Informatics and Applications
2020, Volume 14, Issue 1, pp 94-100
METHOD FOR DEFINING FINITE NONCOMMUTATIVE
ASSOCIATIVE ALGEBRAS OF ARBITRARY EVEN DIMENSION
FOR DEVELOPMENT OF THE POSTQUANTUM CRYPTOSCHEMES
- A. A. Kostina
- A. Yu. Mirin
- D. N. Moldovyan
- R. Sh. Fahrutdinov
Abstract
The paper introduces a new unified method for defining finite noncommutative associative algebras of
arbitrary even dimension m and describes the investigated properties of the algebras for the cases m = 4 and 6,
when the algebras are defined over the ground field GF(p) with a large size of the prime number p. Formulas
describing the set of p2 (p4) global left-sided units contained in the 4-dimensional (6-dimensional) algebra are
derived. Only local invertibility takes place in the algebras investigated. Formulas for computing the unique local
two-sided unit related to the fixed locally invertible vector are derived for each of the algebras. A new form of the
hidden discrete logarithm problem is proposed as postquantum cryptographic primitive. The latter was used to
develop the postquantum digital signature scheme.
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[+] About this article
Title
METHOD FOR DEFINING FINITE NONCOMMUTATIVE ASSOCIATIVE ALGEBRAS OF ARBITRARY EVEN DIMENSION FOR DEVELOPMENT OF THE POSTQUANTUM CRYPTOSCHEMES
Journal
Informatics and Applications
2020, Volume 14, Issue 1, pp 94-100
Cover Date
2020-03-30
DOI
10.14357/19922264200113
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
finite noncommutative algebra; associative algebra; computationally difficult problem; discrete logarithm; digital signature; postquantum cryptography
Authors
A. A. Kostina  , A. Yu. Mirin , D. N. Moldovyan , and R. Sh. Fahrutdinov
Author Affiliations
St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, 39, 14th Line V.O.,
St. Petersburg 199178, Russian Federation
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