Paper 2009/234

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

Rune Steinsmo Ødegård 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 $\mu (R_{16})=0.99985$.

Note: A similar paper will be published in proceedings of the SAM'09 - The 2009 International Conference on Security and Management.