Date of Award
6-2009
Document Type
Union College Only
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Kathyrn Lesh
Language
English
Keywords
algorithm, intersection, equation, curve, theorem
Abstract
The security of many cryptosystems relies on the difficulty of factoring a number that is a product of two prime numbers (usually hundreds of digits long) so it is important to understand ways that one might attempt to find divisors of these large composite numbers. The Elliptic Curve Factoring Algorithm, first developed by H.W. Lenstra, is a method to factor numbers using elliptic curves over a finite field. By taking an equation for an elliptic curve (of the form y2 = x3 + Ax + B) and performing addition on the points on the elliptic curve over a finite field, we are sometimes able to find a factor. Demonstrating when the algorithm is successful is dependent on Hasse’s Theorem, which we also prove.
Recommended Citation
Britton, Sarah G., "The elliptic curve factoring algorithm" (2009). Honors Theses. 1274.
https://digitalworks.union.edu/theses/1274