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- Article name
- Parameterizable methods for specifying vector finite fields for cryptoalgorithms on nonlinear mappings
- Authors
- Moldovyan D. N., , mdn.spectr@mail.ru, St. Petersburg Electrotechnical Univeristy "LETI", St. Petersburg, Russia
Kostina A. A., , anya@hotbox.ru, St. Petersburg Federal Research Center of the RAS (SPC RAS), St. Petersburg, Russia
Morozova E. V., , evmgumrf@mail.ru, Admiral Makarov State University of Maritime and Inland Shipping, St. Petersburg, Russia
- Keywords
- computer security / post-quantum cryptography / nonlinear mappings / finite algebras / associative algebras
- Year
- 2024 Issue 1 Pages 3 - 10
- Code EDN
- QAYIUE
- Code DOI
- 10.52190/2073-2600_2024_1_3
- Abstract
- Unified methods for generating basis vector multiplication tables (BVMTs) for specifying finite commutative algebras, which are vector finite fields, are considered. The latter are of interest for specifying nonlinear, hard-to-reverse mappings with a secret trapdoor within the framework of the concept of implementing these mappings as exponentiation operations in secret vector finite fields. The use of a specific modification of a field as an element of a secret key presupposes the possibility of specifying it according to a large number of independent structural constants in the BVMT. Generation of BVMTs with a large number of structure constants for specifying finite associative algebras requires the use of formalized methods. As the latter, methods for parameterizing unified methods for specifying associative algebras of various dimensions are considered. Mathematical formulas that implement such methods are presented. With the help of the latter, TUBVs were generated, which are of potential interest for the development of cryptographic algorithms on nonlinear hard-to-reverse mappings.
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