Abstract
In the bare public-key model, introduced by Canetti et al. [STOC 2000], it is only assumed that each verifier deposits during a set-up phase a public key in a file accessible by all users at all times.As pointed out by Micali and Reyzin [Crypto 2001], the notion of soundness in this model is more subtle and complex than in the classical model. Indeed Micali and Reyzin have introduced four different notions which are called (from weaker to stronger): one-time, sequential, concurrent and resettable soundness. In this paper we introduce the counter public-key model (the cPK model for short), an augmentation of the bare public-key model in which each verifier is equipped with a counter and, like in the original bare public-key model, the key of the verifier can be used for any polynomial number of interactions with provers. In the cPK model, we give a three-round concurrently-sound resettable zero-knowledge argument of membership for NP. Previously similar results were obtained by Micali and Reyzin [EuroCrypt 2001] and then improved by Zhao et al. [EuroCrypt 2003] in models in which, roughly speaking, each verifier is still equipped with a counter, but the key of the verifier could only be used for a fixed number of interactions.
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References
Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof-Systems. SIAM J. on Computing 18, 186–208 (1989)
Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: Proceedings of the 30th ACM Symposium on Theory of Computing (STOC 1998), pp. 409–418. ACM, New York (1998)
Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable Zero-Knowledge. In: Proceedings of the 32nd ACM Symposium on Theory of Computing (STOC 2000), pp. 235–244. ACM, New York (2000)
Richardson, R., Kilian, J.: On the Concurrent Composition of Zero-Knowledge Proofs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 415–431. Springer, Heidelberg (1999)
Kilian, J., Petrank, E.: Concurrent and Resettable Zero-Knowledge in Poly-Logarithmic Rounds. In: Proceedings of the 33rd ACM Symposium on Theory of Computing (STOC 2001), pp. 560–569. ACM, New York (2001)
Kilian, J., Petrank, E., Rackoff, C.: Lower Bounds for Zero Knowledge on the Internet. In: Proceedings of the 39th Symposium on Foundations of Computer Science (FOCS 1998), pp. 484–492 (1998)
Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-Box Concurrent Zero-Knowledge Requires ω(logn) Rounds. In: Proceedings of the 33rd ACM Symposium on Theory of Computing (STOC 2001), pp. 570–579. ACM, New York (2001)
Dwork, C., Sahai, A.: Concurrent Zero-Knowledge: Reducing the Need for Timing Constraints. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 442–457. Springer, Heidelberg (1998)
Goldreich, O.: Concurrent Zero-Knowledge with Timing, Revisited. In: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC 2002), pp. 332–340. ACM, New York (2002)
Blum, M., De Santis, A., Micali, S., Persiano, G.: Non-Interactive Zero-Knowledge. SIAM J. on Computing 20, 1084–1118 (1991)
Damgard, I.: Efficient Concurrent Zero-Knowledge in the Auxiliary String Model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 418–430. Springer, Heidelberg (2000)
Di Crescenzo, G.: Removing Complexity Assumptions from Concurrent Zero-Knowledge Proofs. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, p. 426. Springer, Heidelberg (2000)
Di Crescenzo, G., Ostrovsky, R.: On Concurrent Zero-Knowledge with Pre-processing. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 485. Springer, Heidelberg (1999)
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)
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)
Reyzin, L.: Zero-Knowledge with Public Keys, Ph.D. Thesis. MIT (2001)
Micali, S., Reyzin, L.: Min-Round Resettable Zero-Knowledge in the Public-key Model. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 373–393. Springer, Heidelberg (2001)
Zhao, Y., Deng, X., Lee, C., Zhu, H.: ResettableZero-Knowledge in the Weak Public-Key Model. In: EUROCRYPT 2001. LNCS, vol. 2045, pp. 123–139. Springer, Heidelberg (2003)
Rompel, J.: One-Way Functions are Necessary and Sufficient for Digital Signatures. In: Proceedings of the 22nd ACM Symposium on Theory of Computing (STOC 1990), pp. 12–19 (1990)
Pass, R.: Simulation in Quasi-Polynomial Time and Its Applications to Protocol Composition. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 160–176. Springer, Heidelberg (2001)
Dwork, C., Naor, M.: Zaps and their applications. In: IEEE Symposium on Foundations of Computer Science, pp. 283–293 (2000)
Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably-Sound Zero-Znowledge and its Applications. In: Proceeding of the 42nd Symposium on Foundations of Computer Science (FOCS 2001), pp. 116–125 (2001)
Feige, U., Lapidot, D., Shamir, A.: Multiple Non-Interactive Zero Knowledge Proofs Under General Assumptions. SIAM J. on Computing 29, 1–28 (1999)
De Santis, A., Persiano, G.: Zero-Knowledge Proofs of Knowledge Without Interaction. In: Proceedings of the 33rd Symposium on Foundations of Computer Science (FOCS 1992), pp. 427–436 (1992)
Lapidot, D., Shamir, A.: Publicly Verifiable Non-Interactive Zero-Knowledge Proofs. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 353–365. Springer, Heidelberg (1991)
Katz, J., Ostrovsky, R.: Round-Optimal Secure Two-Party Computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004)
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Di Crescenzo, G., Persiano, G., Visconti, I. (2004). Improved Setup Assumptions for 3-Round Resettable Zero Knowledge. In: Lee, P.J. (eds) Advances in Cryptology - ASIACRYPT 2004. ASIACRYPT 2004. Lecture Notes in Computer Science, vol 3329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30539-2_37
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