MXL2: Solving Polynomial Equations over GF(2) Using an Improved Mutant Strategy

Authors:
Mohamed Saied Mohamed;Wael Said Mohamed;Jintai Ding;Johannes Buchmann
Affiliations:
TU Darmstadt, FB Informatik, Darmstadt, Germany 64289;TU Darmstadt, FB Informatik, Darmstadt, Germany 64289;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA OH 45220;TU Darmstadt, FB Informatik, Darmstadt, Germany 64289
Venue:
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Year:
2008

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Abstract

MutantXL is an algorithm for solving systems of polynomial equations that was proposed at SCC 2008. This paper proposes two substantial improvements to this algorithm over GF(2) that result in significantly reduced memory usage. We present experimental results comparing MXL2to the XL algorithm, the MutantXL algorithm and Magma's implementation of F4. For this comparison we have chosen small, randomly generated instances of the MQ problem and quadratic systems derived from HFE instances. In both cases, the largest matrices produced by MXL2are substantially smaller than the ones produced by MutantXL and XL. Moreover, for a significant number of cases we even see a reduction of the size of the largest matrix when we compare MXL2against Magma's F4implementation.