The Noisy Oracle Problem

We describe a model in which a computationally bounded verifier consults with a computationally unbounded oracle, in the presence of malicious faults on the communication lines. We require a fairness condition which in essence says that some of the oracle's messages arrive uncorrupted. We show that a deterministic polynomial time verifier can test membership in any language in P-space, but cannot test membership in languages not in P-space, even if he is allowed to toss random coins in private. We discuss the zero knowledge aspects of our model, and demonstrate zero knowledge tests of membership for any language in P-space.