Skip to main content

Quasi-Dyadic CFS Signatures

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6584))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Chapter  Google Scholar 

  2. Bernstein, D.J.: List decoding for binary Goppa codes. Preprint (2008), http://cr.yp.to/papers.html#goppalist

  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. 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)

    Chapter  Google Scholar 

  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), http://users.info.unicaen.fr/~ldallot/download/articles/CFSProof-dallot.pdf

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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), http://eprint.iacr.org/

  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)

    Chapter  Google Scholar 

  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. Gulamhusein, M.N.: Simple matrix-theory proof of the discrete dyadic convolution theorem. Electronics Letters 9(10), 238–239 (1973)

    Article  Google Scholar 

  12. Kobara, K.: Flexible quasi-dyadic code-based public-key encryption and signature. Cryptology ePrint Archive, Report 2009/635 (2009)

    Google Scholar 

  13. McEliece, R.: A public-key cryptosystem based on algebraic coding theory. The Deep Space Network Progress Report, DSN PR 42–44 (1978), http://ipnpr.jpl.nasa.gov/progressreport2/42-44/44N.PDF

  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)

    Chapter  Google Scholar 

  15. Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problems of Control and Information Theory 15(2), 159–166 (1986)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  17. Patterson, N.J.: The algebraic decoding of Goppa codes. IEEE Transactions on Information Theory 21(2), 203–207 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  18. Schechter, S.: On the inversion of certain matrices. Mathematical Tables and Other Aids to Computation 13(66), 73–77 (1959), http://www.jstor.org/stable/2001955

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Zheng, D., Li, X., Chen, K.: Code-based ring signature scheme. I. J. Network Security 5(2), 154–157 (2007)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barreto, P.S.L.M., Cayrel, PL., Misoczki, R., Niebuhr, R. (2011). Quasi-Dyadic CFS Signatures. In: Lai, X., Yung, M., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2010. Lecture Notes in Computer Science, vol 6584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21518-6_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21518-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21517-9

  • Online ISBN: 978-3-642-21518-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics