I am teaching an undergraduate course in number theory and am looking for topics that students could take on to write an expository paper (~10 pages). No new results are expected of them. Many of the students have an undergraduate course in abstract algebra and a course in real analysis (but few have any complex analysis background).

The only topics that I have come up with are

1.) Elliptic curves

2.) Cryptography

Of course these are related but I think these could be two projects. Other topics (such as the prime number theorem) seem too difficult to me. What other good projects are there? In particular are there good projects based on analysis? References would be greatly appreciated, including references for the two projects above.