Advertisement

Improved Lattice-Based Threshold Ring Signature Scheme

  • Slim Bettaieb
  • Julien Schrek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7932)

Abstract

We present in this paper an improvement of the lattice-based threshold ring signature proposed by Cayrel, Lindner, Rückert and Silva (CLRS) [LATINCRYPT ’10]. We generalize the same identification scheme CLRS to obtain a more efficient threshold ring signature. The security of our scheme relies on standard lattice problems. The improvement is a significant reduction of the size of the signature. Our result is a t-out-of-N threshold ring signature which can be seen as t different ring signatures instead of N for the other schemes. We describe the ring signature induced by the particular case of only one signer. To the best of our knowledge, the resulted signatures are the most efficient lattice-based ring signature and threshold signature.

Keywords

Threshold ring signatures lattices 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Mathematische Annalen 261(4), 515–534 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Coppersmith, D.: Finding small solutions to small degree polynomials. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 20–31. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing., pp. 99–108. ACM (1996)Google Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Bresson, E., Stern, J., Szydlo, M.: Threshold ring signatures and applications to ad-hoc groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 465–480. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    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. 12–26. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Dallot, L., Vergnaud, D.: Provably secure code-based threshold ring signatures. In: Parker, M.G. (ed.) Cryptography and Coding 2009. LNCS, vol. 5921, pp. 222–235. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Zheng, D., Li, X., Chen, K.: Code-based ring signature scheme. IJ Network Security 5(2), 154–157 (2007)Google Scholar
  10. 10.
    Aguilar Melchor, C., Cayrel, P.-L., Gaborit, P.: A new efficient threshold ring signature scheme based on coding theory. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 1–16. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Cayrel, P.-L., Lindner, R., Rückert, M., Silva, R.: A lattice-based threshold ring signature scheme. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 255–272. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Cayrel, P.-L., Lindner, R., Rückert, M., Silva, R.: Improved zero-knowledge identification with lattices. In: Heng, S.-H., Kurosawa, K. (eds.) ProvSec 2010. LNCS, vol. 6402, pp. 1–17. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Wang, J., Sun, B.: Ring signature schemes from lattice basis delegation. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds.) ICICS 2011. LNCS, vol. 7043, pp. 15–28. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Brakerski, Z., Kalai, Y.: A framework for efficient signatures, ring signatures and identity based encryption in the standard model. Technical report, Cryptology ePrint Archive, Report 2010/086 (2010)Google Scholar
  15. 15.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 197–206. ACM (2008)Google Scholar
  16. 16.
    Kawachi, A., Tanaka, K., Xagawa, K.: Concurrently secure identification schemes based on the worst-case hardness of lattice problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 372–389. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Aguilar Melchor, C., Cayrel, P., Gaborit, P., Laguillaumie, F.: A new efficient threshold ring signature scheme based on coding theory. IEEE Transactions on Information Theory 57(7), 4833–4842 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Cayrel, P.L., Veron, P.: Improved code-based identification scheme. arXiv preprint arXiv:1001.3017 (2010)Google Scholar
  21. 21.
    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
  22. 22.
    El Yousfi Alaoui, S.M., Dagdelen, Ö., Véron, P., Galindo, D., Cayrel, P.-L.: Extended security arguments for signature schemes. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 19–34. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Slim Bettaieb
    • 1
  • Julien Schrek
    • 1
  1. 1.XLIM-DMIUniversité de LimogesLimoges CedexFrance

Personalised recommendations