The last line speaks for the article itself.

Damn Interesting.

I’m not saying I know ALL about it.

What I will say is I know enough to distill it down like this.

If we are looking at information that has been encoded in some logical fashion, we can use what we know about the information itself to make very educated guesses about it.

In the case of a birthday this becomes especially true if we have both encoded and decoded data.

Since we can presume with certainty there was a logical process to encoding the data, we can work out the logic of that process by whittled-down brute-force. We can statistically analyze the data and assume which encodings are which birthdays for those that are at the peaks/troughs of commonality.

Even if you’re wrong, shuffling things around just a little and trying again is something a program can do fairly fast.

Once we’ve matched several encoded/decoded value pairs, we can just start trying things until we produce a “middle” of logic that gets you from one to the other. Once we have a piece of logic that fits/works for the pairs we fully know, we can very likely use that logic to decode all the rest of the encoded data.

This does oversimplify and make it sound easier than it is. With modern techniques we know about near-specifically to prevent this sort of thing it becomes significantly harder. (“salting”, for one – we add a bit more into what’s going into the logic for that encoded birthday, like someone’s middle initial, say)