单向函数对于非平凡零知识是必不可少的

[1993] The 2nd Israel Symposium on Theory and Computing Systems Pub Date : 1993-06-07 DOI:10.1109/ISTCS.1993.253489

R. Ostrovsky, A. Wigderson

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引用次数: 165

摘要

如果单向函数存在，那么PSPACE中的每种语言都有零知识证明。作者证明了除非存在非常弱的单向函数，否则只能对BPP中的语言给出零知识证明。对于BPP的平均情形定义，他们在一致单向函数不存在的假设下证明了一个类似的结果。因此，非常宽松地说，零知识要么是无用的(只存在于“简单”的语言中)，要么是普遍的(存在于所有可证明的语言中)。

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One-way functions are essential for non-trivial zero-knowledge

If one-way functions exist, then there are zero-knowledge proofs for every language in PSPACE. The authors prove that unless very weak one-way functions exist, zero-knowledge proofs can be given only for languages in BPP. For average-case definitions of BPP they prove an analogous result under the assumption that uniform one-way functions do not exist. Thus, very loosely speaking, zero-knowledge is either useless (exists only for 'easy' languages), or universal (exists for every provable language).<>

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[1993] The 2nd Israel Symposium on Theory and Computing Systems

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