Date of Completion


Degree Type

Honors Thesis - Campus Access


Mathematics (MATH)

First Advisor

Lily Khadjavi


Elliptic curves have a rich algebraic structure which can, in fact, be used in applications to cryptography. In this paper we give the necessary background to understand a few such applications. We define the group formed by rational points on an elliptic curve and then, working with curves over finite fields, show how divisors can be used to define the Weil Pairing. Two applications to cryptography are explained: Lenstra's Elliptic Curve Method, inspired by Pollard's p - 1 algorithm, and Joux's three party key exchange, extending the idea of a two-party key exchange such as Diffie-Hellman.