системы Эль-Гамаля построен пример шифрсистемы, гомоморфной относительно двух выполняемых операций: групповой и квазигрупповой.

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“…According to [10] quasi-group (Ω, * ) is a CP-groupoid. Some medial quasi-groups have already been used in [8] to create encryption system for homomorphic quasi-group operations * .…”

Section: Basic Definitionsmentioning

confidence: 99%

“…It was already proposed in [8] to use some classes of groupoids for encryption systems which are homomorphic with respect to a unique operation. In this paper we consider the extension of the El-Gamal [9] cryptosystem to quasi-groups linear over the Abelian group.…”

Section: Introductionmentioning

confidence: 99%

Application of non-associative structures for construction of homomorphic cryptosystems

Katyshev

Zyazin

Baryshnikov

2020

Матем. вопр. криптогр.

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Nonassociative Algebras, Rings and Modules over Them

Lüdkovsky

2023

Mathematics

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The review is devoted to nonassociative algebras, rings and modules over them. The main actual and recent trends in this area are described. Works are reviewed on radicals in nonassociative rings, nonassociative algebras related with skew polynomials, commutative nonassociative algebras and their modules, nonassociative cyclic algebras, rings obtained as nonassociative cyclic extensions, nonassociative Ore extensions of hom-associative algebras and modules over them, and von Neumann finiteness for nonassociative algebras. Furthermore, there are outlined nonassociative algebras and rings and modules over them related to harmonic analysis on nonlocally compact groups, nonassociative algebras with conjugation, representations and closures of nonassociative algebras, and nonassociative algebras and modules over them with metagroup relations. Moreover, classes of Akivis, Sabinin, Malcev, Bol, generalized Cayley–Dickson, and Zinbiel-type algebras are provided. Sources also are reviewed on near to associative nonassociative algebras and modules over them. Then, there are the considered applications of nonassociative algebras and modules over them in cryptography and coding, and applications of modules over nonassociative algebras in geometry and physics. Their interactions are discussed with more classical nonassociative algebras, such as of the Lie, Jordan, Hurwitz and alternative types.

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Some Homomorphic Cryptosystems Based on Nonassociative Structures

Cited by 2 publications

References 7 publications

Application of non-associative structures for construction of homomorphic cryptosystems

Application of non-associative structures for construction of homomorphic cryptosystems

Nonassociative Algebras, Rings and Modules over Them

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