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.

Library of Congress Subject Headings

Proof theory

Publication Date

5-19-1999

Document Type

Thesis

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Radziszowski, Stanislaw

Advisor/Committee Member

Wilcox, Theodore

Advisor/Committee Member

Hart, David

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA9.54 .N65 1999

Campus

RIT – Main Campus

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