International Workshop on Public Key Cryptography

PKC 2011: Public Key Cryptography – PKC 2011 pp 441-458

Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants

  • Luk Bettale
  • Jean-Charles Faugère
  • Ludovic Perret
Conference paper

DOI: 10.1007/978-3-642-19379-8_27

Volume 6571 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bettale L., Faugère JC., Perret L. (2011) Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants. In: Catalano D., Fazio N., Gennaro R., Nicolosi A. (eds) Public Key Cryptography – PKC 2011. PKC 2011. Lecture Notes in Computer Science, vol 6571. Springer, Berlin, Heidelberg

Abstract

We investigate the security of a generalization of HFE (multivariate and odd-characteristic variants). First, we propose an improved version of the basic Kipnis-Shamir key recovery attack against HFE. Second, we generalize the Kipnis-Shamir attack to Multi-HFE. The attack reduces to solve a MinRank problem directly on the public key. This leads to an improvement of a factor corresponding to the square of the degree of the extension field. We used recent results on MinRank to show that our attack is polynomial in the degree of the extension field. It appears that multi-HFE is less secure than original HFE for equal-sized keys. Finally, adaptations of our attack overcome several variants (i.e. minus modifier and embedding). As a proof of concept, we have practically broken the most conservative parameters given by Chen, Chen, Ding, Werner and Yang in 9 days for 256 bits security. All in all, our results give a more precise picture on the (in)security of several variants of HFE proposed these last years.

Keywords

Hidden Field EquationsMinRankGröbner bases
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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Luk Bettale
    • 1
    • 2
  • Jean-Charles Faugère
    • 1
    • 2
  • Ludovic Perret
    • 1
    • 2
  1. 1.UPMC Univ Paris 06, UMR 7606, LIP6INRIA, Paris-Rocquencourt Center, SALSA ProjectParisFrance
  2. 2.UMR 7606, LIP6CNRSParisFrance