Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL

In this paper, we present an efficient attack of the multivariate Quadratic Quasigroups (MQQ) cryptosystem. Our cryptanalysis breaks MQQ cryptosystems by solving systems of multivariate quadratic polynomial equations using a modified version of the MutantXL algorithm. We present experimental results comparing the behavior of our implementation of MutantXL to Magma’s implementation of F4 on MQQ systems (≥ 135 bit). Based on our results we show that the MutantXL implementation solves with much less memory than Magma’s implementation of F4 algorithm.