Date of Award
5-1-2025
Degree Name
Master of Science
Department
Mathematics
First Advisor
Ban, Dubravka
Abstract
This thesis explores the mathematical foundations and cryptographic applications ofelliptic curves. To understand elliptic curves, we start by introducing group theory, ring theory, and field theory. Then, we dive into elliptic curves, their algebraic structure, and the group law defined on their points. We then examine elliptic curves over finite fields, leading to the discrete logarithm problem and key cryptographic applications such as Weil Pairings, the Diffie-Hellman key exchange, Digital Signature Algorithm, and Elliptic Curve Digital Signature Algorithms. Using the theory and its application, this thesis highlights the significance of elliptic curves in modern cryptography.
Access
This thesis is Open Access and may be downloaded by anyone.