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**Mohamed, Mohamed Saied Emam and Cabarcas, Daniel and Ding, Jintai and Buchmann, Johannes and Bulygin, Stanislav** **Lee, Donghoon and Hong, Seokhie (eds.)** (2010):

*MXL3: An efficient algorithm for computing Gröbner bases of zero-dimensional ideals.*

Lecture Notes in ComputerIn: Proceedings of the 12th International Conference on Information Security and Cryptography - ICISC 2009, Springer, Seoul, Korea, pp. 87-100, ISBN 978-3-642-14422-6,

DOI: 10.1007/978-3-642-14423-3_7,

[Conference or Workshop Item]

## Abstract

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.

Item Type: | Conference or Workshop Item |
---|---|

Erschienen: | 2010 |

Editors: | Lee, Donghoon and Hong, Seokhie |

Creators: | Mohamed, Mohamed Saied Emam and Cabarcas, Daniel and Ding, Jintai and Buchmann, Johannes and Bulygin, Stanislav |

Title: | MXL3: An efficient algorithm for computing Gröbner bases of zero-dimensional ideals |

Language: | ["languages_typename_1" not defined] |

Abstract: | 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. |

Title of Book: | Proceedings of the 12th International Conference on Information Security and Cryptography - ICISC 2009 |

Volume: | Lecture Notes in Computer |

Number: | 5984 |

Publisher: | Springer |

ISBN: | 978-3-642-14422-6 |

Uncontrolled Keywords: | Secure Data; Multivariate polynomial systems, Groebner basis, XL algorithm, Mutant, MutantXL algorithm |

Divisions: | 20 Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt LOEWE > LOEWE-Zentren 20 Department of Computer Science LOEWE |

Event Location: | Seoul, Korea |

Date Deposited: | 04 Aug 2016 15:08 |

DOI: | 10.1007/978-3-642-14423-3_7 |

Identification Number: | TUD-CS-2009-0214 |

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