We give a construction of a non-interactive zero-knowledge (NIZK) argument for all \({\textsf{NP}}\) languages based on a succinct non-interactive argument (SNARG) for all \({\textsf{NP}}\) languages and a one-way function. The succinctness requirement for the SNARG is rather mild: We only require that the proof size be \(|\pi |={\textsf{poly}}(\lambda )(|x|+|w|)^\delta \) for some constant \(\delta <1\), where |x| is the statement length, |w| is the witness length, and \(\lambda \) is the security parameter. Especially, we do not require the efficiency of the verification to be sublinear in |x| or |w|. As a corollary, we give a generic conversion from a SNARK to a zero-knowledge SNARG assuming the existence of one-way functions where SNARK is a SNARG with knowledge-extractability. For this conversion, we require the SNARK to be fully succinct, i.e., the proof size is \({\textsf{poly}}(\lambda )(|x|+|w|)^{o(1)}\). Before this work, such a conversion was only known if we additionally assume the existence of a NIZK. Along the way of obtaining our result, we give a generic compiler to upgrade a NIZK for all \({\textsf{NP}}\) languages with non-adaptive zero-knowledge to one with adaptive zero-knowledge. Though this can be shown by carefully combining known results, to the best of our knowledge, no explicit proof of this generic conversion has been presented.

我们基于对所有\ ({\textsf{ NP} }}\)语言和一个单向函数。SNARG 的简洁性要求相当温和：我们只要求证明大小为\(|\pi |={\textsf{poly}}(\lambda )(|x|+|w|)^\delta \)对于一些常量\(\delta <1\)，其中 | × | 是语句长度，| 瓦| 是见证长度，\(\lambda\)是安全参数。特别是，我们不要求验证效率在|中是次线性的。× | 或 | w|。作为推论，我们给出了从 SNARK 到零知识 SNARG 的通用转换，假设存在单向函数，其中 SNARK 是具有知识可提取性的 SNARG。对于这种转换，我们要求 SNARK 完全简洁，即证明大小为\({\textsf{poly}}(\lambda )(|x|+|w|)^{o(1)}\) . 在这项工作之前，只有当我们另外假设存在 NIZK 时，这种转换才为人所知。在获得结果的过程中，我们提供了一个通用编译器，可以将所有具有非自适应零知识的\({\textsf{NP}}\)语言的 NIZK 升级为具有自适应零知识的语言。虽然这可以通过仔细组合已知结果来证明，但据我们所知，还没有提供这种通用转换的明确证据。