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 MXL2 to the XL algorithm, the MutantXL algorithm and Magma's implementation of F{sub}4. 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 MXL2 are 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 MXL2 against Magma's F{sub}4 implementation.
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