Master's Thesis

## Abstract

The first chapters discuss some elementary theory of hyperelliptic curves and other
mathematical topics used throughout the text.
Then the algorithms Pollard lambda, Pollard rho and Index Calculus
for hyperelliptic curves are analyzed.
A C++ implementation of hyperelliptic curve arithmetic,
Pollard lambda and Pollard rho is given.
This implementation is used to give insight into the theoretical
analyses of Pollard lambda and Pollard rho over the multiplicative
group of a finite field and the Jacobian of a hyperelliptic curve.

**Supervisors:**

Matthijs Coster (MIVD)

Tom H. Koornwinder (UvA, KdVI)

Pieter Moree (MPI Bonn, formerly UvA, KdVI)

Herman J.J. te Riele (CWI)

Master's Thesis version 2

Errata: Master's Thesis (version 1)