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Thu Duong, May
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Electrical & Electronics Engineering

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Journal : Bulletin of Electrical Engineering and Informatics

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Structure of 6-dimensional finite non-commutative algebras with many single-sided units Thu Duong, May; Andreevich Moldovyan, Alexander; Andreevich Moldovyan, Nikolay; Hieu Nguyen, Minh; Thi Do, Bac
Bulletin of Electrical Engineering and Informatics Vol 14, No 3: June 2025
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/eei.v14i3.9064

Abstract

Finite Associative Noncommutative Algebras (FANAs) have gained considerable attention as a key foundational element for post-quantum (PQ) public-key (PK) cryptosystems, particularly those with a hidden group. These systems exploit the complexity of the hidden discrete logarithm problem (HDLP) and the challenge of solving large system of power equations. The structure of 6-dimensional FANAs over the finite field GF(p), which can include global single-sided units in different configurations (p2, p3, and p4), plays an essential role in assessing the security of these cryptosystems. A novel PQ signature algorithm has been proposed based on FANAs with p2 global single-sided units, while the others have been deemed less suitable for supporting the proposed algorithm. The decomposition of these algebras into isomorphic subalgebras, each with a global two-sided unit, significantly contributes to understanding the design of PQ cryptosystems that use FANAs with a large number of global singlesided units as their algebraic framework. 
Co-Authors Andreevich Moldovyan, Alexander Andreevich Moldovyan, Nikolay Hieu Nguyen, Minh Thi Do, Bac