Locally random reductions: Improvements and applications

Abstract

A (r.n)-Iocally random reduction maps a problem instance x into a set of problem instances in such a way that it is easy to construct the answer to x from the answers to y\,...,ya, and yet the distribution on /-element subsets of > depends only on \x\. In this paper we formalize such reductions and give improved methods for achieving them. Then we give a cryptographic application, showing a new way to prove in perfect zero knowledge that committed bits xi,..., xm satisfy some predicate Q. Unlike previous techniques for such perfect zero-knowledge proofs, ours uses an amount of communication that is bounded by a fixed polynomial in m, regardless of the computational complexity of Q. © 1997 International Association for Cryptologic Research.