Testing the properties of large quasigroups

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.