[tridentboy]

I'm sorry, could you please elaborate? I was always under the assumption that hash functions have to be deterministic, and thus, that "every input has a unique output" was a correct statement.

AFAIK the contrary is invalid, so that "not every output is the result of one and only one input".

[chias]

A function being deterministic means that any input will have a single output. But it is not unique for any hash function, SHA-256 included. The definition of a hash function is any function which takes an arbitrary length input and outputs an n-bit output for some fixed value of n. By virtue of the fact that you have infinite inputs and finite outputs, the outputs cannot be unique.

Generally when people make this claim, what they're actually referring to is what's called Collision Resistance (CR) and/or Weak Collision Resistance (WCR), which instead make claims on difficulty of finding such collisions (of which infinitely many exist).

WCR, necessary for almost any cryptographic use, states that for any given input it should be difficult to find a different input which hashes to the same value. CR, generally desirable for cryptographic hash functions, states that it should be difficult to find two different inputs such that their hashes are equal. CR implies WCR, but WCR does not imply CR -- for example, SHA-256 (currently) exhibits CR but SHA-1 only exhibits WCR.

[apeescape]

There are 2^256 potential outputs for SHA-256, while the number of potential inputs is infinite. Therefore, the same output can be generated with different inputs, although finding such "collisions" by chance is extremely unlikely

[surye]

The claim is not that every output has a unique input, which would not be correct, and seems to be what you are addressing.