Can Statistical Zero Knowledge Be Made Noninteractive? or On the Relationship of SZK and NISZK
 Oded Goldreich,
 Amit Sahai,
 Salil Vadhan
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Abstract
We extend the study of noninteractive statistical zeroknowledge proofs. Our main focus is to compare the class NISZK of problems possessing such noninteractive proofs to the class SZK of problems possessing interactive statistical zeroknowledge proofs. Along these lines, we first show that if statistical zero knowledge is nontrivial then so is noninteractive statistical zero knowledge, where by nontrivial we mean that the class includes problems which are not solvable in probabilistic polynomialtime. (The hypothesis holds under various assumptions, such as the intractability of the Discrete Logarithm Problem.) Furthermore, we show that if NISZK is closed under complement, then in fact SZK = NISZK, i.e. all statistical zeroknowledge proofs can be made noninteractive.
The main tools in our analysis are two promise problems that are natural restrictions of promise problems known to be complete for SZK. We show that these restricted problems are in fact complete for NISZK and use this relationship to derive our results comparing the two classes. The two problems refer to the statistical difference, and difference in entropy, respectively, of a given distribution from the uniform one. We also consider a weak form of NISZK, in which only requires that for every inverse polynomial 1=p(n), there exists a simulator which achieves simulator deviation 1=p(n), and show that this weak form of NISZK actually equals NISZK.
 Title
 Can Statistical Zero Knowledge Be Made Noninteractive? or On the Relationship of SZK and NISZK
 Book Title
 Advances in Cryptology — CRYPTO’ 99
 Book Subtitle
 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings
 Pages
 pp 467484
 Copyright
 1999
 DOI
 10.1007/3540484051_30
 Print ISBN
 9783540663478
 Online ISBN
 9783540484059
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1666
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Statistical ZeroKnowledge Proofs
 NonInteractive ZeroKnowledge Proofs
 Industry Sectors
 eBook Packages
 Editors

 Michael Wiener ^{(4)}
 Editor Affiliations

 4. Entrust Technologies
 Authors

 Oded Goldreich ^{(5)}
 Amit Sahai ^{(5)}
 Salil Vadhan ^{(6)}
 Author Affiliations

 5. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel
 6. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
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