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Asked: 2026-05-17T19:15:51+00:00

I was reading wikipedia, and it says Cryptographic hash functions are a third type

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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?

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  1. Editorial Team

    Yes, it’s inevitable that there will be collisions when mapping a long message onto a shorter hash, as the hash cannot contain all possible values of the message. For the same reason you cannot ‘invert’ the hash to uniquely produce either Beowulf or The Hobbit – but if you generated every possible text and filtered out the ones that had your particular hash value, you’d find both texts (amongst billions of others).

    The article is saying that it should be hard for an attacker to find or construct a second message that has the same hash value as a first. Cryptographic hash functions are often used as proof that a message hasn’t been tampered with – if even a single bit of data flips then the hash value should be completely different.

    A couple of years back, Dutch researchers demonstrated weaknesses in MD5 by publishing a hash of their “prediction” for the US presidential election. Of course, they had no way of knowing the outcome in advance – but with the computational power of a PS3 they constructed a PDF file for each candidate, each with the same hash value. The implications for MD5 – already on its way down – as a trusted algorithm for digital signatures became even more dire…

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