On the Existence of Bit Commitment Schemes and Zero-Knowledge Proofs

It has been proved earlier that the existence of bit commitment schema (blobs) implies the existence of sereknowledge proofs of information possession, which are MA-protocols (i.e. the verifier sends only independent random bits) [BrChCr], [GoMiWi]. In this paper we prove the converse result in a slightly modified form: We define a concept called veoHy zero-knowledge, which is like ordinary zero-knowledge, except that we only require that an honed verifier learns nothing from the protocol. We then show that if, using an MA-protocol, P can prove to V in weakly zer&nowledge that he p mea a solution to some hard problem, then this implies the existence of a bit commitment scheme. If the original protocol is (almost) perfect zer*knowledge, then the resulting commitments are secure against an infinitely powerful receiver. Finally, we also show a similar result for a restricted class of non-MA protocols.