TITLE: Zero-knowledge proof for $P \ne NP$?
QUESTION [5 upvotes]: In computational complexity, $P \ne NP$ is a widely believed conjecture. Suppose that someone discovered a proof for it. He wants to publish a proof that he correctly proved the conjecture. I am aware that NP-complete problems have Zero-knowledge proofs. Assuming $P \ne NP$, can we have Zero-knowledge proof (or morally equivalent one) for  $P \ne NP$?

REPLY [4 votes]: First of all, it does not really make sense to talk about zero-knowledge proofs for a single statement such as $P\ne NP$.  You really should be asking about whether there is a zero-knowledge proof for a computational problem, such as: "Given a statement $S$ in the first-order language of set theory, and a positive integer $n$, does there exist a ZFC-proof of $S$ of length at most $n$?"
With this reformulation, you have already partially answered your own question, by noting that there is a standard theorem about the existence of zero-knowledge proofs for any $NP$-complete language. However, there are two caveats to be aware of in that standard theorem. The first caveat is that it assumes the existence of a one-way function, which is a stronger assumption than $P\ne NP$. So if you only have the hypothesis $P\ne NP$ available to you, then that's not quite good enough.  The second caveat is that the usual proof relies on a commitment scheme, which has two parts to it, the binding part and the hiding part.  Ideally we'd like both parts to be statistically secure and not just computationally secure, but it turns out that it is impossible for both parts to be statistically secure unless the polynomial hierarchy collapses to the second level (Fortnow, "The complexity of perfect zero knowledge").  So if you want the strongest possible form of zero knowledge, then the answer to your question is likely no.