Trading group theory for randomness
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
Minimum disclosure proofs of knowledge
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
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
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Applied combinatorics (3rd ed.)
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Computational Complexity and Knowledge Complexity
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
On the complexity of interactive proofs with bounded communication
Information Processing Letters
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantifying knowledge complexity
Computational Complexity
On relationships between statistical zero-knowledge proofs
Journal of Computer and System Sciences
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
On Resource-Bounded Measure and Pseudorandomness
Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science
A Complete Promise Problem for Statistical Zero-Knowledge
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Derandomizing Arthur-Merlin Games Using Hitting Sets
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the knowledge complexity of N P
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On efficient zero-knowledge PCPs
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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We continue the investigation of interactive proofs with bounded communication, as initiated by Goldreich and Håstad (IPL 1998). Let L be a language that has an interactive proof in which the prover sends few (say b) bits to the verifier. We prove that the complement L has a constant-round interactive proof of complexity that depends only exponentially on b. This provides the first evidence that for NP-complete languages, we cannot expect interactive provers to be much more "laconic" than the standard NP proof. When the proof system is further restricted (e.g., when b = 1, or when we have perfect completeness), we get significantly better upper bounds on the complexity of L.