Advertisement

Relation between Verifiable Random Functions and Convertible Undeniable Signatures, and New Constructions

  • Kaoru Kurosawa
  • Ryo Nojima
  • Le Trieu Phong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7372)

Abstract

Verifiable random functions (VRF) and selectively convertible undeniable signature (SCUS) schemes were proposed independently in the literature. In this paper, we observe that they are tightly related. This directly yields several deterministic SCUS schemes based on existing VRF constructions. In addition, we create a new probabilistic SCUS scheme, which is very compact. The confirmation and disavowal protocols of these SCUS are efficient, and can be run either sequentially, concurrently, or arbitrarily. These protocols are based on what we call zero-knowledge protocols for generalized DDH and non-DDH, which are of independent interest.

Keywords

Selectively convertible undeniable signatures verifiable random function standard model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptology 21(2), 149–177 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Boyar, J., Chaum, D., Damgård, I.B., Pedersen, T.P.: Convertible Undeniable Signatures. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 189–205. Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Boyd, C., Foo, E.: Off-Line Fair Payment Protocols Using Convertible Signatures. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 271–285. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Camenisch, J.L., Shoup, V.: Practical Verifiable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Chaum, D., van Antwerpen, H.: Undeniable Signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 212–216. Springer, Heidelberg (1990)Google Scholar
  6. 6.
    Cramer, R., Damgård, I., MacKenzie, P.D.: Efficient Zero-Knowledge Proofs of Knowledge without Intractability Assumptions. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 354–373. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Dodis, Y., Yampolskiy, A.: A Verifiable Random Function with Short Proofs and Keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    El Aimani, L.: Anonymity from Public Key Encryption to Undeniable Signatures. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 217–234. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Galbraith, S.D., Mao, W.: Invisibility and Anonymity of Undeniable and Confirmer Signatures. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 80–97. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Hohenberger, S., Waters, B.: Constructing Verifiable Random Functions with Large Input Spaces. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 656–672. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Jarecki, S.: Handcuffing Big Brother: an Abuse-Resilient Transaction Escrow Scheme (Extended Abstract). In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 590–608. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Kikuchi, R., Phong, L.T., Ogata, W.: A Framework for Constructing Convertible Undeniable Signatures. In: Heng, S.-H., Kurosawa, K. (eds.) ProvSec 2010. LNCS, vol. 6402, pp. 70–86. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Kurosawa, K., Nojima, R., Phong, L.T.: Relation between verifiable random functions and convertible undeniable signatures, and new constructions. Cryptology ePrint Archive, Report 2012/259, Full version of this paper (2012), http://eprint.iacr.org/
  14. 14.
    Kurosawa, K., Takagi, T.: New Approach for Selectively Convertible Undeniable Signature Schemes. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 428–443. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Laguillaumie, F., Vergnaud, D.: Short Undeniable Signatures Without Random Oracles: The Missing Link. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 283–296. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Liskov, M.: Updatable Zero-Knowledge Databases. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 174–198. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Micali, S., Rabin, M.O., Vadhan, S.P.: Verifiable random functions. In: FOCS, pp. 120–130 (1999)Google Scholar
  18. 18.
    Micali, S., Reyzin, L.: Soundness in the Public-Key Model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 542–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Micali, S., Rivest, R.L.: Micropayments Revisited. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 149–163. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Trans. Fundamentals E85-A(2), 481–484 (2002)Google Scholar
  21. 21.
    Neff, C.A.: A verifiable secret shuffle and its application to e-voting. In: ACM Conference on Computer and Communications Security, pp. 116–125 (2001)Google Scholar
  22. 22.
    Phong, L.T., Kurosawa, K., Ogata, W.: Provably Secure Convertible Undeniable Signatures with Unambiguity. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 291–308. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Schnorr, C.-P.: Efficient signature generation by smart cards. J. Cryptology 4(3), 161–174 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Schuldt, J.C.N., Matsuura, K.: An Efficient Convertible Undeniable Signature Scheme with Delegatable Verification. In: Kwak, J., Deng, R.H., Won, Y., Wang, G. (eds.) ISPEC 2010. LNCS, vol. 6047, pp. 276–293. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Shoup, V.: Lower Bounds for Discrete Logarithms and Related Problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)Google Scholar
  26. 26.
    Vergnaud, D.: Approximation diophantienne et courbes elliptiques. Protocoles asymétriques d’authentification non-transférable. PhD Thesis, http://www.di.ens.fr/~vergnaud/TheseVergnaud.ps.gz

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kaoru Kurosawa
    • 1
  • Ryo Nojima
    • 2
  • Le Trieu Phong
    • 2
  1. 1.Ibaraki UniversityJapan
  2. 2.NICTJapan

Personalised recommendations