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 (lookup table) and the concept of homotopy enables consideration of many quasigropus. 978-1-4244-5612-3/09/$26.00 c 2009 IEEE

With the growing importance of data security a growing effort to find new approaches to the cryptographic algorithms designs appears. One of the trends is to research the use of other algebraic structures than the traditional, such as a quasigroup. Quasigroups are equivalent to the more familiar Latin squares. There are many characteristics that must quasigroups have from the cryptography point of view. They have to be non-commutative, non-associative, non-idempotent and so on. If one want to work with quasigroups of a large order, effective methods of testing their properties are necessary. In this paper we present several experiments on various types of guasigroups and their results.

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