Can Statistical Zero Knowledge Be Made Non-interactive? or On the Relationship of SZK and NISZK

Extended Abstract
  • Oded Goldreich
  • Amit Sahai
  • Salil Vadhan
Conference paper

DOI: 10.1007/3-540-48405-1_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1666)
Cite this paper as:
Goldreich O., Sahai A., Vadhan S. (1999) Can Statistical Zero Knowledge Be Made Non-interactive? or On the Relationship of SZK and NISZK. In: Wiener M. (eds) Advances in Cryptology — CRYPTO’ 99. CRYPTO 1999. Lecture Notes in Computer Science, vol 1666. Springer, Berlin, Heidelberg

Abstract

We extend the study of non-interactive statistical zero-knowledge proofs. Our main focus is to compare the class NISZK of problems possessing such non-interactive proofs to the class SZK of problems possessing interactive statistical zero-knowledge proofs. Along these lines, we first show that if statistical zero knowledge is non-trivial then so is non-interactive statistical zero knowledge, where by non-trivial we mean that the class includes problems which are not solvable in probabilistic polynomial-time. (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 zero-knowledge proofs can be made non-interactive.

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.

Keywords

Statistical Zero-Knowledge Proofs Non-Interactive Zero-Knowledge Proofs 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Oded Goldreich
    • 1
  • Amit Sahai
    • 1
  • Salil Vadhan
    • 2
  1. 1.Department of Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

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