Cryptology ePrint Archive: Report 2015/726

Compositions of linear functions and applications to hashing

Vladimir Shpilrain and Bianca Sosnovski

Abstract: Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, $A$ and $B$, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with linear functions of one variable over F_p. The corresponding hash functions are very efficient. In particular, we show that hashing a bit string of length n with our method requires, in general, at most 2n multiplications in F_p, but with particular pairs of linear functions that we suggest, one does not need to perform any multiplications at all. We also give explicit lower bounds on the length of collisions for hash functions corresponding to these particular pairs of linear functions over F_p.

Category / Keywords: Cayley hash functions

Date: received 20 Jul 2015, last revised 2 Feb 2016

Contact author: shpilrain at yahoo com

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Note: More security evidence has been provided.

Version: 20160202:131715 (All versions of this report)

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