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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2020, Volume 26, Issue 1, Pages 23–51 (Mi vsgu622)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Semigroups of binary operations and magma-based cryptography

V. P. Tsvetov

Samara National Research University, Samara, Russian Federation

Abstract: In this article, algebras of binary operations as a special case of finitary homogeneous relations algebras are investigated. The tools of our study are based on unary and associative binary operations acting on the set of ternary relations. These operations are generated by the converse operation and the left-composition of binary relations. Using these tools, we are going to define special kinds of ternary relations that correspond to functions, injections, right- and left-total binary relations. Then we obtain criteria for these properties in terms of ordered semigroups. Note, that there is an embedding of the semigroup of quasigroups operations in the semigroup of magmas operation and further in the semigroup of ternary relations. This is similar to embedding the semigroup of bijections in the semigroup of functions and then in the semigroup of binary relations. Taking a binary operation as the generator of a cyclic semigroup, we can apply an exponential squaring method for the fast computation of its positive integer powers. Given that this is the main method of public key cryptography, we are adapting the Diffie–Hellman–Merkle key exchange algorithm for magmas as a result.

Keywords: algebra of finitary relations, algebra of indicator function, magmas, quasigroups, semigroups, cyclic semigroup of binary operations, public key cryptography, Diffie–Hellman–Merkle key exchange.

DOI: https://doi.org/10.18287/2541-7525-2020-26-1-23-51

Full text: PDF file (326 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

UDC: 512.531; 519.7
Received: 15.01.2020
Revised: 17.02.2020
Accepted:28.02.2020

Citation: V. P. Tsvetov, “Semigroups of binary operations and magma-based cryptography”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 26:1 (2020), 23–51

Citation in format AMSBIB
\Bibitem{Tsv20}
\by V.~P.~Tsvetov
\paper Semigroups of binary operations and magma-based cryptography
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2020
\vol 26
\issue 1
\pages 23--51
\mathnet{http://mi.mathnet.ru/vsgu622}
\crossref{https://doi.org/10.18287/2541-7525-2020-26-1-23-51}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Tsvetov, “Fraktalnye gruppoidy i kriptografiya s otkrytym klyuchom”, Vestn. SamU. Estestvennonauchn. ser., 26:2 (2020), 23–49  mathnet  crossref
  • Вестник Самарского государственного университета. Естественнонаучная серия
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