On the relationship between cryptographically important properties of
finite quasigroups

Zhigliaev Rodion Alekseevich

On the relationship between cryptographically important properties of finite quasigroups

Zhigliaev R. A.

Zhigliaev Rodion Alekseevich

graduate student, Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Chair of Mathematical Theory of Intellectual Systems

Published: 2024, vol. 28, issue 4, pp. 46–60

Download full text (In Russian)

Abstract

In this paper we establish a relationship between some properties of finite quasigroups. It is proved that in the case of quasigroups of prime order, all shapeless quasigroups are polynomially complete. Examples are given to show that the converse statement and the generalization to composite orders are not true.

Keywords: finite quasigroup, polynomial completeness, shapeless quasigroup.

BibTeX

@article{IS-Zhigliaev2024,
  author  = {Zhigliaev, Rodion Alekseevich},
  title   = {{On the relationship between cryptographically important
    properties of finite quasigroups}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2024},
  volume  = {28},
  number  = {4},
  pages   = {46--60},
}

AMSBIB

\Bibitem{IS-Zhigliaev2024}
\by R.\,A.~Zhigliaev
\paper On the relationship between cryptographically important
    properties of finite quasigroups
\jour Intelligent Systems. Theory and Applications
\yr 2024
\vol 28
\issue 4
\pages 46--60
\lang In Russian

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