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Title:
On the Randomness and Regularity of Reduced EDON-\mathcal{R} Compression Function
Authors: Rune Steinsmo Ødegård, 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.
ePrint: https://eprint.iacr.org/2009/234
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