Abstract:

Version History: Extended abstract in FOCS '04.

We prove a number of general theorems about \(\mathbf{ZK}\), the class of problems possessing (computational) zero-knowledge proofs. Our results are unconditional, in contrast to most previous works on \(\mathbf{ZK}\), which rely on the assumption that one-way functions exist. We establish several new characterizations of \(\mathbf{ZK}\) and use these characterizations to prove results such as the following:

1. Honest-verifier \(\mathbf{ZK}\) equals general \(\mathbf{ZK}\).
2. Public-coin \(\mathbf{ZK}\) equals private-coin \(\mathbf{ZK}\).
3. \(\mathbf{ZK}\) is closed under union.
4. \(\mathbf{ZK}\) with imperfect completeness equals \(\mathbf{ZK}\) with perfect completeness.
5. Any problem in \(\mathbf{ZK}\) \(\cap\) \(\mathbf{NP} \) can be proven in computational zero knowledge by a \(\mathbf{BPP^{NP}}\)prover.
6. \(\mathbf{ZK}\) with black-box simulators equals \(\mathbf{ZK}\) with general, non–black-box simulators.

The above equalities refer to the resulting class of problems (and do not necessarily preserve other efficiency measures such as round complexity). Our approach is to combine the conditional techniques previously used in the study of \(\mathbf{ZK}\) with the unconditional techniques developed in the study of \(\mathbf{SZK}\), the class of problems possessing statistical zero-knowledge proofs. To enable this combination, we prove that every problem in \(\mathbf{ZK}\) can be decomposed into a problem in \(\mathbf{SZK}\) together with a set of instances from which a one-way function can be constructed.

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