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International Conference on Information Security and Cryptology

ICISC 2009: Information, Security and Cryptology – ICISC 2009 pp 87–100Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5984))

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.

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Author information

Authors and Affiliations

  1. TU Darmstadt, FB Informatik, Hochschulstrasse 10, 64289, Darmstadt, Germany

    Mohamed Saied Emam Mohamed & Johannes Buchmann

  2. Department of Mathematical Sciences, University of Cincinnati, South China University of Technology,  

    Daniel Cabarcas & Jintai Ding

  3. Center for Advanced Security Research Darmstadt (CASED),  

    Stanislav Bulygin

Authors
  1. Mohamed Saied Emam Mohamed
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  2. Daniel Cabarcas
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  3. Jintai Ding
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  4. Johannes Buchmann
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  5. Stanislav Bulygin
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Editor information

Editors and Affiliations

  1. CIST (Center for Information Security Technologies), Korea University Anam Dong, Sungbuk Gu, Seoul, Korea

    Donghoon Lee

  2. Center for Information Security Technologies(CIST), Korea University, Seoul, Korea

    Seokhie Hong

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Mohamed, M.S.E., Cabarcas, D., Ding, J., Buchmann, J., Bulygin, S. (2010). MXL3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals. In: Lee, D., Hong, S. (eds) Information, Security and Cryptology – ICISC 2009. ICISC 2009. Lecture Notes in Computer Science, vol 5984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14423-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-14423-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14422-6

  • Online ISBN: 978-3-642-14423-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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