MutantXL: Solving Multivariate Polynomial Equations for Cryptanalysis. MutantXL is an algorithm for solving systems of polynomial equations that was proposed at SCC 2008 and improved in PQC 2008. This article gives an overview over the MutantXL algorithm. It also presents experimental results comparing the behavior of the MutantXL algorithm to the F4 algorithm on HFE and randomly generated multi- variate systems. In both cases MutantXL is faster and uses less memory than the Magma’s implementation of F4.