Theoretically couldn’t there be a hashing algorithm that’s one to one if it always spits out a hash as long or longer than the input message?
I’ve never actually walked through the math behind hashing algorithms, but I’m assuming collisions come from truncation. I’m guessing you’re usually not able to know exactly where two inputs that collide for the first n bits end up diverging, so the only way to ensure most hash functions are one to one is if the outputs have infinite length. But, if you had outputs of infinite length for different inputs, eventually they’d have to diverge. Idk if that’s true of all hashing functions/maybe there’s a way to know after what point outputs for different inputs have to diverge for some.
I’ve never actually walked through the math behind hashing algorithms, but I’m assuming collisions come from truncation. I’m guessing you’re usually not able to know exactly where two inputs that collide for the first n bits end up diverging, so the only way to ensure most hash functions are one to one is if the outputs have infinite length. But, if you had outputs of infinite length for different inputs, eventually they’d have to diverge. Idk if that’s true of all hashing functions/maybe there’s a way to know after what point outputs for different inputs have to diverge for some.