Efficient Concurrent Zero Knowledge Arguments for NP in the Bare Public-Key Model

Abstract

提出了一种从3轮公开掷币的对任何NP语言的诚实验证者零知识证明系统到纯公钥模型下4轮(轮最优)对同一语言的具有并发合理性的并发零知识证明系统.该转化方法有如下优点:1) 它只引起O(1)(常数个)额外的模指数运算,相比Di Crescenzo等人在ICALP 05上提出的需要((n)个额外的模指数运算的转化方法,该系统在效率上有着本质上的提高,而所需的困难性假设不变;2) 在离散对数假设下,该转化方法产生一个完美零知识证明系统.注意到Di Crescenzo等人提出的系统只具有计算零知识性质.该转化方法依赖于一个特殊的对承诺中的离散对数的3轮诚实验证者零知识的证明系统.构造了两个基于不同承诺方案的只需要常数个模指数运算的系统,这种系统可能有着独立价值.;This paper shows how to efficiently transform any 3-round public-coin honest verifier zero knowledge argument system for any language in NP into a 4 round (round-optimal) concurrent zero knowledge argument for the same language in the bare public-key model. The transformation has the following properties: 1) incurs only O(1) (small constant, about 20) additional modular exponentiations. Compared to the concurrent zero knowledge protocol proposed by Di Crescenzo and Visconti in ICALP 2005, in which their transformation requires an overhead of ((n), the protocol is significantly more efficient under the same intractability assumptions; 2) yields a perfect zero knowledge argument under DL assumption. Note that the Di Crescenzo, et al.'s argument system enjoys only computational zero knowledge property. The transformation relies on a specific 3-round honest verifier zero knowledge proof of knowledge for committed discrete log. Such protocols that require only O(1) modular exponentiations based on different kinds of commitment scheme are developed and they may be of independent interest.