Interactive and zero-knowledge proofs

Abstract

An interactive proof involves two parties, the prover and the verifier. The goal of the proof is for the prover to convince the verifier that some instance of a decision problem is true. A zero-knowledge proof is an interactive proof where the only information learned by the verifier of the proof is the outcome of the proof. This thesis contains a theoretical overview of interactive and zero-knowledge proofs and describes experiments with implementations of some of them. Two examples of interactive proofs from number theory are given, a protocol for quadratic non-residues and a protocol for subgroup non-membership. The third example of an interactive proof is a protocol for determining the truth value of a quantified Boolean formula. This interactive proof was implemented and the details of that implementation, plus a test of the implementation derived from game theory, are included. There is also a discussion of quantum interactive proofs. The two examples of perfect zero-knowledge proofs that are included are protocols for quadratic residues and for subgroup membership. These protocols were also implemented, and those details are included. For each protocol, there is a discussion of the complexity status of the problems addressed by the protocol. There is also a brief discussion of the history and applications of interactive and zero-knowledge proofs.