Random self-reducibility and zero knowledge interactive proofs of possession of information

Abstract

The notion of a zero knowledge interactive proof that one party "knows" some secret information is explored. It is shown that any "random self-reducible" problem has a zero knowledge interactive proof of this sort. The zero knowledge interactive proofs for graph isomorphism, quadratic residuosity, and "knowledge" of discrete logarithms all follow as special cases. Based on these results, new zero knowledge interactive proofs are exhibited for "knowledge" of the factorization of an integer, nonmembership in cyclic subgroups of Zp*, and determining whether an element generates Zp*. None of these proofs relies on any unproven assumptions.