A graph algorithm for verifying the existence of $n$-subquasigroups in finite $n$-quasigroups

A. Mazurin

Lomonosov Moscow State University

Abstract: A significant number of modern cryptographic algorithms is based on the concept of quasigroups. Algebraic properties of the quasigroups play an important role in assessing criptographic strength. One such property is the absence of proper subquasigroups. This paper presents a graph algorithm for checking the existence of proper $n$-subquasigroups of an arbitrary order in finite $n$-quasigroups. We analyze its time and space complexity and show the advantage of this algorithm over counterparts from other works in terms of the computational speed.

Keywords: $n$-quasigroup, $n$-subquasigroup, graph algorithm.

UDC: 512.548.7

Received: 31.05.2025

DOI: 10.4213/dm1878