[guimplen]

AFAIK, this is more of a belief than a fact. I would be very curious if you would show me a rigorous proof that e.g. SHA256 requires like on the order of 2^256 of operations to find a preimage of a random 256-bit string.

[Dylan16807]

If you have something more clever than 2^256 operations, then that's not brute force.