This article is cited in 3 papers

A new method for developing signature algorithms on finite non-commutative algebras

Alexandr A. Moldovyan, Dmitriy N. Moldovyan

St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 14 Liniya V.O., 39, St. Petersburg, 199178, Russia

Abstract: A new method for developing signature schemes on finite non-commutative associative algebras is introduced. A signature algorithm is developed on a $4$-dimensional algebra defined over the ground field $GF(p)$. The public key element and one of the signature elements represent vectors calculated using exponentiation operations in a hidden commutative group. Decomposition of the algebra into commutative subalgebras is taken into account while designing the algorithm. The method extends the class of algebraic digital signature schemes and opens up the possibility of developing a number of practical post-quantum digital signature algorithms, the main merit of which is comparatively small size of the public key, secret key, and signature.

Keywords and phrases: finite associative algebras, non-commutative algebras, discrete logarithm problem, hidden logarithm problem, multivariate cryptography, public-key cryptoscheme, digital signature, post-quantum signature algorithm.

MSC: 68P25, 68Q12, 68R99, 94A60, 16Z05, 14G50

Received: 07.12.2021

Language: English

DOI: 10.56415/basm.y2022.i1.p56

Bibliographic databases:

•