Hi,
I was reading wikipedia, and it says
Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed length hash which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash.
But why? What I understand is that you can put the long Macbeth story into the hash function and get a X long hash out of it. Then you can put in the Beowulf story to get another hash out of it again X long.
So since this function maps loads of things into a shorter length, there is bound to be overlaps, like I might put in the story of the Hobit into the hash function and get the same output as Beowulf, ok, but this is inevitable right (?) since we are producing a shorter length output from our input? And even if the output is found, why is it a problem?
I can imagine if I invert it and get out Hobit instead of Beowulf, that would be bad but why is it useful to the attacker?
Best,