Elliptic curves and their cryptographic applications

<p>"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.</p>

Name thesis:degree_name

Master of Science (MS) in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year

2013

Author dc:creator

• Wenberg, Samuel L.

• Curves
• Elliptic
• Cryptography
• Physical Sciences and Mathematics

Statement dc:rights

• Access is available to all users

Repository record dc:identifier

https://dc.ewu.edu/theses/160

OAI identifier oai:identifier

oai:dc.ewu.edu:theses-1159