Non-commutative 6-dimensional associative algebras of two different types
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2022-04-28 05:57
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MOLDOVYAN, Alexandr, MOLDOVYAN, Nikolay, SHCHERBACOV, Victor. Non-commutative 6-dimensional associative algebras of two different types. In: Conference on Mathematical Foundations of Informatics, Ed. 2018, 2-6 iulie 2018, Chișinău. Chișinău: "VALINEX" SRL, 2018, pp. 154-163. ISBN 978‐9975‐4237‐7‐9.
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Conference on Mathematical Foundations of Informatics 2018
Conferința "Conference on Mathematical Foundations of Informatics"
2018, Chișinău, Moldova, 2-6 iulie 2018

Non-commutative 6-dimensional associative algebras of two different types

MSC 2010: 16U60, 11G20, 11T71

Pag. 154-163

Moldovyan Alexandr1, Moldovyan Nikolay1, Shcherbacov Victor2
 
1 St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences,
2 Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 3 iulie 2018


Rezumat

This paper introduces two different types of the non-commutative finite associative algebra of 6-dimensional vectors, which have been proposed as potential carriers of the hidden logarithm problem. The algebra of the first type contains global unit, whereas the algebra of the second type contains only local units. It is also introduced two new forms of the hidden logarithm problem. One of the proposed forms is characterized in using non-invertible elements and assumes using the first-type algebra. The second proposed form is characterized in using locally invertible elements and assumes using the second-type algebra.

Cuvinte-cheie
finite algebra, asso- ciative multiplication,

non-commutative algebra, hidden logarithm problem