Algebraic Construction for Zero-Knowledge Sets

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.