An Elliptic Exploration

<p>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. </p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor dc:publisher

Eastern Kentucky University

Year

2016

Author dc:creator

• Swart, David Curtis

• Cryptography
• Elliptic Curves
• Math
• Number Theory
• Schoof's Algorithm
• Applied Mathematics
• Defense and Security Studies

Statement dc:rights

• Copyright 2016 David Curtis Swart

Repository record dc:identifier

https://encompass.eku.edu/etd/433

OAI identifier oai:identifier

oai:encompass.eku.edu:etd-1431