International Workshop on Public Key Cryptography

PKC 2011: Public Key Cryptography – PKC 2011 pp 473-493

Practical Cryptanalysis of the Identification Scheme Based on the Isomorphism of Polynomial with One Secret Problem

  • Charles Bouillaguet
  • Jean-Charles Faugère
  • Pierre-Alain Fouque
  • Ludovic Perret
Conference paper

DOI: 10.1007/978-3-642-19379-8_29

Volume 6571 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bouillaguet C., Faugère JC., Fouque PA., Perret L. (2011) Practical Cryptanalysis of the Identification Scheme Based on the Isomorphism of Polynomial with One Secret Problem. 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

This paper presents a practical cryptanalysis of the Identification Scheme proposed by Patarin at Crypto 1996. This scheme relies on the hardness of the Isomorphism of Polynomial with One Secret (IP1S), and enjoys shorter key than many other schemes based on the hardness of a combinatorial problem (as opposed to number-theoretic problems). Patarin proposed concrete parameters that have not been broken faster than exhaustive search so far. On the theoretical side, IP1S has been shown to be harder than Graph Isomorphism, which makes it an interesting target. We present two new deterministic algorithms to attack the IP1S problem, and we rigorously analyze their complexity and success probability. We show that they can solve a (big) constant fraction of all the instances of degree two in polynomial time. We verified that our algorithms are very efficient in practice. All the parameters with degree two proposed by Patarin are now broken in a few seconds. The parameters with degree three can be broken in less than a CPU-month. The identification scheme is thus quite badly broken.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Charles Bouillaguet
    • 1
  • Jean-Charles Faugère
    • 2
    • 3
  • Pierre-Alain Fouque
    • 1
  • Ludovic Perret
    • 3
    • 2
  1. 1.Ecole Normale SupérieureParisFrance
  2. 2.UPMC Univ. Paris 06, UMR 7606, LIP6INRIA, Paris-Rocquencourt Center, SALSA ProjectParisFrance
  3. 3.UMR 7606, LIP6CNRSParisFrance