On: Decades-Old Computer Science Conjecture Solved in ...

[Leszek]

> And I thought they had ways to construct hash functions so that all the inputs of the same length have a different output?

That's trivially impossible for fixed-size hashes, by the pigeon hole principle.

[SilasX → Leszek]

Sorry, I meant all inputs whose length equals the output length.

The point being, for at least that case you can guarantee a sensitivity of one bit.

[lonelappde → Leszek]

Not if the output is longer than the input, such as for passwords

[gitrebase → lonelappde]

I doubt any study of hash functions restricts itself to studying a very tiny subset of all possible (infinite) inputs. The security of hash functions is always studied under the assumption of arbitrary inputs.