Comparing entropies in statistical zero knowledge with applications to the structure of SZK

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-04 DOI:10.1109/CCC.1999.766262

Oded Goldreich, S. Vadhan

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引用次数: 90

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.

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统计零知识中的熵与SZK结构的应用比较

我们考虑以下(承诺)问题，表示为ED(熵差):输入是一对电路，并且有YES实例(响应)。， NO实例)是这样的对，其中第一个(响应)。(第二)电路产生的分布具有明显更高的熵。一方面，我们证明了任何具有(诚实验证者)统计零知识证明的语言都是karp可约为ED的。另一方面，我们提出了一个关于ED的公共币(诚实验证者)统计零知识证明。从而，我们获得了Okamoto结果的替代证明:HVSZK(即，诚实验证者统计零知识)等于公共币HVSZK。新的证明比原来的简单得多。以上也证明了HVSZK:在补下是闭的(因为ED很容易约简为它的补)。得到的新结果之一是统计零知识的弱概念与标准概念的等价。

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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

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