Are hashing algorithms constructed to guarantee that no fixed point exists?
My assumption is not, because I don’t see what utility that would have. (Please correct me if I’m wrong.) As such, purely for curiosity’s sake, have any fixed points of common algorithms (e.g., MD5, SHA-256, etc.) been found?
No, they are not constructed, to avoid having fixed point because it will not leverage extension attack, as of now, even making counter of lenght equal to some weak hash is infeasible and preimage attack is hard (otherwise we would call it compression, not hashing).
As of today, there are methods for collisions finding, and for SHA 256 for finding fixed points. Yes, it was found, take a look at crypto post.
