Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A note on computational indistinguishability
Information Processing Letters
Statistical zero-knowledge languages can be recognized in two rounds
Journal of Computer and System Sciences
SIAM Journal on Computing
On relationships between statistical zero-knowledge proofs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Universally composable two-party and multi-party secure computation
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
Image Density is Complete for Non-Interactive-SZK (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Can Statistical Zero Knowledge Be Made Non-interactive? or On the Relationship of SZK and NISZK
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Robust Non-interactive Zero Knowledge
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive Zero-Knowledge Proof Systems
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Non-Interactive Zero-Knowledge with Preprocessing
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Comparing Entropies in Statistical Zero Knowledge with Applications to the Structure of SZK
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
An Unconditional Study of Computational Zero Knowledge
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 1
Foundations of Cryptography: Volume 1
Minimum resource zero knowledge proofs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Multiple non-interactive zero knowledge proofs based on a single random string
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Non-interactive circuit based proofs and non-interactive perfect zero-knowledge with preprocessing
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Efficient concurrent zero-knowledge in the auxiliary string model
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Lower bounds for non-interactive zero-knowledge
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Perfect NIZK with adaptive soundness
TCC'07 Proceedings of the 4th conference on Theory of cryptography
The complexity of zero knowledge
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Interactive and noninteractive zero knowledge are equivalent in the help model
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Construction of a non-malleable encryption scheme from any semantically secure one
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
New Techniques for Noninteractive Zero-Knowledge
Journal of the ACM (JACM)
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Non-interactive zero-knowledge (NIZK) proofs have been investigated in two models: the Public Parameter model and the Secret Parameter model. In the former, a public string is “ideally” chosen according to some efficiently samplable distribution and made available to both the Prover and Verifier. In the latter, the parties instead obtain correlated (possibly different) private strings. To add further choice, the definition of zero-knowledge in these settings can either be non-adaptive or adaptive. In this paper, we obtain several unconditional characterizations of computational, statistical and perfect NIZK for all combinations of these settings. Specifically, we show: In the secret parameter model, NIZK = NISZK = NIPZK = AM. In the public parameter model, – for the non-adaptive definition, NISZK ⊆ AM ∩ coAM, – for the adaptive one, it also holds that NISZK ⊂ BPP, – for computational NIZK for “hard” languages, one-way functions are both necessary and sufficient. From our last result, we arrive at the following unconditional characterization of computational NIZK in the public parameter model (which complements well-known results for interactive zero-knowledge): Either NIZK proofs exist only for “easy” languages (i.e., languages that are not hard-on-average), or they exist for all of AM (i.e., all languages which admit non-interactive proofs).