MXL3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals

This paper introduces a new efficient algorithm, called MXL3, for computing Grobner bases of zero-dimensional ideals. The MXL3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Grobner basis. We present experimental results comparing the behavior of MXL3 to F4 on HFE and random generated instances of the MQ problem. In both cases the first implementation of the MXL3 algorithm succeeds faster and uses less memory than Magma's implementation of F4.

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