Date of Award

2013

Document Type

Thesis

Degree Name

Master of Science (MS) in Mathematics

Department

Mathematics

Abstract

"This thesis is a basic overview of elliptic curves and their applications to Cryptography. We begin with basic definitions and a demonstration that, given an elliptic curve addition, the points of an elliptic curve form a mathematical group. We then proceed to delve further into the mathematics, discussing torsion points on the group of elliptic curves before investigating the behavior of elliptic curves over finite fields wherein is given a proof of Hasse's Theorem on elliptic curves. With these tools, we discuss the discrete log problem, and the connection between elliptic curves and the field of cryptography. Finally, we look at elliptic curves over C and establish a trapdoor isomorphism between elliptic curves, and a topological torus"--Document.

Comments

Typescript. Vita.

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