Non-commutative finite associative algebras of 2-dimension vectors

Moldovyan Alexandr; Moldovyan Nikolay; Shcherbacov Victor

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MOLDOVYAN, Alexandr, MOLDOVYAN, Nikolay, SHCHERBACOV, Victor. Non-commutative finite associative algebras of 2-dimension vectors. In: Conference on Mathematical Foundations of Informatics, Ed. 2017, 9-11 noiembrie 2017, Chișinău. Chișinău, Republica Moldova: "VALINEX" SRL, 2017, pp. 117-125. ISBN 978‐9975‐4237‐6‐2.

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Conference on Mathematical Foundations of Informatics 2017

Conferința "Conference on Mathematical Foundations of Informatics"
2017, Chișinău, Moldova, 9-11 noiembrie 2017

Non-commutative finite associative algebras of 2-dimension vectors

Pag. 117-125

Moldovyan Alexandr¹, Moldovyan Nikolay², Shcherbacov Victor³

¹ ITMO University,
² Institute for Informatics and Automation of Russian Academy of Sciences Sankt Petersburg,
³ Institute of Mathematics and Computer Science ASM

Disponibil în IBN: 19 martie 2018

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Rezumat

In this paper properties of the non-commutative finite associative algebra of two-dimension vectors are presented. An interesting features of the algebra is mutual associativity of all modifications of the defined parameterized multiplication operation and existing of a large set of the 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.

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

Ring, vector

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