A nice mathematical topic on which there are plenty of print sources is mathematical cryptology.
“Invitation to Cryptology” by Barr is a nice book, and has plenty of ideas for more specific topics, as well as setting down the mathematics to understand them.
The breaking of the Enigma cipher is an old stand-by, but a paper on public key encryption would be able to include more actual mathematics (Euler’s extension of Fermat’s Little Theorem, and its use as the basis for RSA encryption).
Of course, as I joke when I teach the subject, if you know the RSA algorithm, you might be classed as a munition and find yourself subject to export control.
Didn't the government drop that, or is it still causing Phil Zimmerman problems, all these years later?
Mark