中文摘要：

零知识集合新密码的原语被 Micali， Rabin，和 Kilian 在 FOCS 2003 介绍。它最近强烈地被学习了。然而，所有存在 ZKS 计划由 Micali 等跟随基本结构。也就是说，计划作为承诺单位作为基本结构和水银的承诺采用 Merkle 树到树的节点。为任何询问的证明由认证链组成。我们在这篇论文建议与所有存在计划完全不同的一个新代数学的计划。我们的新计划是在标准强壮的 RSA 假设下面安全的计算联盟者。既不水银的承诺也不树结构在新构造被使用。事实上，没有任何地板门信息，在我们的构造的证明器承诺需要的集合，它是从以前的途径的另一关键重要差别。电子增补材料这篇文章(doi:10.1007/s11390-008-9119-x ) 的联机版本包含增补材料，它对授权用户可得到。

英文摘要：

Zero knowledge sets is a new cryptographic primitive introduced by Micali, Rabin, and Kilian in FOCS 2003. It has been intensively studied recently. However all the existing ZKS schemes follow the basic structure by Micali et al. That is, the schemes employ the Merkle tree as a basic structure and mercurial commitments as the commitment units to nodes of the tree. The proof for any query consists of an authentication chain. We propose in this paper a new algebraic scheme that is completely different from all the existing schemes. Our new scheme is computationally secure under the standard strong RSA assumption. Neither mercurial commitments nor tree structure is used in the new construction. In fact, the prover in our construction commits the desired set without any trapdoor information, which is another key important difference from the previous approaches.