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