Review of Modern Cryptography and Elliptic Curves, A Beginner's Guide by Thomas R. Shemanske

Abstract

The equation y2 = x3 + ax2 + bx + c might seem a little innocuous at first. However, studying the sets of rational points (x; y) obeying this equation has proven to be one of the most far-reaching and fruitful areas of mathematics. For example, it led, aided and abetted by much of the most powerful mathematics of the past century, to Wiles' proof of Fermat's Last Theorem. And furthermore, these so-called "elliptic curves" (the terminology having little to do with ellipses) are actually useful. You can factor numbers with them! And send secret messages!