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
Journal of the ACM (JACM)
On the Composition of Zero-Knowledge Proof Systems
SIAM Journal on Computing
Black-box concurrent zero-knowledge requires \tilde {Ω} (logn) rounds
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concurrent zero-knowledge with timing, revisited
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Strict polynomial-time in simulation and extraction
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
A Note on the Round-Complexity of Concurrent Zero-Knowledge
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Zero Knowledge Proofs of Knowledge in Two Rounds
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Lower Bounds for Zero Knowledge on the Internet
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Universal Arguments and their Applications
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
How to Go Beyond the Black-Box Simulation Barrier
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Journal of the ACM (JACM)
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the (Im)Possibility of Arthur-Merlin Witness Hiding Protocols
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
A Parallel Repetition Theorem for Any Interactive Argument
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Precise concurrent zero knowledge
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Which languages have 4-round zero-knowledge proofs?
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On constant-round concurrent zero-knowledge
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Eye for an eye: efficient concurrent zero-knowledge in the timing model
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
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We investigate the concrete security of black-box zero- knowledge protocols when composed in parallel. As our main result, we give essentially tight upper and lower bounds (up to logarithmic factors in the security parameter) on the following measure of security (closely related to knowledge tightness): the number of queries made by black-box simulators when zero-knowledge protocols are composed in parallel. As a function of the number of parallel sessions, k, and the round complexity of the protocol, m, the bound is roughly k1/m. We also construct a modular procedure to amplify simulator-query lower bounds (as above), to generic lower bounds in the black-box concurrent zero-knowledge setting. As a demonstration of our techniques, we give a self-contained proof of the o(logn /loglogn) lower bound for the round complexity of black-box concurrent zero-knowledge protocols, first shown by Canetti, Kilian, Petrank and Rosen (STOC 2002). Additionally, we give a new lower bound regarding constant-round black-box concurrent zero-knowledge protocols: the running time of the black-box simulator must be at least nΩ(logn).