Abstract
A new public-key model for resettable zero-knowledge (rZK) protocols, which is an extension and generalization of the upper-bounded public-key (UPK) model introduced by Micali and Reyzin [EuroCrypt’01, pp. 373–393], is introduced and is named weak public-key (WPK) model. The motivations and applications of the WPK model are justified in the distributed smart-card/server setting and it seems more preferable in practice, especially in E-commerce over Internet. In this WPK model a 3-round (optimal) black-box resettable zero-knowledge argument with concurrent soundness for \( \mathcal{N}\mathcal{P} \) is presented assuming the security of RSA with large exponents against subexponential-time adversaries. Our result improves Micali and Reyzin’s result of resettable zero-knowledge argument with concurrent soundness for \( \mathcal{N}\mathcal{P} \) in the UPK model. Note that although Micali and Reyzin’ protocol satisfies concurrent soundness in the UPK model, but it does not satisfy even sequential soundness in our WPK model.
Our protocol works in a somewhat “parallel repetition” manner to reduce the error probability and the black-box zero-knowledge simulator works in strict polynomial time rather than expected polynomial time. The critical tools used are: verifiable random functions introduced by Micali, Rabin and Vadhan [FOCS’99, pp. 120–130], zap presented by Dwork and Naor [FOCS’00, pp. 283–293] and complexity leveraging introduced by Canetti, Goldreich, Goldwasser and Micali [STOC’00, pp. 235–244].
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References
B. Barak. How to Go Beyond the Black-Box Simulation Barrier. In IEEE Symposium on Foundations of Computer Science, pages 106–115, 2001.
M. Blum, A. D. Santis, S. Micali and G. Persiano. Non-interactive Zero-Knowledge. SIAM Journal on Computing, 20(6): 1084–1118, 1991.
M. Bellare, M. Fischlin, S. Goldwasser and S. Micali. Identification protocols secure against reset attacks. In B. Pfitzmann (Ed.): Advances in Cryptology-Proceedings of EUROCRYPT 2001, LNCS 2045, pages 495–511. Springer-Verlag, 2001.
M. Blum, P. Feldman and S. Micali. Non-interactive Zero-Knowledge and Its Applications. In ACM Symposium on Theory of Computing, pages 103–112, 1988.
M. Bellare, R. Impagliazzo and M. Naor. Does Parallel Repetition Lower the Error in Computationally Sound Protocols. In IEEE Symposium on Foundations of Computer Science, pages 374–383, 1997.
B. Barak and Y. Lindell. Strict Polynomial-Time in Simulation and Extraction. In ACM Symposium on Theory of Computing, pages 484–493, 2002.
R. Cramer and I. Damgard. Linear Zero-knowledge: A Note on Efficient Zero-Knowledge Proofs and Arguments. In ACM Symposium on Theory of Computing, pages 436–445, 1997.
R. Canetti, O. Goldreich, S. Goldwasser and S. Micali. Resettable Zero-Knowledge. In ACM Symposium on Theory of Computing, pages 235–244, 2000.
R. Canetti, J. Kilian, E. Petrank and A. Rosen. Black-Box Concurrent Zero-Knowledge Requires \( \tilde \Omega \) Rounds. In ACM Symposium on Theory of Computing, pages 570–579, 2001.
A. D. Santis, G. D. Crescenzo, R. Ostrovsky, G. Persiano and A. Sahai. Robust Non-Interactive Zero-Knowledge. In J. Kilian (Ed.): Advances in Cryptology-Proceedings of CRYPTO 2001, LNCS 2139, pages 566–598. Springer-Verlag, 2001.
C. Dwork and M. Naor. Zaps and Their Applications. In IEEE Symposium on Foundations of Computer Science, pages 283–293, 2000.
C. Dwork, M. Naor and A. Sahai. Concurrent Zero-Knowledge. In ACM Symposium on Theory of Computing, pages 409–418, 1998.
C. Dwork and L. Stockmeyer. 2-Round Zero-Knowledge and Proof Auditors. In ACM Symposium on Theory of Computing, pages 322–331, 2002.
U. Feige, A. Fiat and A. Shamir. Zero-knowledge Proof of Identity. Journal of Cryptology, 1(2): 77–94, 1988.
U. Feige, D. Lapidot and A. Shamir. Multiple Non-Interactive Zero-Knowledge Proofs Under General Assumptions. SIAM Journal on Computing, 29(1): 1–28, 1999.
A. Fiat and A. Shamir. How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In A. Odlyzko (Ed.): Advances in Cryptology-Proceedings of CRYPTO’86, LNCS 263, pages 186–194. Springer-Verlag, 1986.
O. Goldreich. Foundation of Cryptography-Basic Tools. Cambridge University Press, 2001.
S. Goldwasser and M. Bellare. Lecture Notes on Cryptography. 2001.
O. Goldreich, S. Goldwasser and S. Micali. How to Construct Random Functions. Journal of the Association for Computing Machinery, 33(4):792–807, 1986.
O. Goldreich and H. Krawczky. On the Composition of Zero-Knowledge Proof Systems. SIAM Journal on Computing, 25(1): 169–192, 1996.
J. Kilian, E. Petrank. An Efficient Non-Interactive Zero-Knowledge Proof System for \( \mathcal{N}\mathcal{P} \) with General Assumptions. Journal of Cryptology, 11(2): 24, 1998.
J. Kilian, E. Petrank, R. Richardson. Concurrent and Resettable Zero-Knowledge in Poly-Logarithmic Rounds. In ACM Symposium on Theory of Computing, pages 560–569, 2001.
A. Lysyanskaya. Unique Signatures and Verifiable Random Functions from the DH-DDH Separation. In M. Yung (Ed.): Advances in Cryptology-Proceedings of CRYPTO 2002, LNCS 2442, pages 597–612. Springer-Verlag, 2002.
S. Micali and L. Reyzin. Soundness in the Public-Key Model. In J. Kilian (Ed.): Advances in Cryptology-Proceedings of CRYPTO 2001, LNCS 2139, pages 542–565. Springer-Verlag, 2001.
S. Micali and L. Reyzin. Min-Round Resettable Zero-Knowledge in the Public-Key Model. In B. Pfitzmann (Ed.): Advances in Cryptology-Proceedings of EUROCRYPT 2001, LNCS 2045, pages 373–393. Springer-Verlag, 2001.
S. Micali, M. Rabin and S. Vadhan. Verifiable Random Functions. In IEEE Symposium on Foundations of Computer Science, pages 120–130, 1999.
L. Reyzin. Zero-Knowledge with Public Keys. Ph. D Thesis, MIT, 2001.
R. Richardson and J. Killian. On the Concurrent Composition of Zero-Knowledge Proofs. In J. Stern (Ed.): Advances in Cryptology-Proceedings of EUROCRYPT 1999, LNCS 1592, pages 415–423. Springer-Verlag, 1999.
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© 2003 International Association for Cryptologic Research
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Zhao, Y., Deng, X., Lee, C.H., Zhu, H. (2003). Resettable Zero-Knowledge in the Weak Public-Key Model. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_8
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DOI: https://doi.org/10.1007/3-540-39200-9_8
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