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- Article name
- Algebraic algorithms with a hidden group over finite fields with binary characteristic
- Authors
- Moldovyan N. A., , nmold@mail.ru, St. Petersburg Federal Research Center of the RAS (SPC RAS), St. Petersburg, Russia
Kostina A. A., , anya@hotbox.ru, St. Petersburg Federal Research Center of the RAS (SPC RAS), St. Petersburg, Russia
Kurysheva A. A., , kurysheva.al@yandex.ru, St. Petersburg Federal Research Centerof of the RAS (SPC RAS), St. Petersburg, Russia
- Keywords
- information security / digital signature / post-quantum cryptography / finite associative algebra / non-commutative algebra / hidden group
- Year
- 2022 Issue 2 Pages 13 - 20
- Code EDN
- JEFCMK
- Code DOI
- 10.52190/2073-2600_2022_2_13
- Abstract
- The features of the implementation of digital signature algorithms on finite noncommutative associative algebras set over the finite fields of binary characteristics are considered. Interest in the implementation of such type is associated with the possibility of improving the productivity of algorithms with a hidden group, as well as with the fact that the security of the algorithms is based on the computational difficulty of solving systems of quadratic equations. The factorization of the order of the hidden group is non-critical for the security of the signature algorithm, so it is possible to use the GF(2z) fields not only with the values of the degree that equals to a Mersenne exponent, but also with other z values. As an algebraic carrier of algorithms, the algebras specified on the sparse basis vector multiplication tables are considered. The main types of commutative groups contained in such algebras are established, which represent interest for using them as a hidden group.
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