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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
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STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
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SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Everything provable is provable in zero-knowledge
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
Sparse pseudorandom distributions (extended abstract)
CRYPTO '89 Proceedings on Advances in cryptology
Making zero-knowledge provers efficient
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Interactive hashing simplifies zero-knowledge protocol design
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Foundations of Secure Interactive Computing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Cryptographically Strong Undeniable Signatures, Unconditionally Secure for the Signer
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge and Code Obfuscation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Responsive Round Complexity and Concurrent Zero-Knowledge
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On Defining Proofs of Knowledge
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
On the concurrent composition of zero-knowledge proofs
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
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In this paper we investigate some properties of zero-knowledge proofs, a notion introduced by Goldwasser, Micali and Rackoff. We introduce and classify various definitions of zero-knowledge. Two definitions which are of special interest are auxiliary-input zero-knowledge and blackbox-simulation zero-knowledge. We explain why auxiliary-input zero-knowledge is a definition more suitable for cryptographic applications than the original [GMR1] definition. In particular, we show that any protocol composed of subprotocols which are auxiliary-input zero-knowledge is itself auxiliary-input zero-knowledge. We show that blackbox simulation zero-knowledge implies auxiliary-input zeroknowledge (which in turn implies the [GMR1] definition). We argue that all known zero-knowledge proofs are in fact blackbox-simulation zero-knowledge (i.e. were proved zero-knowledge using blackbox-simulation of the verifier). As a result, all known zero-knowledge proof systems are shown to be auxiliary-input zero-knowledge and can be used for cryptographic applications such as those in [GMW2]. We demonstrate the triviality of certain classes of zero-knowledge proof systems, in the sense that only languages in BPP have zero-knowledge proofs of these classes. In particular, we show that any language having a Las vegas zeroknowledge proof system necessarily belongs to R. We show that randomness of both the verifier and the prover, and nontriviality of the interaction are essential properties of non-trivial auxiliary-input zero-knowledge proofs. In order to derive most of the results in the paper we make use of the full power of the definition of zero-knowledge: specifically, the requirement that there exist a simulator for any verifier, including "cheating verifiers".