Non-commutative finite associative algebras of 2-dimensional vectors
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Știința și tehnologia calculatoarelor. Calculatoare. Procesarea datelor (4095)
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MOLDOVYAN, Alexandr, MOLDOVYAN, Nikolay, ŞCERBACOV, Victor. Non-commutative finite associative algebras of 2-dimensional vectors. In: Computer Science Journal of Moldova, 2017, nr. 3(75), pp. 344-356. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 3(75) / 2017 / ISSN 1561-4042 /ISSNe 2587-4330

Non-commutative finite associative algebras of 2-dimensional vectors

CZU: 004.056.55+519.254

Pag. 344-356

Moldovyan Alexandr1, Moldovyan Nikolay2, Şcerbacov Victor3
 
1 Universitatea ITMO, Sanct-Petersburg,
2 Institute for Informatics and Automation of Russian Academy of Sciences Sankt Petersburg,
3 Institutul de Matematică şi Informatică al AŞM
 
Disponibil în IBN: 25 decembrie 2017


Rezumat

In this paper properties of the non-commutative finite associative algebra of two-dimensional vectors are presented. Interesting features of algebra are mutual associativity of all modifications of the defined parameterized multiplication operation and existing of a large set of single-side unit elements. In the ordinary case one unique two-side unit element is connected with each element of the algebra, except the elements that are square roots from zero element. There are also presented four different variants of defining commutative associative algebras of 2-dimension vectors. For the case of commutativity the algebra has common unit element for all its elements.

Cuvinte-cheie
finite algebra, Galois field, associative multiplication, parameterized multiplication, cryptoscheme,

Ring, vector