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Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL

Mohamed Saied Emam Mohamed TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Jintai Ding Department of Mathematical Sciences, University of Cincinnati Cincinnati OH 45220, USA Johannes Buchmann TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany

TBD mathscidoc:2207.43105

IACR Cryptol. ePrint Arch., 2008.10
In this paper, we present an efficient attack to the multivariate Quadratic Quasigroups (MQQ) cryptosystem. Our cryptanalysis breaks MQQ cryptosystems by solving systems of multivariate quadratic polynomial equations using a modified version of the MutantXL algorithm. We present experimental results comparing the behavior of our implementation of MutantXL to Magma's implementation of F_4 on MQQ systems (\ge 135 bit). Based on our results we show that the MutantXL implementation solves with much less memory than Magma's implementation of F_4 algorithm.
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@inproceedings{mohamed2008algebraic,
  title={Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL},
  author={Mohamed Saied Emam Mohamed, Jintai Ding, and Johannes Buchmann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721144511916498687},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2008},
}
Mohamed Saied Emam Mohamed, Jintai Ding, and Johannes Buchmann. Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL. 2008. In IACR Cryptol. ePrint Arch.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220721144511916498687.
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