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- Article name
- Unified methods for defining vector finite fields as primitives of multivariate cryptography algorithms
- Authors
- Kostina A. A., , to.ann@inbox.ru, St. Petersburg Federal Research Center of the RAS (SPC RAS), St. Petersburg, Russia
- Keywords
- computer security / post-quantum ciphers / digital signature algorithms / multivariate cryptography / non-linear mappings / bijective mappings / finite algebras / vector finite fields
- Year
- 2023 Issue 2 Pages 3 - 8
- Code EDN
- DPFQXW
- Code DOI
- 10.52190/2073-2600_2023_2_3
- Abstract
- Unified methods for developing multiplication tables of basis vectors are proposed, with the help of which finite commutative algebras over a ground finite field F, which are extensions of the field F, are defined. The latter allow one to specify nonlinear bijective mappings of vectors defined by a set of polynomials over the field F. The methods can be used in the framework of the recently proposed new concept of constructing multivariate cryptography algorithms, which allows one to significantly reduce the size of the public key at a given level of security compared to the well-known post-quantum digital signature and public encryption algorithms, based on the difficulty of inverting nonlinear mappings given by a system of polynomials over the field F.
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