Equality of PZK and SZK

Determine whether the interactive-proof complexity classes PZK (languages admitting perfect zero-knowledge interactive proofs) and SZK (languages admitting statistical zero-knowledge interactive proofs) are equal; that is, decide whether PZK = SZK in the standard Turing model (notwithstanding known oracle separations).

Background

The paper surveys known results about zero-knowledge in various proof models. For interactive proofs (IPs), it is known that PZK is contained in SZK, and SZK is contained in AM ∩ coAM. While many relations are established, the precise relationship between PZK and SZK is a longstanding question. The authors note that recent work shows there is an oracle relative to which PZK ≠ SZK, but this does not resolve the unrelativized question.

This open problem concerns the classical (unrelativized) setting of interactive proofs and is independent of the paper’s main contribution, which constructs perfect zero-knowledge PCPs for all of P. The authors include it to contextualize the broader landscape of perfect zero-knowledge.