Structure of quaternion-type algebras and a post-quantum signature algorithm.

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Title:	Structure of quaternion-type algebras and a post-quantum signature algorithm.
Authors:	May Thu Duong¹ dtmay@ictu.edu.vn, Moldovyan, Alexander Andreevich² maa1305@yandex.ru, Moldovyan, Dmitriy Nikolaevich² mdn.spectr@mail.ru, Minh Hieu Nguyen³ hieuminhmta@gmail.com, Bac Thi Do⁴ dtbac@ictu.edu.vn
Source:	International Journal of Electrical & Computer Engineering (2088-8708). Jun2025, Vol. 15 Issue 3, p2965-2976. 12p.
Subjects:	Commutative algebra, Noncommutative algebras, Digital signatures, Abelian groups, Internet of things
Abstract:	Algebraic digital signature algorithms with a commutative hidden group, which are based on the computational difficulty of solving large systems of power equations, are promising candidates for post-quantum cryptoschemes, especially in securing applications like the internet of things (IoT) and other information technologies. Associative finite non-commutative algebras are used as an algebraic support of the said algorithms. Among such algebras, finite quaternion-type algebras have been identified as strong candidates for providing algebraic support. This paper investigates the decomposition of these algebras into commutative subrings and explores their multiplicative groups, which can serve as potential hidden groups. The analysis reveals the existence of three distinct types of subrings, with derived formulas for the number of subrings and the orders of their multiplicative groups. These findings align with previous studies on fourdimensional algebras defined by sparse basis vector multiplication tables. Using the finite quaternion-type algebras as algebraic support, a novel post-quantum signature algorithm characterized in using two mutually non-commutative hidden groups has been developed. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Algebraic digital signature algorithms with a commutative hidden group, which are based on the computational difficulty of solving large systems of power equations, are promising candidates for post-quantum cryptoschemes, especially in securing applications like the internet of things (IoT) and other information technologies. Associative finite non-commutative algebras are used as an algebraic support of the said algorithms. Among such algebras, finite quaternion-type algebras have been identified as strong candidates for providing algebraic support. This paper investigates the decomposition of these algebras into commutative subrings and explores their multiplicative groups, which can serve as potential hidden groups. The analysis reveals the existence of three distinct types of subrings, with derived formulas for the number of subrings and the orders of their multiplicative groups. These findings align with previous studies on fourdimensional algebras defined by sparse basis vector multiplication tables. Using the finite quaternion-type algebras as algebraic support, a novel post-quantum signature algorithm characterized in using two mutually non-commutative hidden groups has been developed. [ABSTRACT FROM AUTHOR]
ISSN:	20888708
DOI:	10.11591/ijece.v15i3.pp2965-2976