What are the assumptions we make to propose a one-way function? I only know of some number theoretic assumptions, but what are the other assumptions you can possibly make, which if true, would imply that $f$ is a one-way function?
(Considering pre-image resistant hash functions, what is the assumption there? Hashes as far as I know do not rely on any assumption other than the fact that it seems to be hard)
Example: Say we assume factoring a semiprime $N = pq$ is hard. Then we can say that the function $f(p,q) = p*q$ is one-way. What other assumptions exist?