How about the very recent (and still unfinished)
SHA-3 function?
You could talk about crypto hashes in general, the first two SHA algorithms and how SHA-3
came to be.
Another, less mathematical but undoubtedly more difficult, problem can deal with Facebook and Google tracking users on the web. Simply put, how can I, as a user, visit a website that has a "Like" Facebook button or a "+1" by Google, without sending this data? How can I, as a web programmer, offer the "Like" and "+1" button, but
keep them optional?
On a final note, you should spend a few hours on Bruce Schneier's website (cf. the last link I gave). You'd probably get far better ideas.