Mercurial Commitments from General RSA Moduli and Their Applications to Zero-Knowledge Databases/Sets

The contribution of this paper is two-fold. In the first fold, a novel construction of mercurial commitments from the general RSA moduli is presented which is provably secure in the trusted-parameter model assuming that the RSA problem is hard. In the second fold, an immediate application of mercurial commitments from general RSA moduli to zero-knowledge sets is proposed which is provably secure in the trusted-parameter model under the joint assumptions that the RSA problem is hard and collision-free hash functions exist. To the best of our knowledge, this is the first implementation of zero-knowledge sets from the general RSA moduli.