A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It

Alexandr Moldovyan, Dmitriy Moldovyan, Nikolay Moldovyan () and Alyona Kurysheva
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Alexandr Moldovyan: St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th Line V.O., 199178 St. Petersburg, Russia
Dmitriy Moldovyan: St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th Line V.O., 199178 St. Petersburg, Russia
Nikolay Moldovyan: St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th Line V.O., 199178 St. Petersburg, Russia
Alyona Kurysheva: St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th Line V.O., 199178 St. Petersburg, Russia

Mathematics, 2024, vol. 12, issue 13, 1-11

Abstract: To eliminate the limitations of signature randomization in known algebraic algorithms with a hidden group, the security of which is based on the computational complexity of solving large systems of power equations, a method for ensuring complete randomization is proposed. Based on this method, a new algorithm of the indicated type was developed, using a four-dimensional finite non-commutative associative algebra as an algebraic basis. We obtained estimates of the security of algorithms to direct attacks as well as from attacks based on known signatures, which confirm the effectiveness of the proposed signature randomization method. Due to the relatively small size and signature of the public and private keys, the developed algorithm is of interest as a potential practical post-quantum digital signature scheme.

Keywords: finite non-commutative algebra; associative algebra; computationally difficult problem; hidden commutative group; digital signature; post-quantum cryptography (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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