Abstract
Loosely speaking, an interactive proof is said to be zero-knowledge if the view of every “efficient” verifier can be “efficiently” simulated. An outstanding open question regarding zero-knowledge is whether constant-round concurrent zero-knowledge proofs exists for non-trivial languages. We answer this question to the affirmative when modeling “efficient adversaries” as probabilistic quasi-polynomial time machines (instead of the traditional notion of probabilistic polynomial-time machines).
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References
Barak, B., Lindell, Y.: Strict Polynomial-Time in Simulation and Extraction. In: 34th STOC, pp. 484–493 (2002)
Benaloh, J.D.: Cryptographic Capsules: A disjunctive primitive for interactive protocols. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 213–222. Springer, Heidelberg (1987)
Brassard, G., Chaum, D., Crépeau, C.: Minimum Disclosure Proofs of Knowledge. JCSS 37(2), 156–189 (1988); Preliminary version by Brassard and Crépeau. In: 27th FOCS (1986)
Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable Zero-Knowledge. In: 32nd STOC, pp. 235–244 (2000)
Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-Box Concurrent Zero-Knowledge Requires (almost) Logarithmically Many Rounds. SIAM Jour. on Computing 32(1), 1–47 (2002)
Damgård, 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)
Damgård, I., Pedersen, T., Pfitzmann, B.: On the Existence of Statistically Hiding Bit Commitment Schemes and Fail-Stop Signatures. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 250–265. Springer, Heidelberg (1994)
Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: 30th STOC, pp. 409–418 (1998)
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)
Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 181–187. Springer, Heidelberg (1987)
Goldreich, O., Kahan, A.: How to Construct Constant-Round Zero-Knowledge Proof Systems for NP. Jour. of Cryptology 9(2), 167–189 (1996)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that Yield Nothing But Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems. JACM 38(1), 691–729 (1991)
Goldreich, O., Oren, Y.: Definitions and Properties of Zero-Knowledge Proof Systems. Jour. of Cryptology 7(1), 1–32 (1994)
Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof Systems. SIAM Jour. on Computing 18(1), 186–208 (1989)
Halevi, S., Micali, S.: Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996)
Kilian, J., Petrank, E.: Concurrent and Resettable Zero-Knowledge in Poly-logarithmic Rounds. In: 33rd STOC, pp. 560–569 (2001)
Kilian, J., Petrank, E., Rackoff, C.: Lower Bounds for Zero-Knowledge on the Internet. In: 39th FOCS, pp. 484–492 (1998)
Micali, S., Pass, R.: Local Zero Knowledge. In: STOC 2006 (2006)
Pandey, O., Pass, R., Sahai, A., Tseng, D., Venkitasubramaniam, M.: Precise Concurrent Zero-Knowledge (manuscript)
Pass, R.: A Precise Computational Approach to Knowledge. PhD thesis, MIT (2006)
Pass, R.: Simulation in Quasi-Polynomial Time and Its Application to Protocol Composition. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 160–176. Springer, Heidelberg (2003)
Pass, R., Rosen, A.: Bounded-Concurrent Two-Party Computation in Constant Number of Rounds. In: 44th FOCS, pp. 404–413 (2003)
Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent Zero-Knowledge with Logarithmic Round Complexity. In: 43rd FOCS, pp. 366–375 (2002)
Pass, R., Tseng, D., Venkitasubramaniam, M.: Concurrent Zero Knowledge: A Simplified Proof (submission)
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)
Rosen, A.: A note on the round-complexity of Concurrent Zero-Knowledge. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 451–468. Springer, Heidelberg (2000)
Goldwasser, S., Micali, S.: Probabilistic Encryption. JCSS 28(2), 270–299 (1984)
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Pass, R., Venkitasubramaniam, M. (2008). On Constant-Round Concurrent Zero-Knowledge. In: Canetti, R. (eds) Theory of Cryptography. TCC 2008. Lecture Notes in Computer Science, vol 4948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78524-8_30
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