On the Randomness and Regularity of Reduced Edon-R Compression Function

EDON-R is one of the candidate hash functions for the ongoing NIST competition for the next cryptographic hash standard called SHA-3. Its construction is based on algebraic properties of non-commutative and non-associative quasigroups of orders 2 and 2. In this paper we are giving some of our results in investigation of the randomness and regularity of reduced EDON-R compression functions over quasigroups of order 2 and 2. Our experiments show that the Bellare-Khono balance of EDON-R compression function is high. Actually, for the reduced EDON-R with quasigroups of order 2 we show that the compression function is perfectly balanced, while with quasigroups of order 2 the Belare-Khono balance is μ(R16) = 0.99985.