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MXL_3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals

Mohamed Saied Emam Mohamed TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Daniel Cabarcas Department of Mathematical Sciences, University of Cincinnati, South China University of Technology Jintai Ding Department of Mathematical Sciences, University of Cincinnati, South China University of Technology Johannes Buchmann TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Stanislav Bulygin Center for Advanced Security Research Darmstadt (CASED)

TBD mathscidoc:2207.43041

ICISC 2009, 87–100, 2009.12
This paper introduces a new efficient algorithm, called MXL_3, for computing Gröbner bases of zero-dimensional ideals. The MXL_3 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 MXL_3 to F_4 on HFE and random generated instances of the MQ problem. In both cases the first implementation of the MXL_3 algorithm succeeds faster and uses less memory than Magma’s implementation of F_4.
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@inproceedings{mohamed2009mxl_3:,
  title={MXL_3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals},
  author={Mohamed Saied Emam Mohamed, Daniel Cabarcas, Jintai Ding, Johannes Buchmann, and Stanislav Bulygin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714103825716420618},
  booktitle={ICISC 2009},
  pages={87–100},
  year={2009},
}
Mohamed Saied Emam Mohamed, Daniel Cabarcas, Jintai Ding, Johannes Buchmann, and Stanislav Bulygin. MXL_3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals. 2009. In ICISC 2009. pp.87–100. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714103825716420618.
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