Mutant Gröbner Basis Algorithm

This paper explores how to use the concept of mutants in the computation of a Gröbner basis for polynomial equations. We compare our approach to the algorithm F4 of Faugère, and we perform experiments on polynomials system coming from multivariate public key cryptosystems in comparison with the experimental results from Magma implementation of F4. The experimental results demonstrate that the mutant strategy could indeed work better in the case of polynomial systems with underlying structures that could be fully exploited by the mutant strategy.