Evolving Quasigroups by Genetic Algorithms

Abstract. Quasigroups are a well-known combinatorial design equivalent to more familiar Latin squares. Because all possible elements of a quasigroup occur with equal probability, it makes it an interesting tool for the application in computer security and for production of pseudorandom sequences. Most implementations of quasigroups are based on look-up table of the quasigroup, on system of distinct representatives etc. Such representations are infeasible for large quasigroups. An analytic quasigroup is a recent concept that allows usage of certain quasigroups without the need of look-up table. The concept of isotopy enables consideration of many quasigroups and genetic algorithms allow efficient search for good ones. In this paper we describe analytic quasigroup and genetic algorithms for its optimization.

• Type: Journal
• Year: 2010
• Where: DATESO
• Authors: Václav Snásel, Jiri Dvorský, Eliska Ochodkova, Pavel Krömer, Jan Platos, Ajith Abraham
• Keywords: Database, DATESO 2010, Genetic Algorithms, Look-up Table, Quasigroup