Could someone explain how and why it uses "0x1337" in order to validate the key?

Is that magic?

https://github.com/laginimaineb/android_fde_bruteforce/blob/...

Isn't that just m = (m^e mod n)^d mod n? So the value itself does not matter, you could use 42 instead of 0x1337.

Here is a list of gifs showing the expansion in various cities.

Shanghai (http://www.thatsmags.com/uploads/galleries/images/shanghai-m...)

Toronto (http://www.thatsmags.com/uploads/galleries/images/toronto-me...)

Beijing (http://big.assets.huffingtonpost.com/subwaygif2-01.gif)

Moscow (https://upload.wikimedia.org/wikipedia/commons/c/c0/%D0%9C%D...)

New York (https://secondavesagas.files.wordpress.com/2007/09/subwayhis...)

Boston: http://www.vanshnookenraggen.com/_index/2012/04/an-animated-...