Goldwasser and Sipser proved that a private coin interactive proof system can be converted into a public coin system. This conversion preserves round complexity (up to an additive factor of 2), but does not preserve prover complexity or zero-knowledge.
I am interested specifically in the ZK property. One could ask whether the non-preservation of ZK is a limitation of Goldwasser-Sipser or is inherent to this type of conversion.
I interpret a result of Goldreich and Krawczyk as indicating that non-preservation of ZK is inherent to such transformations if they are black-box. In particular, Goldreich and Krawczyk showed that there is no constant-round public-coin black-box zero-knowledge protocols for languages outside BPP.
My question has three parts:
(1) Am I correct to interpret the Goldreich and Krawczyk result as ruling out a private coin to public coin transformation that preserves ZK (in the black box setting)?
(2) What is the intuition for this? In particular, I don't see a clear reason why making the verifier's randomness public makes it harder for the prover to keep their information private.
(3) Are there any results for ZK-preserving non-black-box conversions?
