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Does there exist any (im)possibility results for two-round private-coin non-auxiliary input zero-knowledge proofs for languages outside BPP?

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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
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    $\begingroup$ Hamidreza explicitly talks about non auxiliary input ZK. The paper you quote only deals with auxiliary input ZK. Further, for that case it would be overkill. 2-round AI-ZK is already ruled out unconditionally by Goldreich and Oren. $\endgroup$ – Maeher Jul 30 at 13:30

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