NDLI: An Unconditional Study of Computational Zero Knowledge

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An Unconditional Study of Computational Zero Knowledge

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vadhan, Salil P.
Copyright Year	2006
Abstract	We prove a number of general theorems about ZK, the class of problems possessing computational zeroknowledge proofs. Our results are unconditional, in contrast to most previous works on ZK, which rely on the assumption that oneway functions exist. We establish several new characterizations of ZK and use these characterizations to prove results such as the following:1. Honestverifier ZK equals general ZK.2. Publiccoin ZK equals privatecoin ZK.3. ZK is closed under union.4. ZK with imperfect completeness equals ZK with perfect completeness.5. Any problem in ${\bf ZK} \cap {\bf NP}$ can be proven in computational zero knowledge by a ${\bf BPP}^{{\bf NP}}$ prover.6. ZK with blackbox simulators equals ZK with general, nonblackbox simulators.The above equalities refer to the resulting class of problems and do not necessarily preserve other efficiency measures such as round complexity. Our approach is to combine the conditional techniques previously used in the study of ZK with the unconditional techniques developed in the study of SZK, the class of problems possessing statistical zeroknowledge proofs. To enable this combination, we prove that every problem in ZK can be decomposed into a problem in SZK together with a set of instances from which a oneway function can be constructed.
Starting Page	1160
Ending Page	1214
Page Count	55
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539705447207
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4 (Special Issue on Randomness and Complexity)
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-12-15
Access Restriction	Subscribed
Subject Keyword	pseudoentropy cryptography languagedependent commitment schemes zeroknowledge proofs Cryptography auxiliaryinput oneway functions computational complexity Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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