Large quasigroups in cryptography and their properties testing

One of the current trends in cryptography is to search for new approaches to the cryptographic algorithms design. One such possibility is to use the other algebraic structures, such as a quasigroup, rather than the traditional. Quasigroups are equivalent to more familiar Latin squares. One of quasigroups´ important properties is that all possible elements of certain quasigroup occur with equal probability. Testing properties of quasigroups of a large order isn´t trivial, effective methods are necessary. There are described statistical experiments on various types of data, on various types of guasi-groups in this paper; experiments were done within a framework of a simple quasigorup hash function. The distribution of hash value´s changes, for given quasigroup and for given testing data, with respect to bit change in them and with respect to the positions of changed bits were measured.