The complexity of promise problems with applications to public-key cryptography
Information and Control
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Statistical zero-knowledge languages can be recognized in two rounds
Journal of Computer and System Sciences
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Journal of the ACM (JACM)
SIAM Journal on Computing
Interactive hashing can simplify zero-knowledge protocol design without computational assumptions
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
The knowledge complexity of quadratic residuosity languages
Theoretical Computer Science
Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On relationships between statistical zero-knowledge proofs
Journal of Computer and System Sciences
A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
Randomness-Efficient Non-Interactive Zero-Knowledge (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Image Density is Complete for Non-Interactive-SZK (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
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
On the knowledge complexity of N P
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
An Unconditional Study of Computational Zero Knowledge
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Zero knowledge with efficient provers
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Statistical Zero-Knowledge Arguments for NP from Any One-Way Function
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 1
Foundations of Cryptography: Volume 1
Random self-reducibility and zero knowledge interactive proofs of possession of information
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
A characterization of non-interactive instance-dependent commitment-schemes (NIC)
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Complete problem for perfect zero-knowledge quantum proof
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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We study perfect zero-knowledge proofs (PZK). Unlike statistical zero-knowledge, where many fundamental questions have been answered, virtually nothing is known about these proofs. We consider reductions that yield hard and complete problems in the statistical setting. The issue with these reductions is that they introduce errors into the simulation, and therefore they do not yield analogous problems in the perfect setting. We overcome this issue using an error shifting technique. This technique allows us to remove the error from the simulation. Consequently, we obtain the first complete problem for the class of problems possessing non-interactive perfect zero-knowledge proofs (NIPZK), and the first hard problem for the class of problems possessing public-coin PZK proofs. We get the following applications. Using the error shifting technique, we show that the notion of zero-knowledge where the simulator is allowed to fail is equivalent to the one where it is not allowed to fail. Using our complete problem, we show that under certain restrictions NIPZK is closed under the OR operator. Using our hard problem, we show how a constant-round, perfectly hiding instance-dependent commitment may be obtained (this would collapse the round complexity of public-coin PZK proofs to a constant).