Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Minimum disclosure proofs of knowledge
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Zero-knowledge proofs of identity
Journal of Cryptology
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Witness indistinguishable and witness hiding protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Uses of randomness in algorithms and protocols
Uses of randomness in algorithms and protocols
Journal of the ACM (JACM)
SIAM Journal on Computing
Finite state verifiers II: zero knowledge
Journal of the ACM (JACM)
On the Composition of Zero-Knowledge Proof Systems
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
One-Message Statistical Zero-Knowledge Proofs and Space-Bounded Verifier
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Zero Knowledge Proofs of Knowledge in Two Rounds
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Zero-knowledge with log-space verifiers
SFCS '88 Proceedings of the 29th 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
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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We construct a proof system for any NP statement, in which the proof is a single message sent from the prover to the verifier. No other interaction is required, neither before nor after this single message is sent. In the "envelope" model, the prover sends a sequence of envelopes to the verifier, where each envelope contains one bit of the prover's proof. It suffices for the verifier to open a constant number of envelopes in order to verify the correctness of the proof (in a probabilistic sense). Even if the verifier opens polynomially many envelopes, the proof remains perfectly zero knowledge.We transform this proof system to the "known-space verifier" model of De-Santis et al. [7]. In this model it suffices for the verifier to have space Smin in order to verify proof, and the proof should remain statistically zero knowledge with respect to verifiers that use space at most Smax. We resolve an open question of [7], showing that arbitrary ratios Smax/Smin are achievable. However, we question the extent to which these proof systems (that of [7] and ours) are really zero knowledge. We do show that our proof system is witness indistinguishable, and hence has applications in cryptographic scenarios such as identification schemes.