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
Multi-prover interactive proofs: how to remove intractability assumptions
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
Journal of the ACM (JACM)
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the power of multi-prover interactive protocols
Theoretical Computer Science
Probabilistically checkable proofs with zero knowledge
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Resettable zero-knowledge (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Low Communication 2-Prover Zero-Knowledge Proofs for NP
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
An Unconditional Study of Computational Zero Knowledge
SIAM Journal on Computing
Nondeterministic exponential time has two-prover interactive protocols
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Universally Composable Multi-party Computation Using Tamper-Proof Hardware
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Concurrent statistical zero-knowledge arguments for NP from one way functions
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
David and Goliath commitments: UC computation for asymmetric parties using tamper-proof hardware
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
New constructions for UC secure computation using tamper-proof hardware
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
An equivalence between zero knowledge and commitments
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Interactive locking, zero-knowledge PCPs, and unconditional cryptography
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Founding cryptography on tamper-proof hardware tokens
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Truly efficient string oblivious transfer using resettable tamper-proof tokens
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On efficient zero-knowledge PCPs
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Resettable statistical zero knowledge
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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A Zero-Knowledge PCP (ZK-PCP) is a randomized PCP such that the view of any (perhaps cheating) efficient verifier can be efficiently simulated up to small statistical distance. Kilian, Petrank, and Tardos (STOC '97) constructed ZK-PCPs for all languages in NEXP. Ishai, Mahmoody, and Sahai (TCC '12), motivated by cryptographic applications, revisited the possibility of efficient ZK-PCPs for all of NP where the PCP is encoded as a polynomial-size circuit that given a query i returns the ith symbol of the PCP. Ishai et al showed that there is no efficient ZK-PCP for NP with a non-adaptive verifier, that prepares all of its PCP queries before seeing any answers, unless NP⊆coAM and the polynomial-time hierarchy collapses. The question of whether adaptive verification can lead to efficient ZK-PCPs for NP remained open. In this work, we resolve this question and show that any language or promise problem with efficient ZK-PCPs must be in SZK (the class of promise problems with a statistical zero-knowledge single prover proof system). Therefore, no NP-complete problem can have an efficient ZK-PCP unless NP⊆SZK (which also implies NP⊆coAM and the polynomial-time hierarchy collapses). We prove our result by reducing any promise problem with an efficient ZK-PCP to two instances of the Conditional Entropy Approximation problem defined and studied by Vadhan (FOCS'04) which is known to be complete for the class SZK.