Two Number-Theoretic Problems That Illustrate the Power and Limitations of Randomness
Dissertation for Doctor of Philosophy (Mathematics) at the University of Wisconsin – Madison.
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.
Andrew Shallue. "Two Number-Theoretic Problems That Illustrate the Power and Limitations of Randomness" 2007
Available at: http://works.bepress.com/andrew_shallue/3