Abstract
We introduce a notion of instance-dependent verifiable random functions (InstD-VRFs for short). Informally, an InstD-VRF is, in some sense, a verifiable random function [23] with a special public key, which is generated via a (possibly)interactive protocol and contains an instance y ∈ L ∩ {0,1}* for a specific NP language L, but the security requirements on such a function are relaxed: we only require the pseudorandomness property when y ∈ L and only require the uniqueness property when y ∉ L, instead of requiring both pseudorandomness and uniqueness to hold simultaneously. We show that this notion can be realized under standard assumption.
Our motivation is the conjecture posed by Barak et al.[2], which states there exist resettably-sound resettable zero knowledge arguments for NP. The instance-dependent verifiable random functions is a powerful tool to tackle this problem. We first use them to obtain two interesting instance-dependent argument systems from the Barak’s public-coin bounded concurrent zero knowledge argument [1], and then, we
-
1
Construct the first (constant round) zero knowledge arguments for NP enjoying a certain simultaneous resettability under standard hardness assumptions in the plain model, which we call bounded-class resettable ZK arguments with weak resettable-soundness Though the malicious party (prover or verifier) in such system is limited to a kind of bounded resetting attack, We put NO restrictions on the number of the total resets made by malicious party.
-
2
show that, under standard assumptions, if there exist public-coin concurrent zero knowledge arguments for NP, there exist the resettably-sound resetable zero knowledge arguments for NP.
This work is supported by the National Natural Science Foundation of China under Grant No. 60673069.
Chapter PDF
Similar content being viewed by others
References
Barak, B.: How to go beyond the black-box simulation barrier. In: Proc. of IEEE FOCS 2001, pp. 106–115 (2001)
Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably sound Zero Knowledge and its Applications. In: Proc. of IEEE FOCS 2001, pp. 116–125 (2001)
Barak, B., Goldreich, O.: Universal Arguments and Their Applications. In: Proc. of IEEE CCC 2002, pp. 194–203 (2002)
Blum, M.: How to Prove a Theorem so No One Else can Claim It. In: Proc. of ICM’86, pp. 1444–1451 (1986)
Barak, B., Lindell, Y., Vadhan, S.: Lower Bounds for Non-Black-Box Zero Knowledge. In: Proc. of IEEE FOCS 2003, pp. 384–393 (2003)
Blum, M., Micali, S.: How to Generate Cryptographically Strong Sequences of Pseudo Random Bits. In: Proc. of IEEE FOCS 1982, pp. 112–117 (1982)
Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: Proc. of IEEE FOCS 2001, pp. 136–145 (2001)
Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable Zero Knowledge. In: Proc. of ACM STOC 2000, pp. 235–244 (2000)
Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Concurrent Zero-Knowledge requires Ω(logn) rounds. In: Proc. of ACM STOC 2001, pp. 570–579 (2001)
Dwork, C., Naor, M.: Zaps and Their Applications. In: Proc. of IEEE FOCS 2000, pp. 283–293 (2000)
Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: Proc. of ACM STOC 1998, pp. 409–418 (1998)
Feige, U., Shamir, A.: Witness Indistinguishability and Witness Hiding Protocols. In: Proc. of ACM STOC 1990, pp. 416–426 (1990)
Goldreich, O.: Foundation of Cryptography-Basic Tools. Cambridge University Press, Cambridge (2001)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
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. Computing 18(1), 186–208 (1989)
Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive Zaps and New Techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006)
Hastad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A Pseudorandom Generator from Any One-Way Functions. SIAM Journal on Computing 28(4), 1364–1396 (1999)
Itoh, T., Ohta, Y.: A language-dependent cryptographic primitive. Journal of Cryptology 10(1), 37–49 (1997)
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)
Micali, S., Reyzin, L.: Soundness in the public-key model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 542–565. Springer, Heidelberg (2001)
Micali, S., Rivest, R.: Micropayments revisited. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 149–163. Springer, Heidelberg (2002)
Micali, S., Rabin, M., Vadhan, S.: Verifiable random functions. In: Proc. of IEEE FOCS, pp. 120–130 (1999)
Naor, M.: Bit Commitment using Pseudorandomness. Journal of Cryptology 4(2), 151–158 (1991)
Yao, A.: Theory and Applications of Trapdoor Functions. In: Proc. of IEEE FOCS 1982, pp. 80–91 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deng, Y., Lin, D. (2007). Instance-Dependent Verifiable Random Functions and Their Application to Simultaneous Resettability. In: Naor, M. (eds) Advances in Cryptology - EUROCRYPT 2007. EUROCRYPT 2007. Lecture Notes in Computer Science, vol 4515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72540-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-72540-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72539-8
Online ISBN: 978-3-540-72540-4
eBook Packages: Computer ScienceComputer Science (R0)