Advertisement

A CDH-Based Ring Signature Scheme with Short Signatures and Public Keys

  • Sven Schäge
  • Jörg Schwenk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6052)

Abstract

In this work we present a new CDH-based ring signature scheme with some striking advantages. On the one hand it is secure without random oracles, perfectly anonymous, and unforgeable solely under the CDH assumption in bilinear groups. This makes the security of our ring signature schemes rely on weaker (and less) assumptions than all previous (full) ring signature schemes secure without random oracles. On the other hand the scheme is very space efficient; a public key consists of just a single group element and a ring signature accounts for only n + 1 group elements, where n is the size of the ring. This is only about half the number of components when compared to other ring signature schemes that do not exploit ring re-use. As all computations are in groups of prime order, we do not need a trusted setup procedure. All these features do not come for free. The main drawback of our scheme is that it only provides security against chosen subring attacks where the attacker is not allowed to query private keys.

Keywords

CDH assumption bilinear group ring signature scheme programmable hash function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Au, M.H., Susilo, W., Mu, Y.: Constant-size dynamic k-TAA. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 111–125. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)Google Scholar
  3. 3.
    Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay (ed.) [29], pp. 409–426Google Scholar
  4. 4.
    Bender, A., Katz, J., Morselli, R.: Ring signatures: Stronger definitions, and constructions without random oracles. In: Halevi, Rabin (eds.) [19], pp. 60–79Google Scholar
  5. 5.
    Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Boneh, D., Mironov, I., Shoup, V.: A secure signature scheme from bilinear maps. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 98–110. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Boyen, X.: Mesh signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 210–227. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Brickell, E.F., Camenisch, J., Chen, L.: Direct anonymous attestation. In: Atluri, V., Pfitzmann, B., McDaniel, P.D. (eds.) ACM Conference on Computer and Communications Security, pp. 132–145. ACM, New York (2004)Google Scholar
  9. 9.
    Camenisch, J., Van Herreweghen, E.: Design and implementation of the demix anonymous credential system. In: Atluri, V. (ed.) ACM Conference on Computer and Communications Security, pp. 21–30. ACM, New York (2002)Google Scholar
  10. 10.
    Camenisch, J., Lysyanskaya, A.: A signature scheme with efficient protocols. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Camenisch, J., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology. In: STOC, pp. 209–218 (1998), revisited (preliminary version)Google Scholar
  13. 13.
    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
  14. 14.
    Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)Google Scholar
  15. 15.
    Chow, S.S.M., Wei, V.K.-W., Liu, J.K., Yuen, T.H.: Ring signatures without random oracles. In: Lin, F.-C., Lee, D.-T., Lin, B.-S., Shieh, S., Jajodia, S. (eds.) ASIACCS, pp. 297–302. ACM, New York (2006)CrossRefGoogle Scholar
  16. 16.
    Coron, J.-S., Patarin, J., Seurin, Y.: The random oracle model and the ideal cipher model are equivalent. In: Wagner (ed.) [30], pp. 1–20Google Scholar
  17. 17.
    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, pp. 609–626. Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Halevi, S., Rabin, T. (eds.): TCC 2006. LNCS, vol. 3876. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  20. 20.
    Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. In: Wagner (ed.) [30], pp. 21–38Google Scholar
  21. 21.
    Huang, Q., Wong, D.S., Zhao, Y.: Generic transformation to strongly unforgeable signatures. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 1–17. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Jakobsson, M., Sako, K., Impagliazzo, R.: Designated verifier proofs and their applications. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 143–154. Springer, Heidelberg (1996)Google Scholar
  23. 23.
    Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential aggregate signatures and multisignatures without random oracles. In: Vaudenay (ed.) [29], pp. 465–485Google Scholar
  24. 24.
    Okamoto, T.: Efficient blind and partially blind signatures without random oracles. In: Halevi, Rabin (eds.) [19], pp. 80–99Google Scholar
  25. 25.
    Persiano, G., Visconti, I.: An efficient and usable multi-show non-transferable anonymous credential system. In: Juels, A. (ed.) FC 2004. LNCS, vol. 3110, pp. 196–211. Springer, Heidelberg (2004)Google Scholar
  26. 26.
    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
  27. 27.
    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
  28. 28.
    Shoup, V.: Sequences of games: a tool for taming complexity in security proofs, November 30 (2004) (manuscript); Revised ersion from January 18 (2006/2004)Google Scholar
  29. 29.
    Vaudenay, S. (ed.): EUROCRYPT 2006. LNCS, vol. 4004. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  30. 30.
    Wagner, D. (ed.): CRYPTO 2008. LNCS, vol. 5157. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  31. 31.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sven Schäge
    • 1
  • Jörg Schwenk
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityRuhr-Universität BochumGermany

Personalised recommendations