Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University833210.18287/2541-7525-2020-26-2-23-49Research ArticleFRACTAL MAGMAS AND PUBLIC-KEY CRYPTOGRAPHYTsvetovV. P.<p>Candidate of Physical and Mathematical Sciences, assistant professor of the Department of Information Security</p>tsf-su@mail.ruhttps://orcid.org/0000-0001-6744-224XSamara National Research University2706202026223490102202101022021Copyright © 2020, Tsvetov V.P.2020<p>In this paper, we deal with magmas – the simplest algebras with a single binary operation. The main result of our research is algorithms for generating chain of finite magmas based on the self-similarity principle of its Cayley tables. In this way the cardinality of a magma’s domain is twice as large as the previous one for each magma in the chain, and its Cayley table has a block-like structure. As an example, we consider a cyclic semigroup of binary operations generated by a finite magma’s operation with a low-cardinality domain, and a modify the Diffie-Hellman-Merkle key exchange protocol for this case.</p>группоиды, полугруппы, таблицы Кэли, циклические полугруппы бинарных
операций, криптография на группоидах, протокол Диффи — Хелмана — Меркла.magmas, semigroups, Cayley tables, cyclic semigroup of binary operations, magma-based
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