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Algebraic Attack on the MQQ Public Key Cryptosystem

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 Fabian Werner TU Darmstadt, FB Informatik, Hochschulstrasse 10, 64289 Darmstadt, Germany

TBD mathscidoc:2207.43045

CANS 2009, 392–401, 2009.12
In this paper, we present an efficient attack on the multivariate Quadratic Quasigroups (MQQ) public key cryptosystem. Our cryptanalysis breaks the MQQ cryptosystem by solving a system of multivariate quadratic polynomial equations using both the MutantXL algorithm and the F4 algorithm. We present the experimental results that show that MQQ systems is broken up to size n equal to 300. Based on these results we show also that MutantXL solves MQQ systems with much less memory than the F4 algorithm implemented in Magma.
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@inproceedings{mohamed2009algebraic,
  title={Algebraic Attack on the MQQ Public Key Cryptosystem},
  author={Mohamed Saied Emam Mohamed, Jintai Ding, Johannes Buchmann, and Fabian Werner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714110843799774622},
  booktitle={CANS 2009},
  pages={392–401},
  year={2009},
}
Mohamed Saied Emam Mohamed, Jintai Ding, Johannes Buchmann, and Fabian Werner. Algebraic Attack on the MQQ Public Key Cryptosystem. 2009. In CANS 2009. pp.392–401. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714110843799774622.
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