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- Article name
- Methods for setting non-commutative algebras as carriers of post-quantum cryptoschemes
- Authors
- Abrosimov I. K., , ivnabr@yandex.ru, St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), Institute for Informatics and Automation of the Russian Academy of Sciences, St.-Petersburg, Russia
Fahrutdinov R. Sh., , fahr@cobra.ru, St. Petersburg Federal Research Center of the RAS, St. Petersburg, Russia
Mirin A. Yu., , mirin@cobra.ru, St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), Institute for Informatics and Automation of the Russian Academy of Sciences, St. Petersburg, Russia
- Keywords
- post-quantum cryptography / finite non-commutative algebras / finite associative algebras / local units
- Year
- 2020 Issue 4 Pages 11 - 17
- Code EDN
- Code DOI
- Abstract
- In framework of the development of generalized methods for setting finite non-commutative associative algebras of different dimensions for use as algebraic carriers of post-quantum public-key cryptosystems based on the hidden discrete logarithm problem, a new unified method for setting algebras of this type is proposed and the application of the previously known embedding method for constructing four-dimensional and eight-dimensional algebras is considered. It is shown that the embedding method makes it possible to obtain eight-dimensional algebras with the vector multiplication operation, which has a lower computational complexity, while the new method has advantages when setting four-dimensional algebras.
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