Any hash function provably collides for at least two inputs, unless we're talking about perfect hashing. The only exception would be a hash function that does n

Any hash function provably collides for at least two inputs, unless we're talking about perfect hashing. The only exception would be a hash function that does not compress, where the output is larger than the input. That's not a hash-function, though. > you just lose the will never collide guarantee There is no such guarantee, in fact, the opposite is guaranteed. It's just very unlikely that you get a collision - that's a desirable property of any hash function -, and it should be hard to create a collision because the function is hard to reverse - that's a desirable property of any cryptographic hash function, as the OP laid out.