## Cryptology ePrint Archive: Report 1998/026

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

*Oded Goldreich and Salil Vadhan*

**Abstract: **We consider the following (promise) problem, denoted ED (for Entropy
Difference): The input is a pairs 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.

**Category / Keywords: **Zero-Knowledge, Universal Hashing

**Publication Info: **Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive.

**Date: **received Dec 24th, 1998.

**Contact author: **salil at theory lcs mit edu

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

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