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Practical Algebraic Cryptanalysis for Dragon-Based Cryptosystems

  • Johannes Buchmann
  • Stanislav Bulygin
  • Jintai Ding
  • Wael Said Abd Elmageed Mohamed
  • Fabian Werner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6467)

Abstract

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.

Keywords

Linear Polynomial Algebraic Attack Permutation Polynomial Gaussian Elimination Method Linearization Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Johannes Buchmann
    • 1
  • Stanislav Bulygin
    • 2
  • Jintai Ding
    • 3
  • Wael Said Abd Elmageed Mohamed
    • 1
  • Fabian Werner
    • 4
  1. 1.FB InformatikTU DarmstadtDarmstadtGermany
  2. 2.Center for Advanced Security Research Darmstadt (CASED)Germany
  3. 3.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  4. 4.TU DarmstadtGermany

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