Date of Award
Dr. Justin Brown
This paper examines subfield curve extensions on a number of elliptic curves over finite fields in characteristic 2. The data generated is aimed to assist further understanding into the nature of elliptic curves, and any possible characteristics or patterns that they share. The total rational points on base fields were found using C++, and points on their field extensions were calculated using Scientific Workplace. Different extensions were then categorized based on the factorization of their respective points. We found that the total number of points on a base field will divide the total number of points of any extension of that field, and that the examined curves were all paired with another distinct curve. In addition, we discovered that the total points in only 3.85% of studied field extensions factored into the points of the base field times a large prime.
DeArmond, Joel, "Elliptic Curve Cryptography: Extensions of Subfield Curves in Characteristic 2" (2017). Pence-Boyce STEM Student Scholarship. 1.