Practical Algebraic Cryptanalysis for Dragon-Based Cryptosystems

Johannes Buchmann TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Stanislav Bulygin Center for Advanced Security Research Darmstadt (CASED) Jintai Ding Department of Mathematical Sciences, University of Cincinnati, Cincinnati OH 45220, USA Wael Said Abd Elmageed Mohamed TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Fabian Werner TU Darmstadt

TBD mathscidoc:2207.43050

CANS 2010, 140-155, 2010.12
Recently, the Little Dragon Two and Poly-Dragon multivariate based public-key cryptosystems were proposed as efficient and secure schemes. In particular, the inventors of the two schemes claim that Little Dragon Two and Poly-Dragon resist algebraic cryptanalysis. In this paper, we show that MXL2, an algebraic attack method based on the XL algorithm and Ding’s concept of Mutants, is able to break Little Dragon Two with keys of length up to 229 bits and Poly-Dragon with keys of length up to 299. This contradicts the security claim for the proposed schemes and demonstrates the strength of MXL2 and the Mutant concept. This strength is further supported by experiments that show that in attacks on both schemes the MXL2 algorithm outperforms the Magma’s implementation of F4.
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@inproceedings{johannes2010practical,
  title={Practical Algebraic Cryptanalysis for Dragon-Based Cryptosystems},
  author={Johannes Buchmann, Stanislav Bulygin, Jintai Ding, Wael Said Abd Elmageed Mohamed, and Fabian Werner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714132719597245627},
  booktitle={CANS 2010},
  pages={140-155},
  year={2010},
}
Johannes Buchmann, Stanislav Bulygin, Jintai Ding, Wael Said Abd Elmageed Mohamed, and Fabian Werner. Practical Algebraic Cryptanalysis for Dragon-Based Cryptosystems. 2010. In CANS 2010. pp.140-155. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714132719597245627.
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