Date of Award
January 2016
Degree Type
Open Access Thesis
Document Type
Master Thesis
Degree Name
Master of Science (MS)
Department
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
Abstract
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.
Copyright
Copyright 2016 David Curtis Swart
Recommended Citation
Swart, David Curtis, "An Elliptic Exploration" (2016). Online Theses and Dissertations. 433.
https://encompass.eku.edu/etd/433
