Efficient Designated Confirmer Signatures Without Random Oracles or General Zero-Knowledge Proofs

(Extended Abstract)
  • Craig Gentry
  • David Molnar
  • Zulfikar Ramzan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3788)

Abstract

Most prior designated confirmer signature schemes either prove security in the random oracle model (ROM) or use general zero-knowledge proofs for NP statements (making them impractical). By slightly modifying the definition of designated confirmer signatures, Goldwasser and Waisbard presented an approach in which the Confirm and ConfirmedSign protocols could be implemented without appealing to general zero-knowledge proofs for NP statements (their “Disavow” protocol still requires them). The Goldwasser-Waisbard approach could be instantiated using Cramer-Shoup, GMR, or Gennaro-Halevi-Rabin signatures.

In this paper, we provide an alternate generic transformation to convert any signature scheme into a designated confirmer signature scheme, without adding random oracles. Our key technique involves the use of a signature on a commitment and a separate encryption of the random string used for commitment. By adding this “layer of indirection,” the underlying protocols in our schemes admit efficient instantiations (i.e., we can avoid appealing to general zero-knowledge proofs for NP statements) and furthermore the performance of these protocols is not tied to the choice of underlying signature scheme. We illustrate this using the Camenisch-Shoup variation on Paillier’s cryptosystem and Pedersen commitments. The confirm protocol in our resulting scheme requires 10 modular exponentiations (compared to 320 for Goldwasser-Waisbard) and our disavow protocol requires 41 modular exponentiations (compared to using a general zero-knowledge proof for Goldwasser-Waisbard). Previous schemes use the “encryption of a signature” paradigm, and thus run into problems when trying to implement the “confirm” and “disavow” protocols efficiently.

References

  1. 1.
    Asokan, N., Shoup, V., Waidner, M.: Optimistic fair exchange of digital signatures. IEEE Journal on Selected Areas in Communications 18(4), 591–610 (2000)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM CCS 1993 (1993)Google Scholar
  3. 3.
    Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993)Google Scholar
  4. 4.
    Camenisch, J., Michels, M.: Confirmer Signature Schemes Secure Against Adaptive Adversaries. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, p. 243. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Camenisch, J., Lysyanskaya, A.: Signature Schemes and Anonymous Credentials from Bilinear Maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Camenisch, J., Shoup, V.: Practical Verifable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003); Full version available from www.shoup.net
  7. 7.
    Chaum, D.: Designated Confirmer Signatures. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 86–91. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  8. 8.
    Chaum, D., Pedersen, T.P.: Wallet Databases with Observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)Google Scholar
  9. 9.
    Chaum, D., van Antwerpen, H.: Undeniable Signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 212–216. Springer, Heidelberg (1990)Google Scholar
  10. 10.
    Cramer, R., Shoup, V.: Signature Schemes Based on the Strong RSA Assumption. In: ACM CCS 1999 (1999)Google Scholar
  11. 11.
    Damgard, I.: Efficient concurrent zero-knowledge in the auxiliary string model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, p. 418. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Cramer, R., Shoup, V.: A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Message Attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, p. 13. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Cramer, R., Damgard, I., Shoup, V.: 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
  14. 14.
    Gennaro, R., Halevi, S., Rabin, T.: Secure Hash-and-Sign Signatures Without the Random Oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 123. Springer, Heidelberg (1999)Google Scholar
  15. 15.
    Goldreich, O., Kahan, A.: How to Construct Constant-Round Zero-Knowledge Proof Systems for NP. Journal of Cryptology 9(3), 167–189Google Scholar
  16. 16.
    Goldwasser, S., Micali, S., Rivest, R.: A Digital Signature Scheme Secure Against Adaptive Chosen Message Attacks. SICOMP 17(2), 281–308 (1988)MATHMathSciNetGoogle Scholar
  17. 17.
    Goldwasser, S., Waisbard, E.: Transformation of Digital Signature Schemes into Designated Confirmer Signature Schemes. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 77–100. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Cramer, R., Damgard, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)Google Scholar
  20. 20.
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC 1990 (1990)Google Scholar
  21. 21.
    Okamoto, T.: Designated Confirmer Signatures and Public Key Encryption Are Equivalent. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 61–74. Springer, Heidelberg (1994)Google Scholar
  22. 22.
    Paillier, P.: Public-key cryptosystems based on composite degree residue classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 223. Springer, Heidelberg (1999)Google Scholar
  23. 23.
    Pedersen, T.P.: A threshold cryptosystem without a trusted third party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)Google Scholar
  24. 24.
    Schnorr, C.P.: Efficient Identification and Signatures for Smart Cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 498–506. Springer, Heidelberg (1990)Google Scholar
  25. 25.
    Shamir, A., Tauman, Y.: Improved Online-Offline Signature Schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 355. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  26. 26.
    Michels, M., Stadler, M.: Generic constructions for secure and efficient confirmer signature schemes. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 406–421. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  27. 27.
    Garay, J., MacKenzie, P., Yang, K.: Strengthening Zero-Knowledge Protocols Using Signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 177–194. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  28. 28.
    MacKenzie, P., Yang, K.: On Simulation-Sound Trapdoor Commitments. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 382–400. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Craig Gentry
    • 1
  • David Molnar
    • 2
  • Zulfikar Ramzan
    • 1
  1. 1.DoCoMo USA Labs 
  2. 2.University of CaliforniaBerkeley

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