[betterunix2]

Hash functions are OWFs, but OWFs are not necessarily hash functions. Among other things, for an OWF inverting the function is only hard on average, and recovering some information about the "preimage" may not be hard (the only guarantee is that there is something about the input that is hard to compute). Also, there are common uses of hash functions that are not even theoretically sound (anything in the random oracle model), so we should be careful when discussing the "theoretical basis" for hash functions...

[throwawaymath]

Yes, hash functions only approximate one way functions since we haven't technically created one - your point here is what I was referring to by mentioning the random oracle model.

But the random oracle model is fully theoretically sound - I'm not sure where you got the impression it isn't. Do you think everything outside the standard model of cryptography isn't theoretically sound? What, then, is your definition of soundness?

[betterunix2]

ROM is not sound because there are constructions that are provably secure that cannot be securely instantiated. I do not deny that it is pragmatic or that the problems have not been relevant in practice, but the ROM is just a heuristic.