Études in non-interactive zero-knowledge

Abstract

N a ZERO-KNOWLEDGE PROOF [GMR85], Prover interactively convinces Verifier that theorem 7r is true in such a way that (a) a corrupt Prover cannot convince Verifier of a false theorem and (b) a corrupt Verifier cannot "learn" anything other than the fact that r is true. In a NON-INTERACTIVE ZERO-KNOWLEDGE PROOF [BFM88], the Prover must do the above by sending only a single message to Verifier! To make this possible, Prover and Verifier are not tabula rasa, but rather born with some setup information. Much in the fashion of a musical TUDE, in this thesis, we explore several variations on the setup assumptions for non-interactive zero-knowledge in order to enjoy a richer understanding. Our labor brings forth * various unconditional characterizations of computational and statistical NIZK proofs, * new constructions that have practical applications to non-malleable encryption and CCAz encryption, * new constructions which form the building blocks of "fair" versions of interactive zero-knowledge and collusion-free multi-party computation protocols, * and conceptual contributions which underlie the recent works on how cryptography can be used to achieve equilibrium in game theory.