Abstract
In this paper we make some observations on the zaps and their applications developed by Dwork and Naor [13]. We clarify the relations among public-coin witness indistinguishability (WI), public-coin honest verifier zero-knowledge (HVZK) and public-coin special honest verifier zero-knowledge (SHVZK). Specifically, we observe that the existence of zaps under the existence of one-way permutations actually strictly separates public-coin WI and public-coin SHVZK assuming \(\mathcal{NP}\nsubseteqq \mathcal{BPP}\) . We also show that public-coin HVZK does not implies WI assuming the existence of one-way permutations. For zap-based applications, we present an improved Dwork-Naor 2-round timed deniable authentication scheme that improves the communication and computation complexity of the original protocol presented by Dwork and Naor [13]. Specifically, in the improved protocol the first message (from the verifier to the authenticator) is independent on the message to be authenticated by the authenticator.
This research is supported by a research grant of City University of Hong Kong (No. 7001358).
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Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations Among Notions of Security for Public-Key Encryption Schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)
Bellare, M., Sahai, A.: Non-Malleable Encryption: Equivalence between Two Notions and an Indistinguishability-Based Characterization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 519–536. Springer, Heidelberg (1999)
Boneh, D., Naor, M.: Timed Commitments and Applications. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000)
Cramer, R., Damgard, I.: On Electronic Payment Systems. A lecture note for the course of Cryptographic Protocol Theory at Aarhus University (2003), Available from: http://www.daimi.au.dk/~ivan/CPT.html
Cramer, R., Damgard, I., Schoenmakers, B.: Proofs 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)
Cramer, R., Shoup, V.: A Practical Public-Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)
Damgard, I.: On Σ-protocols. A lecture note for the course of Cryptographic Protocol Theory at Aarhus University (2003), Available from: http://www.daimi.au.dk/~ivan/CPT.html
Santis, D., Crescenzo, G.D., Ostrovsky, R., Persiano, G., Sahai, A.: Robust Non-Interactive Zero-Knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 566–598. Springer, Heidelberg (2001)
Santis, A.D., Persiano, G.: Zero-Knowledge Proofs of Knowledge Without Interaction. In: IEEE Symposium on Foundations of Computer Science, pp. 427–436 (1992)
Dolev, D., Dwork, C., Naor, M.: Non-Malleable Cryptography. In: ACM Symposium on Theory of Computing, pp. 542–552 (1991)
Dwork, C., Naor, M.: Pricing via Processing-or-Combatting Junk Mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993)
Dwork, C., Naor, M.: Method for Message Authentication from Non-Malleable Crypto Systems. US Patent No. 05539826, issued August 29 (1996)
Dwork, C., Naor, M.: Zaps and Their Applications. In: IEEE Symposium on Foundations of Computer Science, pp. 283-293 (2000), Available on-line from: http://www.wisdom.weizmann.ac.il/~naor/
Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: ACM Symposium on Theory of Computing, 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)
Dwork, C., Stockmeyer, L.: 2-Round Zero-Knowledge and Proof Auditors. In: ACM Symposium on Theory of Computing, pp. 322–331 (2002)
Feige, U., Lapidot, D., Shamir, A.: Multiple Non-Interactive Zero-Knowledge Proofs Under General Assumptions. SIAM Journal on Computing 29(1), 1–28 (1999)
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. 186–194. Springer, Heidelberg (1987)
Goldreich, O.: Concurrent Zero-Knowledge with Timing, Revisited. In: ACM Symposium on Theory of Computing, pp. 332–340 (2002)
Goldreich, O., Oren, Y.: Definitions and Properties of Zero-Knowledge Proof Systems. Journal of Cryptology 7(1), 1–32 (1994)
Kilian, J., Petrank, E.: An Efficient Non-Interactive Zero-Knowledge Proof System for NP with General Assumptions. Journal of Cryptology 11(2), 24 (1998)
Lindell, Y.: A Simple Construction of CCA2-Secure Public-Key Enryption Under General Assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 241–255. Springer, Heidelberg (2003)
Naor, M., Yung, M.: Public-Key Cryptosystems Provably Secure Against Chosen Ciphertext Attacks. In: ACM Symposium on Theory of Computing, pp. 427–437 (1990)
Pass, R.: Simulation in Quasi-Polynomial Time, and Its Application to Protocol Composition. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 160–177. Springer, Heidelberg (2003)
Sahai, A.: Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen Ciphertext Security. In: IEEE Symposium on Foundations of Computer Science, pp. 543–553 (1999)
Zhao, Y., Deng, X., Lee, C.H., Zhu, H.: Resettable Zero-Knowledge in the Weak Public-Key Model. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 123–140. Springer, Heidelberg (2003)
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Zhao, Y., Lee, C.H., Zhao, Y., Zhu, H. (2004). Some Observations on Zap and Its Applications. In: Jakobsson, M., Yung, M., Zhou, J. (eds) Applied Cryptography and Network Security. ACNS 2004. Lecture Notes in Computer Science, vol 3089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24852-1_13
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