Date of Award

January 2016

Degree Type

Open Access Thesis

Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Patrick J. Costello

Department Affiliation

Mathematics and Statistics

Second Advisor

Steve Szabo

Department Affiliation

Mathematics and Statistics

Third Advisor

Bangteng Xu

Department Affiliation

Mathematics and Statistics


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 provide examples of working with these algorithms. At the end of this paper, I will also demonstrate the ECC encryption and decryption process.