It is known (simple HW exercise) that:

If P = NP, that OWFs (one way functions) can not exist.

It is also known that there is a Universal OWF: namely, there is a function f: s.t. if any OWF exists, then f is a OWF. [This is a standard result of concatenating many functions.]

Question: Is the following question open: (P != NP) => (OWFs exist) ?

[And what is known about this question?]

Thanks