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Definitions and properties of zero-knowledge proof systems. (English) Zbl 0791.94010
Summary: We investigate some properties of zero-knowledge proofs, a notion introduced by O. Goldwasser, S. Micali, and C. Rackoff [Proc. 17th STOC, 291-304 (1985)]. We introduce and classify two definitions of zero-knowledge: 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 definition. In particular we show that any protocol solely 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 zero-knowledge (which in turn implies the original definition). We argue that all known zero- knowledge proofs are in fact blackbox-simulation zero-knowledge (i.e., we 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 [O. Goldreich, S. Micali, and A. Wigderson, How to play any mental game or a completeness theorem for protocols with honest majority, Proc. 19th STOC, pp. 218-229 (1987)].
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 zero-knowledge proof system necessarily belongs to $$RP$$. We show that randomness of both the verifier and the prover, and nontriviality of the interaction are essential properties of (nontrivial) auxiliary-input zero-knowledge proofs.

##### MSC:
 94A60 Cryptography 68P25 Data encryption (aspects in computer science) 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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##### References:
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