Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A perfect zero-knowledge proof for a problem equivalent to discrete logarithm
CRYPTO '88 Proceedings on Advances in cryptology
The (true) complexity of statistical zero knowledge
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Making zero-knowledge provers efficient
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the complexity of hyperelliptic discrete logarithm problem
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
How intractable is the discrete logarithm for a general finite group?
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Perfect NIZK with adaptive soundness
TCC'07 Proceedings of the 4th conference on Theory of cryptography
On the complexity of computational problems regarding distributions
Studies in complexity and cryptography
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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A hierarchy of probabilistic complexity classes generalizing NP has recently emerged in the work of [Ba], [GMR], and [GS]. The IP hierarchy is defined through the notion of an interactive proof system, in which an all powerful prover tries to convince a probabilistic polynomial time verifier that a string w is in a language L. The verifier tosses coins and exchanges messages back and forth with the prover before he decides whether to accept w. This proof-system yields "probabilistic" proofs: the verifier may erroneously accept or reject w with small probability. In [GMR] such a protocol was defined to be a zero-knowledge protocol if at the end of the interaction the verifier has learned nothing except that w ∈ L. We study complexity theoretic implications of a language having this property. In particular we prove that if L admits a zeroknowledge proof then L can also be recognized by a two round interactive proof. This complements a result by Fortnow [F] where it is proved that the complement of L has a two round interactive proof protocol. The methods of proof are quite similar to those of Fortnow [F]. As in his case the proof works under the assumption that the original protocol is only zero-knowledge with respect to a specific verifier.