Independent Zero-Knowledge Sets

We define and construct Independent Zero-Knowledge Sets (ZKS) protocols. In a ZKS protocols, a Prover commits to a set S, and for any x, proves non-interactively to a Verifier if x ∈ S or x / ∈ S without revealing any other information about S. In the independent ZKS protocols we introduce, the adversary is prevented from successfully correlate her set to the one of a honest prover. Our notion of independence in particular implies that the resulting ZKS protocol is non-malleable. On the way to this result we define the notion of independence for commitment schemes. It is shown that this notion implies non-malleability, and we argue that this new notion has the potential to simplify the design and security proof of non-malleable commitment schemes. Efficient implementations of ZKS protocols are based on the notion of mercurial commitments. Our efficient constructions of independent ZKS protocols requires the design of new commitment schemes that are simultaneously independent (and thus non-malleable) and mercurial.