The existence of two-round zero-knowledge proofs Does there exist any (im)possibility results for two-round private-coin non-auxiliary input zero-knowledge proofs for languages outside BPP?
Under the following assumptions there does not even exist three-round private-coin zero-knowledge proofs for languages outside BPP. See here.

The theorem holds assuming: 


Sub-exponentially secure one-way functions.
Sub-exponentially secure indistinguishability obfuscation for circuits.
Exponentially secure input-hiding obfuscation for multi-bit point functions