Non-interactive Zaps and New Techniques for NIZK
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In 2000, Dwork and Naor proved a very surprising result: that there exist “Zaps”, two-round witness-indistinguishable proofs in the plain model without a common reference string, where the Verifier asks a single question and the Prover sends back a single answer. This left open the following tantalizing question: does there exist a non-interactive witness indistinguishable proof, where the Prover sends a single message to the Verifier for some non-trivial NP-language? In 2003, Barak, Ong and Vadhan answered this question affirmatively by derandomizing Dwork and Naor’s construction under a complexity theoretic assumption, namely that Hitting Set Generators against co-nondeterministic circuits exist.
In this paper, we construct non-interactive Zaps for all NP-languages. We accomplish this by introducing new techniques for building Non-Interactive Zero Knowledge (NIZK) Proof and Argument systems, which we believe to be of independent interest, and then modifying these to yield our main result. Our construction is based on the Decisional Linear Assumption, which can be seen as a bilinear group variant of the Decisional Diffie-Hellman Assumption.
Furthermore, our single message witness-indistinguishable proof for Circuit Satisfiability is of size O(k|C|) bits, where k is a security parameter, and |C| is the size of the circuit. This is much more efficient than previous constructions of 1- or 2-move Zaps.
KeywordsNon-interactive zero-knowledge witness indistinguishability bilinear groups Decisional Linear Assumption
- [BBS04]Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)Google Scholar
- [BFM88]Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: Proceedings of STOC 1988, pp. 103–112 (1988)Google Scholar
- [DN00]Dwork, C., Naor, M.: Zaps and their applications. In: Proceedings of FOCS 2000, pp. 283–293 (2000)Google Scholar
- [FLS99]Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs under general assumptions. SIAM Journal of Computing 29(1), 1–28 (1999); Earlier version entitled Multiple Non-Interactive Zero Knowledge Proofs Based on a Single Random String appeared at FOCS (1990) zbMATHCrossRefMathSciNetGoogle Scholar
- [FS90]Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: Proceedings of STOC 1990, pp. 416–426 (1990)Google Scholar
- [Gro06]Groth, J.: Simulation-sound non-interactive zero-knowledge proofs for a practical language and constant size group signatures (manuscript, 2006)Google Scholar