, Volume 7, Issue 1, pp 132
First online:
Definitions and properties of zeroknowledge proof systems
 Oded GoldreichAffiliated withDepartment of Computer Science, Technion
 , Yair OrenAffiliated withDepartment of Computer Science, Technion
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In this paper we investigate some properties of zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff. We introduce and classify two definitions of zeroknowledge: auxiliaryinput zeroknowledge and blackboxsimulation zeroknowledge. We explain why auxiliaryinput zeroknowledge is a definition more suitable for cryptographic applications than the original [GMR1] definition. In particular, we show that any protocol solely composed of subprotocols which are auxiliaryinput zeroknowledge is itself auxiliaryinput zeroknowledge. We show that blackboxsimulation zeroknowledge implies auxiliaryinput zeroknowledge (which in turn implies the [GMR1] definition). We argue that all known zeroknowledge proofs are in fact blackboxsimulation zeroknowledge (i.e., we proved zeroknowledge using blackboxsimulation of the verifier). As a result, all known zeroknowledge proof systems are shown to be auxiliaryinput zeroknowledge and can be used for cryptographic applications such as those in [GMW2].
We demonstrate the triviality of certain classes of zeroknowledge proof systems, in the sense that only languages in BPP have zeroknowledge proofs of these classes. In particular, we show that any language having a Las Vegas zeroknowledge 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) auxiliaryinput zeroknowledge proofs.
Key words
Zeroknowledge Computational complexity Computational indistinguishability Cryptographic composition of protocols Title
 Definitions and properties of zeroknowledge proof systems
 Journal

Journal of Cryptology
Volume 7, Issue 1 , pp 132
 Cover Date
 199412
 DOI
 10.1007/BF00195207
 Print ISSN
 09332790
 Online ISSN
 14321378
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Zeroknowledge
 Computational complexity
 Computational indistinguishability
 Cryptographic composition of protocols
 Industry Sectors
 Authors

 Oded Goldreich ^{(1)}
 Yair Oren ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Technion, Haifa, Israel