The Graph Clustering Problem has a Perfect Zero-Knowledge Proof.

Abstract

The input to the Graph Clustering Problem consists of a sequence of integers m 1 ; :::; m t and a sequence of P t i=1 m i graphs. The question is whether the equivalence classes, under the graph isomorphism relation, of the input graphs have sizes which match the input sequence of integers. In this note we show that this problem has a (perfect) zero-knowledge interactive proof system. Keywords: Graph Isomorphism, Zero-Knowledge Interactive Proofs. 1 Introduction The remarkable notion of perfect zero-knowledge proofs was introduced by Goldwasser, Micali and Rackoff [GoMiRa]. A perfect zero-knowledge proof system is a method for a prover to convince a polynomial-time bounded verifier with very high probability that a certain assertion is true without revealing any additional information (in an information-theoretic sense). Not many are the languages which have been shown to have a perfect zero-knowledge proof system; in particular, all of them share number-theoretic or random self-red...