> The best that you can say is that there is no known algorithm that can calculate a pre-image for any given hash function in less than some super linear time.

> The best that you can say is that there is no known algorithm that can calculate a pre-image for any given hash function in less than some super linear time. If your algorithm is not linear in the size of the key/hash space, it's not a brute force algorithm. It's a cryptographic break. There is no proof that such algorithm does not exist, nor is there any proof that it does. Therefore you can't claim it definitely does. That's my point.