Advertisement

A New Efficient Threshold Ring Signature Scheme Based on Coding Theory

  • Carlos Aguilar Melchor
  • Pierre-Louis Cayrel
  • Philippe Gaborit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5299)

Abstract

Ring signatures were introduced by Rivest, Shamir and Tauman in 2001. Bresson, Stern and Szydlo extended the ring signature concept to t-out-of-N threshold ring signatures in 2002. We present in this paper a generalization of Stern’s code based authentication (and signature) scheme to the case of t-out-of-N threshold ring signature. The size of our signature is in \(\mathcal{O}(N)\) and does not depend on t. Our protocol is anonymous and secure in the random oracle model, it has a very short public key and has a complexity in \(\mathcal{O}(N)\). This protocol is the first efficient code-based ring signature scheme and the first code-based threshold ring signature scheme. Moreover it has a better complexity than number-theory based schemes which have a complexity in \(\mathcal{O}(Nt)\).

Keywords

Threshold ring signature code-based cryptography Stern’s Scheme syndrome decoding 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abe, M., Ohkubo, M., Suzuki, K.: 1-out-of-N signatures from a variety of keys. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501. Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Bender, A., Katz, J., Morselli, R.: Ring Signatures: Stronger Definitions, and Constructions Without Random Oracles. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 60–79. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory IT-24(3) (1978)Google Scholar
  4. 4.
    Boyen, X.: Mesh Signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 210–227. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Bresson, E., Stern, J., Szydlo, M.: Threshold ring signatures and applications to ad-hoc groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442. Springer, Heidelberg (2002)Google Scholar
  6. 6.
    Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH codes of length 511. IEEE Transactions on Information Theory IT-44, 367–378 (1988)zbMATHGoogle Scholar
  7. 7.
    Chandran, N., Groth, J., Sahai, A.: Ring signatures of sub-linear size without random oracles. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 423–434. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  9. 9.
    Courtois, N., Finiasz, M., Sendrier, N.: How to achieve a MCEliece based digital signature scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248. Springer, Heidelberg (2001)Google Scholar
  10. 10.
    Dodis, Y., Kiayias, A., Nicolosi, A., Shoup, V.: Anonymous identification in ad-hoc groups. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  12. 12.
    Gaborit, P., Girault, M.: Lightweight code-based authentication and signature ISIT 2007 (2007)Google Scholar
  13. 13.
    Herranz, J., Saez, G.: Forking lemmas for ring signature schemes. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 266–279. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Kuwakado, H., Tanaka, H.: Threshold Ring Signature Scheme Based on the Curve. Transactions of Information Processing Society of Japan 44(8), 2146–2154 (2003)MathSciNetGoogle Scholar
  15. 15.
    Liu, J.K., Wei, V.K., Wong, D.S.: A Separable Threshold Ring Signature Scheme. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 352–369. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, Amsterdam (1977)zbMATHGoogle Scholar
  17. 17.
    Naor, M.: Deniable Ring Authentication. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 481–498. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Pierce, J.N.: Limit distributions of the minimum distance of random linear codes. IEEE Trans. Inf. theory IT-13, 595–599 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  20. 20.
    Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. 21.
    Sendrier, N.: Cryptosystèmes à clé publique basés sur les codes correcteurs d’erreurs, Mémoire d’habilitation, Inria 2002 (2002), http://www-rocq.inria.fr/codes/Nicolas.Sendrier/pub.html
  22. 22.
    Shacham, H., Waters, B.: Efficient Ring Signatures without Random Oracles. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 166–180. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Shamir, A.: How to share a secret. Com. of the ACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773. Springer, Heidelberg (1994)Google Scholar
  25. 25.
    Stern, J.: A new paradigm for public key identification. IEEE Transactions on Information THeory 42(6), 2757–2768 (1996), http://www.di.ens.fr/~stern/publications.html MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Tsang, P.P., Wei, V.K., Chan, T.K., Au, M.H., Liu, J.K., Wong, D.S.: Separable Linkable Threshold Ring Signatures. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 384–398. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  27. 27.
    Vardy, A.: The intractability of computing the minimum distance of a code. IEEE Transactions on Information Theory 43(6), 1757–1766 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Véron, P.: A fast identification scheme. In: Proceedings of IEEE International Symposium on Information Theory 1995, Whistler, Canada (Septembre 1995)Google Scholar
  29. 29.
    Wong, D.S., Fung, K., Liu, J.K., Wei, V.K.: On the RSCode Construction of Ring Signature Schemes and a Threshold Setting of RST. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 34–46. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  30. 30.
    Xu, J., Zhang, Z., Feng, D.: A ring signature scheme using bilinear pairings. In: Lim, C.H., Yung, M. (eds.) WISA 2004. LNCS, vol. 3325. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  31. 31.
    Zhang, F., Kim, K.: ID-Based Blind Signature and Ring Signature from Pairings. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  32. 32.
    Zheng, D., Li, X., Chen, K.: Code-based Ring Signature Scheme. International Journal of Network Security 5(2), 154–157 (2007), http://ijns.nchu.edu.tw/contents/ijns-v5-n2/ijns-2007-v5-n2-p154-157.pdf MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carlos Aguilar Melchor
    • 1
  • Pierre-Louis Cayrel
    • 1
  • Philippe Gaborit
    • 1
  1. 1.Université de Limoges, XLIM-DMILimoges CedexFrance

Personalised recommendations