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Zero Knowledge Sets, introduced by Micali, Rabin and Kilian in [17], allow a prover to commit to a secret set S in a way such that it can later prove, non interactively, statements of the form x ∈ S (or x ∉ S), without revealing any further information (on top of what explicitly revealed by the inclusion/exclusion statements above) on S, not even its size. Later, Chase et al. [5] abstracted away the Micali, Rabin and Kilian’s construction by introducing an elegant new variant of commitments that they called (trapdoor) mercurial commitments. Using this primitive, it was shown in [5,4] how to construct zero knowledge sets from a variety of assumptions (both general and number theoretic).

In this paper we introduce the notion of trapdoor q-mercurial commitments (qTMCs), a notion of mercurial commitment that allows the sender to commit to an ordered sequence of exactly q messages, rather than to a single one. Following …