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JOURNALS // Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography] // Archive

Mat. Vopr. Kriptogr., 2020 Volume 11, Issue 3, Pages 31–39 (Mi mvk330)

Application of non-associative structures for construction of homomorphic cryptosystems

S. Yu. Katysheva, A. V. Zyazina, A. V. Baryshnikovb

a Russian Technological University (MIREA), Moscow
b Certification Research Center LLC, Moscow

Abstract: Homomorphic encoding allows to perform certain mathematical operations with the encoded text and to get the encoded outcome that corresponds to the result of operations processed with a plaintext. There exist both fully homomorphic and partially homomorphic options (with respect to one or more operations). For practical use of such an encoding it is necessary to have a homomorphism with respect for at least one operation. Using non-associative operations, we construct in this paper an example of a cryptosystem based on the El-Gamal system that is homomorphic with respect to two on-going operations: a group and a quasigroup ones.

Key words: public-key cryptosystem, homomorphic encryption, non-associative algebraic structures.

UDC: 512.548.2

Received 06.II.2019

Language: English

DOI: 10.4213/mvk330



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