#### Degree Year

2018

#### Document Type

Thesis

#### Degree Name

Bachelor of Arts

#### Department

Mathematics

#### Advisor(s)

Benjamin Linowitz

#### Keywords

Algebraic geometry, Computational complexity, Cryptography, Discrete logarithm problem, Elliptic curve cryptography, Finite fields, Group theory, Hyperelliptic curve cryptography

#### Abstract

At its core, cryptography relies on problems that are simple to construct but difficult to solve unless certain information (the “key”) is known. Many of these problems come from number theory and group theory. One method of obtaining groups from which to build cryptosystems is to define algebraic curves over finite fields and then derive a group structure from the set of points on those curves. This thesis serves as an exposition of Elliptic Curve Cryptography (ECC), preceded by a discussion of some basic cryptographic concepts and followed by a glance into one generalization of ECC: cryptosystems based on hyperelliptic curves.

#### Repository Citation

Wilcox, Nicholas, "A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography" (2018). *Honors Papers*. 176.

https://digitalcommons.oberlin.edu/honors/176