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- Article name
- Alternative method for developing algorithms of multivariate cryptography
- Authors
- Moldovyan D. N., , mdn.spectr@mail.ru, St. Petersburg Electrotechnical Univeristy "LETI", St. Petersburg, Russia
- Keywords
- information security / public-key cryptosystems / public encryption / digital signature / post-quantum cryptography / multivariate cryptography / finite algebra / finite field
- Year
- 2022 Issue 3 Pages 13 - 21
- Code EDN
- VKCAOV
- Code DOI
- 10.52190/2073-2600_2022_3_13
- Abstract
- A new method of implementing nonlinear mappings for constructing new algorithms for public encryption and electronic digital signature algorithms related to multivariate cryptosystems, that is one of the fields of post-quantum cryptography, is proposed. The method is associated with defining a nonlinear mapping in the form of an operation of raising vectors with coordinates in the base field GF(q) to the second and third degrees as elements of a finite algebra, which is an extension of the field GF(q) of degree k ³ 2. The use of mappings of this type is focused on the formation of a public key in the form of a one-way nonlinear mapping with a trap door, which is a superposition of two nonlinear mappings and an intermediate linear mapping of a permutation type. The conditions for the formation of finite fields in the form of finite algebras and the issues of choosing the values of q and k are considered. The developed method is intended for the development of new algorithms of multivariate cryptography, which significantly reduce the size of the public key compared to known algorithms of this type.
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