Algebraic properties of subquasigroups and construction of finite quasigroups. (English. Russian original) Zbl 1522.20234
Algebra Logic 61, No. 4, 251-270 (2022); translation from Algebra Logika 61, No. 4, 375-400 (2022).
Authors’ abstract: Many important properties are identified and criteria are developed for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of proper subquasigroups in a given finite quasigroup, or finds all its proper subquasigroups. This has an important application in checking the cryptographic suitability of a quasigroup. Using arithmetic of finite fields, we introduce a binary operation to construct quasigroups of order pr. Criteria are developed under which the quasigroups mentioned have desirable cryptographic properties, such as polynomial completeness and absence of proper subquasigroups. Effective methods are given for constructing cryptographically suitable quasigroups. The efficiency of the methods is illustrated by some academic examples and implementation of all proposed algorithms in the computer algebra system Singular.
Reviewer: Wiesław A. Dudek (Wrocław)
Software:
SINGULARReferences:
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