Searching for quasigroups for hash functions with genetic algorithms

In this study we discuss a method for evolution of quasigroups with desired properties based on genetic algorithms. Quasigroups are a well-known combinatorial design equivalent to the more familiar Latin squares. One of their most important properties is that all possible elements of certain quasigroup occur with equal probability. The quasigroups are evolved within a framework of a simple hash function. Prior implementations of quasigroups were based on look-up table of the quasigroup, which is infeasible for large quasigroups. In contrast, analytic quasigroup can be implemented easily. It allows the evaluation of hash function without storing large amount of data (look-up table) and the concept of homotopy enables consideration of many quasigropus.