Identity-based trapdoor mercurial commitments and applications

In this paper, we first introduce the notion of identity-based trapdoor mercurial commitment which enjoys the advantages of both the identity-based trapdoor commitment and trapdoor mercurial commitment, while using the idea of “Customized Identity”. Inherently, an identity-based trapdoor mercurial commitment is an underlying building block for constructing identity-based (non-interactive) zero-knowledge sets. That is, a prover can commit to a set S in a way that reveals nothing about S and prove to a verifier, in zero-knowledge, statements of the form x∈S and x∉S. Besides, although the (non-interactive) proof is publicly verifiable, it is also bound to the identity of the prover in a way which is recognizable to any verifier.