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Selected Works of Andrew Shallue
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Two Number-Theoretic Problems That Illustrate the Power and Limitations of Randomness
(2007)
  • Andrew Shallue, Illinois Wesleyan University
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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.

Keywords
  • Algorithm,
  • algorithmic number theory,
  • elliptic curve.
Disciplines
Publication Date
2007
Comments
Dissertation for Doctor of Philosophy (Mathematics) at the University of Wisconsin – Madison.
Citation Information
Andrew Shallue. "Two Number-Theoretic Problems That Illustrate the Power and Limitations of Randomness" (2007)
Available at: http://works.bepress.com/andrew_shallue/3/