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A New Version of McEliece PKC Based on Convolutional Codes

  • Carl Löndahl
  • Thomas Johansson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7618)

Abstract

This paper presents new versions of the McEliece PKC that use time-varying convolutional codes. In opposite to the choice of Goppa codes, the proposed construction uses large parts of randomly generated parity-checks, presumably making structured attacks more difficult. The drawback is that we have a small but nonzero probability of not being successful in decoding, in which case we need to ask for a retransmission.

Keywords

Linear Code Block Code LDPC Code Parity Check Convolutional Code 
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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References

  1. 1.
    Augot, D., Finiasz, M., Sendrier, N.: A Family of Fast Syndrome Based Cryptographic Hash Functions. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 64–83. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Baldi, M.: LDPC Codes in the McEliece Cryptosystem: Attacks and Countermeasures. In: NATO Science for Peace and Security Series – D: Information and Communication Security. LNCS, vol. 23, pp. 160–174 (2009)Google Scholar
  3. 3.
    Becker, A., Joux, A., May, A., Meurer, A.: Decoding Random Binary Linear Codes in 2n/20: How 1 + 1 = 0 Improves Information Set Decoding. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 520–536. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Bernstein, D.J., Lange, T., Peters, C.: Attacking and Defending the McEliece Cryptosystem. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 31–46. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Courtois, N., Finiasz, M., Sendrier, N.: How to Achieve a McEliece-Based Digital Signature Scheme. In: Goos, G., Hartmanis, J., van Leeuwen, J. (eds.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Delsarte, P.: Bilinear forms over a finite field. Journal of Combinatorial Theory, Series A 25, 226–241 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Engelbert, D., Overbeck, R., Schmidt, A.: A summary of McEliece-type cryptosystems and their security (2007)Google Scholar
  8. 8.
    Faugère, J.C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic Cryptanalysis of McEliece Variants with Compact Keys. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 279–298. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Stern, J.: A Method for Finding Codewords of Small Weight. In: Wolfmann, J., Cohen, G.D. (eds.) Coding Theory and Applications. LNCS, vol. 388, pp. 106–113. Springer (1989)Google Scholar
  10. 10.
    Johannesson, R., Zigangirov, K.S.: Fundamentals of Convolutional Coding. IEEE Series on Digital and Mobile Communication. IEEE Press (1999)Google Scholar
  11. 11.
    Johansson, T., Löndahl, C.: An improvement to Stern’s algorithm, internal report (2011), http://lup.lub.lu.se/record/2204753
  12. 12.
    Lin, S., Costello, D.J.: Error Control Coding, 2nd edn. Prentice-Hall, Inc. (2004)Google Scholar
  13. 13.
    May, A., Meurer, A., Thomae, E.: Decoding random linear codes in \(\tilde{\mathcal{O}}(2^{0.054n})\). In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 107–124. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report 42–44, 114–116 (1978)Google Scholar
  15. 15.
    Niederreiter, H.: Knapsack-type crytosystems and algebraic coding theory. Problems of Control and Information Theory 15(2), 157–166 (1986)MathSciNetGoogle Scholar
  16. 16.
    Sidelnikov, V.M., Shestakov, S.O.: On the insecurity of cryptosystems based on generalized Reed-Solomon codes. Discrete Mathematics and Applications 2(4), 439–444 (1992)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Sun, H.M.: Improving the Security of the McEliece Public-Key Cryptosystem. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 200–213. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carl Löndahl
    • 1
  • Thomas Johansson
    • 1
  1. 1.Dept. of Electrical and Information TechnologyLund UniversityLundSweden

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