Quasi-Dyadic CFS Signatures

  • Paulo S. L. M. Barreto
  • Pierre-Louis Cayrel
  • Rafael Misoczki
  • Robert Niebuhr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6584)


Courtois-Finiasz-Sendrier (CFS) digital signatures critically depend on the ability to efficiently find a decodable syndrome by random sampling the syndrome space, previously restricting the class of codes upon which they could be instantiated to generic binary Goppa codes. In this paper we show how to construct t-error correcting quasi-dyadic codes where the density of decodable syndromes is high, while also allowing for a reduction by a factor up to t in the key size.


post-quantum cryptography coding-based cryptography digital signatures efficient parameters and algorithms 


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  1. 1.
    Berger, T.P., Cayrel, P.-L., Gaborit, P., Otmani, A.: Reducing key length of the mcEliece cryptosystem. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 77–97. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Bernstein, D.J.: List decoding for binary Goppa codes. Preprint (2008),
  3. 3.
    Cayrel, P.-L., Gaborit, P., Galindo, D., Girault, M.: Improved identity-based identification using correcting codes. CoRR, abs/0903.0069 (2009)Google Scholar
  4. 4.
    Courtois, N.T., Finiasz, M., Sendrier, N.: How to achieve a mcEliece-based digital signature scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Dallot, L.: Towards a concrete security proof of courtois, finiasz and sendrier signature scheme. In: Lucks, S., Sadeghi, A.-R., Wolf, C. (eds.) WEWoRC 2007. LNCS, vol. 4945, pp. 65–77. Springer, Heidelberg (2008), CrossRefGoogle Scholar
  6. 6.
    Dallot, L., Vergnaud, D.: Provably secure code-based threshold ring signatures. In: Parker, M.G. (ed.) CC 2009. LNCS, vol. 5921, pp. 222–235. Springer, Heidelberg (2009)Google Scholar
  7. 7.
    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
  8. 8.
    Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: A distinguisher for high rate mceliece cryptosystems. Cryptology ePrint Archive, Report 2010/331 (2010),
  9. 9.
    Finiasz, M., Sendrier, N.: Security bounds for the design of code-based cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 88–105. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Gaborit, P.: Shorter keys for code based cryptography. In: International Workshop on Coding and Cryptography – WCC 2005, Bergen, Norway, pp. 81–91. ACM Press, New York (2005)Google Scholar
  11. 11.
    Gulamhusein, M.N.: Simple matrix-theory proof of the discrete dyadic convolution theorem. Electronics Letters 9(10), 238–239 (1973)CrossRefGoogle Scholar
  12. 12.
    Kobara, K.: Flexible quasi-dyadic code-based public-key encryption and signature. Cryptology ePrint Archive, Report 2009/635 (2009)Google Scholar
  13. 13.
    McEliece, R.: A public-key cryptosystem based on algebraic coding theory. The Deep Space Network Progress Report, DSN PR 42–44 (1978),
  14. 14.
    Misoczki, R., Barreto, P.S.L.M.: Compact mcEliece keys from goppa codes. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 376–392. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problems of Control and Information Theory 15(2), 159–166 (1986)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Otmani, A., Tillich, J.-P., Dallot, L.: Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes. Mathematics in Computer Science 3(2), 129–140 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Patterson, N.J.: The algebraic decoding of Goppa codes. IEEE Transactions on Information Theory 21(2), 203–207 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Schechter, S.: On the inversion of certain matrices. Mathematical Tables and Other Aids to Computation 13(66), 73–77 (1959), MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26, 1484–1509 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Umana, V.G., Leander, G.: Practical key recovery attacks on two McEliece variants. In: International Conference on Symbolic Computation and Cryptography – SCC 2010 (2010) (to appear)Google Scholar
  21. 21.
    Zheng, D., Li, X., Chen, K.: Code-based ring signature scheme. I. J. Network Security 5(2), 154–157 (2007)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paulo S. L. M. Barreto
    • 1
  • Pierre-Louis Cayrel
    • 2
  • Rafael Misoczki
    • 1
  • Robert Niebuhr
    • 3
  1. 1.Departamento de Engenharia de Computação e Sistemas Digitais (PCS)Escola Politécnica, Universidade de São PauloBrazil
  2. 2.CASED – Center for Advanced Security Research DarmstadtDarmstadtGermany
  3. 3.Fachbereich Informatik Kryptographie und ComputeralgebraTechnische Universität DarmstadtDarmstadtGermany

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