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SM ISO690:2012 MOLDOVYAN, Dmitriy, MOLDOVYAN, Nikolay, SHCHERBACOV, Victor. Non-commutative nite associative algebras of 3-dimensional vectors. In: Quasigroups and Related Systems, 2018, vol. 26, nr. 1(39), pp. 109-120. ISSN 1561-2848. |
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Quasigroups and Related Systems | |
Volumul 26, Numărul 1(39) / 2018 / ISSN 1561-2848 | |
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CZU: 512.548+519.254 | |
MSC 2010: 94A60,16Z05,14G50,11T71,16S50 | |
Pag. 109-120 | |
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Rezumat | |
Properties of the non-commutative finite associative algebras of 3-dimensional vectors are presented. An interesting feature of these algebras is mutual associativity of all modifications of the defined parameterized multiplication operation and existence of a large set of single-side unit elements. In the ordinary case one unique two-side unit element is connected with every element of the algebra, except the elements that are square roots of zero element. It is shown that the used method suites for defining finite non-commutative associative algebras of arbitrary dimension m > 2: The considered finite associative algebras are interesting for cryptographic applications. |
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Cuvinte-cheie niteasso ciativealgebra, dicultproblem, Homomorphism, non-commutativegroup, non-commutativering, public-keycryptoscheme.Therep ortedstudywasfundedbyRussianFoundationforBasicResearch(pro ject#18-07-00932) |
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