The following description from http://shattered.it caught my eye:
How do I detect this attack?
You can use the online tool above to submit files and have them checked for a cryptanalytic collision attack on SHA-1. The code behind this was developed by Marc Stevens (CWI) and Dan Shumow (Microsoft) and is publicly available on GitHub.
It is based on the concept of counter-cryptanalysis and it is able to detect known and unknown SHA-1 cryptanalytic collision attacks given just a single file from a colliding file pair.
I know basically nothing about cryptography, so I don't really know the full meaning of the phrase SHA-1 cryptanalytic collision attacks. The way I read the description, it states that I can analyze an arbitrary file on my hard drive and be told whether that file has been the target of a collision attack. If that is the case and if the tool's only knowledge of the world is the contents of my file, I can't see how such a thing could be possible.
I'm hoping someone can explain, in (relatively) simple terms, why my understanding is wrong or how this is actually possible.