Comparing Entropies in Statistical Zero Knowledge with Applications to the Structure of SZK

  • Authors:
  • Oded Goldreich;Salil Vadhan

  • Affiliations:
  • -;-

  • Venue:
  • COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
  • Year:
  • 1999

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Abstract

We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pair of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy.On one hand we show that any language having a (honest-verifier) statistical zero-knowledge proof is Karp-reducible to ED. On the other hand, we present a public-coin (honest-verifier) statistical zero-knowledge proof for ED. Thus, we obtain an alternative proof of Okamoto's result by which HVSZK (i.e., honest-verifier statistical zero knowledge) equals public-coin HVSZK. The new proof is much simpler than the original one. The above also yields a trivial proof that HVSZK is closed under complementation (since ED easily reduces to its complement). Among the new results obtained is an equivalence of a weak notion of statistical zero knowledge to the standard one.