Relations among Two-Party Commitment Resources and Optimality Results

Commitment schemes that come along with a zero-knowledge proof allow a prover to commit to a set of bits b1, . . . ,bn and at some later point prove that some predicate P (b1, . . . ,bn) holds. Some constructions in the literature of this particular resource have been investigated, but they do not emphasize on the composability property of the construction and usually do not present optimality results. In this thesis we formalize a large class of protocols in the constructive cryptography framework for a concrete problem, i.e. constructing commitment schemes that allow an inequality proof from commitment schemes that allow an equality proof, and present an optimality result on the soundness of such protocols, measured on the number of additional commitments. We also present a construction for commitment schemes with arbitrary relations.

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