Abstract
We provide a new characterization of certain zero-knowledge protocols as non-interactive instance-dependent commitment-schemes (NIC). To obtain this result we consider the notion of V-bit protocols, which are very common, and found many applications in zero-knowledge. Our characterization result states that a protocol has a V-bit zero-knowledge protocol if and only if it has a NIC. The NIC inherits its hiding property from the zero-knowledge property of the protocol, and vice versa.
Our characterization result yields a framework that strengthens and simplifies many zero-knowledge protocols in various settings. For example, applying this framework to the result of Micciancio et al. [18] (who showed that some problems, including Graph-Nonisomorphism and Quadratic-Residuousity, unconditionally have a concurrent zero-knowledge proof) we easily get that arbitrary, monotone boolean formulae over a large class of problems (which contains, e.g., the complement of any random self-reducible problem) unconditionally have a concurrent zero-knowledge proof.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aiello, W., Håstad, J.: Statistical zero-knowledge languages can be recognized in two rounds. J. of Computer and System Sciences 42(3), 327–345 (1991)
Angluin, D., Lichtenstein, D.: Provable security in cryptosystems: a survey. Technical Report 288, Department of Computer Science, Yale University (1983)
Barak, B.: How to go beyond the black-box simulation barrier. In: FOCS, pp. 106–115 (2001)
Bellare, M., Micali, S., Ostrovsky, R.: Perfect zero-knowledge in constant rounds. In: 22nd STOC, pp. 482–493 (1990)
Blum, M.: How to prove a theorem so no one else can claim it. In: Proceedings of the ICM, pp. 1444–1451 (1986)
Boppana, R.B., Håstad, J., Zachos, S.: Does co-NP have short interactive proofs? Inf. Process. Lett. 25(2), 127–132 (1987)
Cramer, R.: Modular Design of Secure yet Practical Cryptographic Protocols. PhD thesis, CWI and Uni. of Amsterdam (1996)
Cramer, R., Damgård, I., MacKenzie, P.D.: Efficient zero-knowledge proofs of knowledge without intractability assumptions. In: Public Key Cryptography, pp. 354–372 (2000)
Dåmgard, I., Cramer, R.: On monotone function closure of perfect and statistical zero-knowledge (1996)
Damgård, I.B.: On the existence of bit commitment schemes and zero-knowledge proofs. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 17–27. Springer, Heidelberg (1990)
Damgård, I.B.: On Σ-protocols (2005), available online at www.daimi.au.dk/~ivan/Sigma.pdf
Fortnow, L.: The complexity of perfect zero-knowledge. In: Micali, S. (ed.) Advances in Computing Research, vol. 5, pp. 327–343. JAC Press (1989)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(3), 691–729 (1991)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
Itoh, T., Ohta, Y., Shizuya, H.: A language-dependent cryptographic primitive. J. Cryptology 10(1), 37–50 (1997)
Micali, S., Pass, R.: Local zero knowledge. In: STOC, pp. 306–315 (2006)
Micciancio, D., Ong, S.J., Sahai, A., Vadhan, S.P.: Concurrent zero knowledge without complexity assumptions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 1–20. Springer, Heidelberg (2006)
Micciancio, D., Vadhan, S.P.: Statistical zero-knowledge proofs with efficient provers: Lattice problems and more. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 282–298. Springer, Heidelberg (2003)
Naor, M.: Bit commitment using pseudorandomness. J. Cryptology 4(2), 151–158 (1991)
Nguyen, M.-H., Vadhan, S.: Zero knowledge with efficient provers. In: STOC 2006. Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, Seattle, WA, USA, pp. 287–295. ACM Press, New York (2006)
Ong, S.J., Vadhan, S.: Zero knowledge and soundness are symmetric. Electronic Colloquium on Computational Complexity (ECCC) (TR06-139) (2006)
Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS, pp. 366–375 (2002)
Sahai, A., Vadhan, S.P.: A complete problem for statistical zero-knowledge. J. ACM 50(2), 196–249 (2003)
De Santis, A., Di Crescenzo, G., Persiano, G., Yung, M.: On monotone formula closure of SZK. In: IEEE Symposium on Foundations of Computer Science, pp. 454–465. IEEE Computer Society Press, Los Alamitos (1994)
Tompa, M., Woll, H.: Random self-reducibility and zero-knowledge interactive proofs of possession of information. In: 28th FOCS, pp. 472–482 (1987)
Vadhan, S.P.: An unconditional study of computational zero knowledge. In: FOCS, pp. 176–185 (2004)
Watrous, J.: Zero-knowledge against quantum attacks. In: STOC, pp. 296–305 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kapron, B., Malka, L., Srinivasan, V. (2007). A Characterization of Non-interactive Instance-Dependent Commitment-Schemes (NIC). In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-73420-8_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73419-2
Online ISBN: 978-3-540-73420-8
eBook Packages: Computer ScienceComputer Science (R0)