Fun with Elliptic Curves

Lisa Bromberg

Date of Award

2008

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Elliptic Curves, Number Theory, Cryptography

Area of Concentration

Mathematics

Abstract

Within the last twenty years, elliptic curve cryptography has developed as a more efficient alternative to classical cryptosystems. In this thesis we study the basics of elliptic curves and develop the tools necessary to implement elliptic curve analogs of classical encryption schemes. In particular, we implement an encryption scheme based on the elliptic curve analog of the discrete logarithm problem, the ElGamal encryption method. We conclude the thesis by computing an example using this encryption scheme.

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