On some properties of Boolean matrices from Latin squares

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
²⁵⁶
and 2
⁵¹²
. In this paper we are giving some of our results in investigation of the mathematical properties of the quasigroups used in Edon-R.