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Efficient Zero Knowledge on the Internet

  • Ivan Visconti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)

Abstract

The notion of concurrent zero knowledge has been introduced by Dwork et al. [STOC 1998] motivated by the growing use of asynchronous networks as the Internet.

In this paper we show a transformation that, for any language L admitting a Σ-protocol, produces a 4-round concurrent zero-knowledge argument system with concurrent soundness in the bare public-key (BPK, for short) model. The transformation only adds O(1) modular exponentiations, and uses standard number-theoretic assumptions and polynomial-time simulation.

A tool that we construct and use for our main result is that of efficient concurrent equivocal commitments. We give an efficient construction of this gadget in the BPK model that can be of independent interest.

Keywords

Proof System Discrete Logarithm Commitment Scheme Modular Exponentiation Common Reference String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof-Systems. In: proc. of (STOC 1985)., pp. 291–304 (1985)Google Scholar
  2. 2.
    Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: proc. of STOC, pp. 409–418. ACM, New York (1998)Google Scholar
  3. 3.
    Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-Box Concurrent Zero-Knowledge Requires ω(logn) Rounds. In: proc. of STOC, pp. 570–579. ACM Press, New York (2001)Google Scholar
  4. 4.
    Micciancio, D., Petrank, E.: Simulatable Commitments and Efficient Concurrent Zero-Knowledge. In: EUROCRYPT 2001, vol. 2045, pp. 140–159. Springer-Verlag, Heidelberg (2003)Google Scholar
  5. 5.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent Zero-Knowledge with Logarithmic Round Complexity. In: proc. of FOCS 2002, pp. 366–375 (2002)Google Scholar
  6. 6.
    Di Crescenzo, G., Ostrovsky, R.: On Concurrent Zero-Knowledge with Pre-processing (Extended Abstract). In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Blum, M., De Santis, A., Micali, S., Persiano, G.: Non-Interactive Zero-Knowledge. SIAM J. on Computing 20, 1084–1118 (1991)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Damgård, I.B.: Efficient Concurrent Zero-Knowledge in the Auxiliary String Model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, Springer, Heidelberg (2000)Google Scholar
  9. 9.
    Persiano, G., Visconti, I.: Single-Prover Concurrent Zero Knowledge in Almost Constant Rounds. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 228–240. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable Zero-Knowledge. In: proc. of STOC, pp. 235–244. ACM Press, New York (2000)Google Scholar
  11. 11.
    Micali, S., Reyzin, L.: Soundness in the Public-Key Model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, Springer, Heidelberg (2001)Google Scholar
  12. 12.
    Di Crescenzo, G., Persiano, G., Visconti, I.: Constant-Round Resettable Zero Knowledge with Concurrent Soundness in the Bare Public-Key Model. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 237–253. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Pass, R.: Simulation in Quasi-Polynomial Time and Its Applications to Protocol Composition. In: proc. of Eurocrypt 2003. LNCS, vol. 2045, pp. 160–176 (2003)Google Scholar
  14. 14.
    Brassard, J., Chaum, D., Crepéau, C.: Minimum Disclosure Proofs of Knowledge. Journal of Computer and System Science 37, 156–189 (1988)MATHCrossRefGoogle Scholar
  15. 15.
    Pass, R., Rosen, A.: New and Improved Constructions of Non-Malleable Cryptographic Protocols. In: proc. of STOC, pp. 533–542. ACM Press, New York (2005)Google Scholar
  16. 16.
    Di Crescenzo, G., Visconti, I.: Concurrent Zero Knowledge in the Public-Key Model. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 816–827. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Catalano, D., Visconti, I.: Hybrid Trapdoor Commitments and Their Applications. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 298–310. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Cramer, R.J.F., Schoenmakers, B., Damgård, I.B.: Proof 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
  19. 19.
    De Santis, A., Di Crescenzo, G., Persiano, G., Yung, M.: On Monotone Formula Closure of SZK. In: Proc. of FOCS, pp. 454–465 (1994)Google Scholar
  20. 20.
    Schnorr, C.P.: Efficient Signature Generation for Smart Cards. Journal of Cryptology 4, 239–252 (1991)CrossRefGoogle Scholar
  21. 21.
    Shamir, A., Feige, U.: Zero Knowledge Proofs of Knowledge in Two Rounds. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 526–544. Springer, Heidelberg (1990)Google Scholar
  22. 22.
    Damgård, I.B.: On the Existence of Bit Commitment Schemes and Zero-Knowledge Proofs. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 17–27. Springer, Heidelberg (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ivan Visconti
    • 1
  1. 1.Dip. di Informatica ed Appl.Università di SalernoBaronissiItaly

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