From the paper of Impagliazzo and Rudich "Limits on the Provable Consequences of One-Way Permutations":
We provide strong evidence that it will be difficult to prove that secure secret agreement is possible assuming only that a one-way permutation exists. We model the existence of a one-way permutation by allowing all parties access to a randomly chosen permutation oracle. A random permutation oracle is provable one-way in the strongest possible sense.
Given that we don't know if one-way function exists, how should one interpret this? Doesn't the above say one-way fucntion does exist?
Also, they exhibit an oracle relative to which one-way permutation exists, but not key agreement. Again, how is that possible? What does that mean? A black-box key agreement can be constructed independently ignoring both the oracle and the one-way permutation.