Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
A new type of digital signature algorithms with a hidden group
Authors: Dmitriy N. Moldovyan
Keywords: finite associative algebra, non-commutative algebra, commutative finite group, discrete logarithm problem, hidden logarithm problem, public key, digital signature, multivariate cryptography, post-quantum cryptosystem.
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Keywords: finite associative algebra, non-commutative algebra, commutative finite group, discrete logarithm problem, hidden logarithm problem, public key, digital signature, multivariate cryptography, post-quantum cryptosystem.
Abstract
The known designs of digital signature schemes with a hidden group, which use finite non-commutative algebras as algebraic support, are based on the computational complexity of the so-called hidden discrete logarithm problem. A similar design, used to develop a signature algorithm based on the difficulty of solving a system of many quadratic equations in many variables, is introduced. The significant advantage of the proposed method compared with multivariate-cryptography signature algorithms is that the said system of equations, which occurs as the result of performing the exponentiation operations in the hidden group, has a random look and is specified in a finite field of a higher order. This provides the ability to develop post-quantum signature schemes with significantly smaller public-key sizes at a given level of security.ORCID: https://orcid.org/0000-0001-5039-7198
Department of Information Systems,
Saint Petersburg Electrotechnical University ”LETI”,
Prof. Popov, 5, St. Petersburg, 197022,
Russia
E-mail:
Department of Information Systems,
Saint Petersburg Electrotechnical University ”LETI”,
Prof. Popov, 5, St. Petersburg, 197022,
Russia
E-mail:
DOI
https://doi.org/10.56415/csjm.v31.06Fulltext
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