## Cryptology ePrint Archive: Report 2009/234

On the Randomness and Regularity of Reduced EDON-$\mathcal{R}$ Compression Function

Rune Steinsmo \Oe degå rd and Danilo Gligoroski

Abstract: EDON-$\mathcal{R}$ 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 randomness and regularity of reduced EDON-$\mathcal{R}$ compression functions over quasigroups of order $2^{8}$ and $2^{16}$. Our experiments show that the Bellare-Khono balance of EDON-$\mathcal{R}$ compression function is high. Actually, for the reduced EDON-$\mathcal{R}$ with quasigroups of order $2^8$ we show that the compression function is perfectly balanced, while with quasigroups of order $2^{16}$ the Belare-Khono balance is $\mu(R_{16}) = 0.99985$.

Category / Keywords: foundations / hash function, randomness, regularity, balance

Publication Info: SAM'09 - The 2009 International Conference on Security and Management