MXL3: an efficient algorithm for computing gröbner bases of zero-dimensional ideals. This paper introduces a new efficient algorithm, called MXL3, for computing Gröbner 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 Gröbner 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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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Tanaka, Satoshi; Cheng, Chen-Mou; Sakurai, Kouichi: Evaluation of solving time for multivariate quadratic equation system using XL algorithm over small finite fields on GPU (2015)
- Ding, Jintai; Clough, Crystal; Araujo, Roberto: Inverting square systems algebraically is exponential (2014)
- Ullah, E.; Abbas Khan, S.: Computing border bases using mutant strategies (2014)
- Albrecht, Martin R.; Cid, Carlos; Faugère, Jean-Charles; Perret, Ludovic: On the relation between the MXL family of algorithms and Gröbner basis algorithms (2012)
- Eder, Christian; Gash, Justin; Perry, John: Modifying Faugère’s F5 algorithm to ensure termination (2011)