Algebraic Attack on the MQQ Public Key Cryptosystem

Authors:
Mohamed Saied Mohamed;Jintai Ding;Johannes Buchmann;Fabian Werner
Affiliations:
TU Darmstadt, FB Informatik, Darmstadt, Germany 64289;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA 45220;TU Darmstadt, FB Informatik, Darmstadt, Germany 64289;TU Darmstadt, FB Informatik, Darmstadt, Germany 64289
Venue:
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Year:
2009

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Abstract

In this paper, we present an efficient attack on the multivariate Quadratic Quasigroups (MQQ) public key cryptosystem. Our cryptanalysis breaks the MQQ cryptosystem by solving a system of multivariate quadratic polynomial equations using both the MutantXL algorithm and the F4 algorithm. We present the experimental results that show that MQQ systems is broken up to size n equal to 300. Based on these results we show also that MutantXL solves MQQ systems with much less memory than the F4 algorithm implemented in Magma.