Mercurial Commitments with Applications to Zero-Knowledge Sets

We introduce a new flavor of commitment schemes, which we call mercurial commitments. Informally, mercurial commitments are standard commitments that have been extended to allow for soft decommitment. Soft decommitments, on the one hand, are not binding but, on the other hand, cannot be in conflict with true decommitments. We then demonstrate that a particular instantiation of mercurial commitments has been implicitly used by Micali, Rabin and Kilian to construct zero-knowledge sets. (A zero-knowledge set scheme allows a Prover to (1) commit to a set S in a way that reveals nothing about S and (2) prove to a Verifier, in zero-knowledge, statements of the form x ∈ S and x /∈ S.) The rather complicated construction of Micali et al. becomes easy to understand when viewed as a more general construction with mercurial commitments as an underlying building block. By providing mercurial commitments based on various assumptions, we obtain several different new zero-knowledge set constructions.