This summer I am going to give some lectures to some REU students. I am still tossing around ideas for what I am going to talk about, but one thing I would at least like to give one or two lectures on, is Cryptology.
I had a fairly standard undergraduate course on Number Theory where we learned basic cyphers and some things about encryption. However, I am hoping to talk about the relationship of elliptic curves to encryption. Is there an appropriate level book that covers this relationship? Many of the students are strong, but lack some background. Many will have some experience with number theory, but may lack Abstract Algebra and Advanced Calculus.
In the absence of a nice book talking about elliptic curves relation to cryptology, I will probably talk about the excellent book by Ash and Gross.
I was just hoping to add this topic into my mix of lectures so I thought the MO community could offer some suggestions.
Thanks in advance!
EDIT: I wanted to add that Diffe-Hulman will definitely be covered as one of the main research projects will focus on it. The elliptic curves comes by request of the students, who have heard cool things about them 😀
Best Answer
An Introduction to Mathematical Cryptography by Hoffstein, Pipher, and Silverman is an excellent book. It discusses elliptic curves.