Part 2. Special Issues in Intellectual Systems Theory

On the relationship between cryptographically important properties of finite quasigroups

R. A. Zhigliaev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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