Physical Sciences and Mathematics Commons^™

An Elliptic Exploration, David Curtis Swart

Online Theses and Dissertations

In this paper I will be giving an introduction to an interesting kind of equation called elliptic curves, and how they can be used to protect our national security through Cryptology. We will explore the unique operation for adding points on elliptic curves and the group structure that it creates, as well as the ECC method, which stands among the RSA and AES methods as one of the modern day's most secure systems of cryptography. In addition, I will also introduce several algorithms and methods that are useful for working with ECC such as Schoof's Algorithm, and I will also …