Abstract
We examine the concurrent composition of zero-knowledge proofs. By concurrent composition, we indicate a single prover that is involved in multiple, simultaneous zero-knowledge proofs with one or multiple verifiers. Under this type of composition it is believed that standard zero-knowledge protocols are no longer zero-knowledge. We show that, modulo certain complexity assumptions, any statement in NP has k ∈-round proofs and arguments in which one can efficiently simulate any k O(1) concurrent executions of the protocol.
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G. Brassard, D. Chaum, C. Crépeau. Minimum Disclosure Proofs of Knowledge. Journal of Computer and System Sciences, Vol. 37, 1988, pp. 156–189.
C. Brassard, C. Crepeau and M. Yung, “Constant-Round Perfect Zero-Knowledge Computationally Convincing Protocols”, Theoretical Computer Science, Vol. 84, 1991, pp. 23–52.
T. Beth and Y. Desmedt. Identification tokens — or: Solving the chess grandmaster problem. In A. J. Menezes and S. A. Vanstone, editors, Proc. CRYPTO 90, pages 169–177. Springer-Verlag, 1991. Lecture Notes in Computer Science No. 537.
Damgård, Torben P. Pedersen, and Birgit Pfitzmann. On the existence of statistically hiding bit commitment schemes and fail-stop signatures. In Douglas R. Stinson, editor, Proc. CRYPTO 93, pages 250–265. Springer, 1994. Lecture Notes in Computer Science No. 773.
D. Dolev, C. Dwork, and M. Naor. Non-malleable cryptography. In ACM, editor, Proceedings of the twenty third annual ACM Symposium on Theory of Computing, New Orleans, Louisiana, May 6–8, 1991, pages 542–552, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA, 1991. IEEE Computer Society Press.
Cynthia Dwork, Moni Naor, and Amit Sahai. Concurrent zero knowledge. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 409–418, New York, May23–26 1998. ACM Press.
C. Dwork and A. Sahai. Concurrent zero-knowledge: Reducing the need for timing constraints. Lecture Notes in Computer Science, 1462, 1998.
U. Feige, D. Lapidot, and A. Shamir. Multiple non-interactive, zero-knowledge proofs based on a single random string. In Proc. 31st Ann. IEEE Symp. on Foundations of Computer Science, pages 308–317, 1990.
U. Feige and A. Shamir, “Zero Knowledge Proofs of Knowledge in Two Rounds”, Advances in Cryptology — Crypto 89 proceedings, pp. 526–544, 1990.
O. Goldreich, H. Krawczyk. On the Composition of Zero-Knowledge Proof Systems. SIAM J. on Computing, Vol. 25, No.1, pp. 169–192, 1996
S. Goldwasser, S. Micali, C. Rackoff. The Knowledge Complexity of Interactive Proofs. Proc. 17th STOC, 1985, pp. 291–304.
S. Goldwasser, S. Micali, C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM J. on Computing, Vol. 17, 2(1988), pp. 281–308.
S. Goldwasser, S. Micali, A. Wigderson. Proofs that Yield Nothing But their Validity or All Languages in NP have Zero-Knowledge Proofs. J. of the ACM, Vol. 38, No. 3, July 1991, pp. 691–729.
Johan Hastad, Russell Impagliazzo, Leonid A. Levin, and Michael Luby. Construction of a pseudo-random generator from any one-way function. Technical Report TR-91-068, International Computer Science Institute, Berkeley, CA, December 1991.
Kilian, Petrank, and Rackoff. Lower bounds for zero knowledge on the internet. In FOCS: IEEE Symposium on Foundations of Computer Science (FOCS), 1998.
Paul C. Kocher. Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In Neal Koblitz, editor, Advances in Cryptology—CRYPTO’ 96, volume 1109 of Lecture Notes in Computer Science, pages 104–113. Springer-Verlag, 18–22 August 1996.
Moni Naor. Bit commitment using pseudo-randomness. In Advances in Cryptology: CRYPTO’ 89, pages 128–137, Berlin, August 1990. Springer.
Y. Oren. On the cunning powers of cheating verifiers: Some observations about zero knowledge proofs. In Ashok K. Chandra, editor, Proceedings of the 28th Annual Symposium on Foundations of Computer Science, pages 462–471, Los Angeles, CA, October 1987. IEEE Computer Society Press.
R. Ostrovsky and G. Di Crescenzo. Personal Communication, September 15, 1998.
M. Tompa and H. Woll. Random self-reducibility and zero-knowledge interactive proofs of possession of information. In Proc. 28th Ann. IEEE Symp. on Foundations of Computer Science, pages 472–482, 1987.
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Richardson, R., Kilian, J. (1999). On the Concurrent Composition of Zero-Knowledge Proofs. In: Stern, J. (eds) Advances in Cryptology — EUROCRYPT ’99. EUROCRYPT 1999. Lecture Notes in Computer Science, vol 1592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48910-X_29
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DOI: https://doi.org/10.1007/3-540-48910-X_29
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