Graduation Year
2015
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Lenny Fukshansky
Reader 2
Christopher Towse
Terms of Use & License Information
Rights Information
© 2015 Tatiana E. Bradley
Abstract
The crux of elliptic curve cryptography, a popular mechanism for securing data, is an asymmetric problem. The elliptic curve discrete logarithm problem, as it is called, is hoped to be generally hard in one direction but not the other, and it is this asymmetry that makes it secure.
This paper describes the mathematics (and some of the computer science) necessary to understand and compute an attack on the elliptic curve discrete logarithm problem that works in a special case. The algorithm, proposed by Nigel Smart, renders the elliptic curve discrete logarithm problem easy in both directions for elliptic curves of so-called "trace one." The implication is that these curves can never be used securely for cryptographic purposes. In addition, it calls for further investigation into whether or not the problem is hard in general.
Recommended Citation
Bradley, Tatiana, "A Cryptographic Attack: Finding the Discrete Logarithm on Elliptic Curves of Trace One" (2015). Scripps Senior Theses. 716.
https://scholarship.claremont.edu/scripps_theses/716
