Hash Functions Based on Large Quasigroups

In this article we discuss a simple hash function based upon properties of a well-known combinatorial design called quasigroups. The quasigroups are equivalent to the more familiar Latin squares and one of their most important properties is that all possible element of certain quasigroup occurs with equal probability. Actual implementations are based on look-up table implementation of the quasigroup, which is unusable for large quasigroups. In contrast, presneted hash function can be easily implemented. It allows us to compute hash function without storing large amount of data (look-up table). The hash function computation is illustrated by experiments summarized in the last section of this paper.