Advertisement

On Kabatianskii-Krouk-Smeets Signatures

  • Pierre-Louis Cayrel
  • Ayoub Otmani
  • Damien Vergnaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)

Abstract

Kabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on random error-correcting codes. In this paper we investigate the security and the efficiency of their proposal. We show that a passive attacker who may intercept just a few signatures can recover the private key. We give precisely the number of signatures required to achieve this goal. This enables us to prove that all the schemes given in the original paper can be broken with at most 20 signatures. We improve the efficiency of these schemes by firstly providing parameters that enable to sign about 40 messages, and secondly, by describing a way to extend these few-times signatures into classical multi-time signatures. We finally study their key sizes and a mean to reduce them by means of more compact matrices.

Keywords

Code-based cryptography digital signature random error-correcting codes Niederreiter cryptosystem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.A.: On the intractability of certain coding problems. IEEE Transactions on Information Theory 24(3), 384–386 (1978)MATHCrossRefGoogle Scholar
  2. Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: Application to McEliece’s cryptosystem and to narrow-sense BCH codes of length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 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
  4. Engelbert, D., Overbeck, R., Schmidt, A.: A summary of McEliece-type cryptosystems and their security, Cryptology ePrint Archive, Report 2006/162 (2006), http://eprint.iacr.org/
  5. Gaborit, P.: Shorter keys for code based cryptography. In: WCC 2005. LNCS, vol. 3969, pp. 81–91. Springer, Heidelberg (2006)Google Scholar
  6. Kabatianskii, G., Krouk, E., Smeets, B.J.M.: A digital signature scheme based on random error-correcting codes. In: Darnell, M. (ed.) Cryptography and Coding. LNCS, vol. 1355, pp. 161–167. Springer, Heidelberg (1997)Google Scholar
  7. Lamport, L.: Constructing digital signatures from a one way function, Tech. Report CSL-98, SRI International (October 1979)Google Scholar
  8. Lee, P.J., Brickell, E.F.: An observation on the security of McEliece’s public-key cryptosystem. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 275–280. Springer, Heidelberg (1988)Google Scholar
  9. Leon, J.S.: A probabilistic algorithm for computing minimum weights of large error-correcting codes. IEEE Transactions on Information Theory 34(5), 1354–1359 (1988)CrossRefMathSciNetGoogle Scholar
  10. Li, Y.X., Deng, R.H., Wang, X.-M.: On the equivalence of McEliece’s and Niederreiter’s public-key cryptosystems. IEEE Transactions on Information Theory 40(1), 271–273 (1994)MATHCrossRefMathSciNetGoogle Scholar
  11. MacWilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes, 5th edn. North–Holland, Amsterdam (1986)Google Scholar
  12. McEliece, R.J.: A public-key system based on algebraic coding theory, pp. 114–116, Jet Propulsion Lab, DSN Progress Report 44 (1978)Google Scholar
  13. Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1989)Google Scholar
  14. Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problems Control Inform. Theory 15(2), 159–166 (1986)MATHMathSciNetGoogle Scholar
  15. Perrig, A.: The BiBa one-time signature and broadcast authentication protocol. In: Proceedings of the 8th ACM Conference on Computer and Communications Security, pp. 28–37. ACM Press, New York (2001)CrossRefGoogle Scholar
  16. Reyzin, L., Reyzin, N.: Better than BiBa: Short One-Time Signatures with Fast Signing and Verifying. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 144–153. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. Stern, J.: A method for finding codewords of small weight. In: Wolfmann, J., Cohen, G. (eds.) Coding Theory and Applications. LNCS, vol. 388, pp. 106–113. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  18. Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)Google Scholar
  19. Véron, P.: Problème SD, opérateur trace, schémas d’identification et codes de goppa, Ph.D. thesis, Université Toulon et du Var, Toulon, France (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Pierre-Louis Cayrel
    • 1
  • Ayoub Otmani
    • 2
  • Damien Vergnaud
    • 3
  1. 1.DMI/XLIM - Université de Limoges, 123 avenue Albert Thomas, 87060 LimogesFrance
  2. 2.GREYC - Ensicaen, Boulevard Maréchal Juin, 14050 Caen CedexFrance
  3. 3.b-it COSEC - Bonn/Aachen International Center for Information Technology - Computer Security Group, Dahlmannstr. 2, D-53113 BonnGermany

Personalised recommendations