Cryptanalysis of the Niederreiter Public Key Scheme Based on GRS Subcodes

  • Christian Wieschebrink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6061)

Abstract

In this paper a new structural attack on the McEliece/Niederreiter public key cryptosystem based on subcodes of generalized Reed-Solomon codes proposed by Berger and Loidreau is described. It allows the reconstruction of the private key for almost all practical parameter choices in polynomial time with high probability.

Keywords

Public key cryptography McEliece encryption Niederreiter encryption error-correcting codes generalized Reed-Solomon codes Sidelnikov-Shestakov attack 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    McEliece, R.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report, Jet Prop. Lab., California Inst. Tech. 42-44, 114–116 (1978)Google Scholar
  2. 2.
    van Tilborg, H.: Encyclopedia of Cryptography and Security. Springer, Heidelberg (2005)MATHCrossRefGoogle Scholar
  3. 3.
    Minder, L., Shokrollahi, A.: Cryptanalysis of the Sidelnikov cryptosystem. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 347–360. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Gibson, K.: The security of the Gabidulin public-key cryptosystem. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 212–223. Springer, Heidelberg (1996)Google Scholar
  5. 5.
    Sidelnikov, V., Shestakov, S.: On insecurity of cryptosystems based on generalized Reed-Solomon codes. Discrete Math. Appl. 2, 439–444 (1992)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Berger, T., Loidreau, P.: How to mask the structure of codes for a cryptographic use. Designs, Codes and Cryptography 35, 63–79 (2005)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Wieschebrink, C.: An attack on a modified Niederreiter encryption scheme. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 14–26. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Berlekamp, E., Welch, L.: Error correction of algebraic block codes, US Patent No. 4,633,470 (1986)Google Scholar
  9. 9.
    Guruswami, V., Sudan, M.: Improved decoding of Reed-Solomon and algebraic-geometric codes. In: Proceedings of 39th Annual Symposium on Foundations of Computer Science, pp. 28–37 (1998)Google Scholar
  10. 10.
    MacWilliams, F., Sloane, N.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1997)Google Scholar
  11. 11.
    Niederreiter, N.: Knapsack-type cryptosystems and algebraic coding theory. Problems of Control and Information Theory 15, 159–166 (1986)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christian Wieschebrink
    • 1
  1. 1.Federal Office for Information Security (BSI)BonnGermany

Personalised recommendations