Anyone who ever decoded the messages on the back of their cereal box knows at least a little cryptography. In fact, these schemes (usually called shift ciphers, although they have lots of other names) were actually used by Julius Caesar once upon a time. Unsurprisingly, cryptography has come a long way since then. The 1970's saw the invention of public-key cryptography, which allows people who have never met to communicate privately. Now these ideas are used in basically any secure communication you can name (ATMs, online banking, etc.). These methods are quite mathematical in nature, and are based on results in abstract algebra and number theory. The plan for this quarter is to cover this background, hopefully going far enough to talk (maybe briefly) about some recent advances like the use of elliptic curves. More concretely, we'll roughly go through the first three chapters of this book with some other topics sprinkled in. Since the book is available electronically through the UCSD library, there's no need to buy it unless you want to.
Logistically, we'll meet for one hour each week. At the beginning I'll probably do most of the talking, but I hope to do more listening to you guys as the quarter goes on. There won't be any specific required textbook or homework, but I'll try to provide material that helps reinforce what we talk about when we meet, such as printouts from the references below. The only "requirement" is a short presentation at the end of the quarter, but we'll have plenty of time to prepare for that.
References:
An Introduction to Mathematical Cryptography - Hoffstein, Pipher, and Silverman
Understanding Cryptography - Paar
The notes from "Computation number theory" through "Asymmetric encryption" on this page.