A New Construction of Zero-Knowledge Sets Secure in Random Oracle Model

Zero knowledge sets is a new cryptographic primary in- troduced by Micali, Rabin, and Kilian in FOCS 2003. It is intensively investigated recently. However all schemes follow the basic frame by Micali et al. That is, the schemes employ Merkle tree as basic frame and mercurial com- mitments as commitment units to nodes of the tree. The proof for any query constitutes of an authentication chain. We propose in this paper a new algebraic scheme that is completely different from all existing schemes. The new scheme is computationally secure under standard assump- tion: Strong RSA assumption. It employs neither mercurial commitments nor tree frame as all previous schemes did. In fact, the prover (also as the committer) in our construc- tion commits the desired set without trapdoor information, which is another important difference from the previous ap- proaches.