Zero-knowledge with log-space verifiers

Interactive proof systems are considered in which the best set of possible verifiers is restricted to the class of probabilistic log-space automata. A. Condon (1988) introduced this model and showed that if the protocols are allowed to run for arbitrarily many rounds, exponential-time languages can be proved to a log-space verifier. To better approximate the usual notion of interactive proof systems, a number of researchers have considered a more realistic, further restricted model in which protocols are polynomially bounded, both in the number of rounds of communication and in the number of computational steps allowed to the verifier. A notion of language-recognition zero-knowledge is defined for this model, and it is shown that anything provable in this model can be proved in language-recognition zero-knowledge.<>