Interactive hashing can simplify zero-knowledge protocol design without computational assumptions

Abstract

We show that any 3-round protocol (in general, any bounded round protocol) in which the verifier sends only random bits, and which is zero-knowledge against an honest verifier can be transformed into a protocol that is zereknowledge an general. The transformation is based on the interactive hashing technique of Naor, Ostrovsky, Venkatesan and Yung. No assumption is made on the computing power of prover or verifier, and the transformation therefore is valid in both the proof and argument model, and does not rely on any computational assumptions such as the existence of one-way permutations. The technique is also applicable to proofs of knowledge. The transformation preserves perfect and statistical zero-knowledge. As corollaries, we show first a generalization of a result by Damgkrd on construction of bit-commitments from zero-knowledge proofs. Other corollaries give results on non-interactive zero-knowledge, one-sided proof systems, and black-box simulation.