Knowledge implies time/space efficiency

Abstract

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 35-36).The probabilistically checkable proof (PCP) system enables proofs to be verified in time polylogarithmic in the length of a classical proof. Computationally sound (CS) proofs improve upon PCPs by additionally shortening the length of the transmitted proof to be polylogarithmic in the length of the classical proof. In this thesis we explore the ultimate limits of non-interactive proof systems with respect to time/space efficiency and the new criterion of composability. We deduce the existence of our proposed proof system by way of a natural new assumption about proofs of knowledge. In fact, a main contribution of our result is showing that knowledge can be "traded" for time and space efficiency in noninteractive proof systems.by Paul Valiant.S.M