#### Abstract

This thesis contains work on two problems in algorithmic number theory. The first problem is to give an algorithm that constructs a rational point on an elliptic curve over a finite field. A fast and easy randomized algorithm has existed for some time. We prove that in the case where the finite field has characteristic 2, there is a deterministic algorithm with the same asymptotic running time as the existing randomized algorithm.

#### Disciplines

Mathematics | Number Theory

#### Recommended Citation

Shallue, Andrew, "Two Number-Theoretic Problems That Illustrate the Power and Limitations of Randomness" (2007). *Scholarship*. 75.

https://digitalcommons.iwu.edu/math_scholarship/75

## Comments

Dissertation for Doctor of Philosophy (Mathematics) at the University of Wisconsin – Madison.