Advertisement

Solving Structured Polynomial Systems and Applications to Cryptology

(Plenary Talk)
  • Jean-Charles Faugère
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5743)

Abstract

Cryptography is a collection of mathematical techniques used to secure the transmission and storage of information. A fundamental problem in cryptography is to evaluate the security of cryptosystems against the most powerful techniques. To this end, several general methods have been proposed: linear cryptanalysis, differential cryptanalysis, ... Extensively used cryptographic standards - such as AES [1] - are all resistant against linear and differential attacks. In this talk, we will describe another general method - Algebraic Cryptanalysis - which can be used to evaluate the security of such cryptosystems.

References

  1. 1.
    Daemen, J., Rijmen, V.: The Design of Rijndael: The Wide Trail Strategy. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  2. 2.
    Buchberger, B.: An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal (German), PhD Thesis, Univ of Innsbruck, Math. Institute, Austria, English Translation: J. of Symbolic Computation, Special Issue on Logic, Math and Comp Science: Interactions 41(3-4), 475-511 (1965)Google Scholar
  3. 3.
    Bardet, M., Faugère, J.-C., Salvy, B., Yang, B.-Y.: Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems. In: Proc. of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry (2005)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.B.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  5. 5.
    Courtois, N.: Efficient Zero-knowledge Authentication Based on a Linear Algebra Problem MinRank. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, p. 402. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Faugère, J.-C., Levy-dit-Vehel, F., Perret, L.: Cryptanalysis of MinRank. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 280–296. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Faugère, J.-C.: A New Efficient Algorithm for Computing Gröbner Basis without Reduction to Zero: F5. In: Proceedings of ISSAC, July 2002, pp. 75–83. ACM press, New York (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jean-Charles Faugère
    • 1
  1. 1.SALSA Project INRIA, Centre Paris-Rocquencourt, UPMC, Univ Paris 06, LIP6, CNRS, UMR 7606, LIP6, UFR Ingénierie 919, LIP6 Passy KennedyParis Cedex 05

Personalised recommendations