Security Analysis of Multivariate Polynomials for Hashing

Authors:
Luk Bettale;Jean-Charles Faugère;Ludovic Perret
Affiliations:
INRIA, Centre Paris-Rocquencourt, SALSA Project, UPMC, Univ Paris 06, LIP6, CNRS, UMR 7606, LIP6, Paris, France 75016;INRIA, Centre Paris-Rocquencourt, SALSA Project, UPMC, Univ Paris 06, LIP6, CNRS, UMR 7606, LIP6, Paris, France 75016;INRIA, Centre Paris-Rocquencourt, SALSA Project, UPMC, Univ Paris 06, LIP6, CNRS, UMR 7606, LIP6, Paris, France 75016
Venue:
Information Security and Cryptology
Year:
2009

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Abstract

In this paper, we investigate the security of a hash function based on the evaluation of multivariate polynomials [17]. The security of such hash function is related to the difficulty of solving (under-defined) systems of algebraic equations. To solve these systems, we have used a general hybrid approach [8] mixing exhaustive search and Gröbner bases solving. This shows that this approach is general and can be used in several contexts. For the sparse construction, we have refined this strategy. From a practical point of view, we have been able to break several challenges proposed by Ding and Yang [17] in real time.