I know that for encryption we require non-linearity because it impedes the ability to attack the cipher by solving for the key with linear equations.
Does hashing require non-linear components as well? I presume it does, but I do not know why.
How would a hash built from a linear psuedo-random permutation be vulnerable to collision/preimage search?
I would like to work with the assumption that the linear permutation has appropriate diffusion and is sufficiently complicated/iterated enough to preclude trivial attacks.