| Type of Document |
Master's Thesis |
| Author |
McGee, John J.
|
| URN |
etd-04252006-161727 |
| Title |
René Schoof's Algorithm for Determining the Order of the Group of Points on an Elliptic Curve over a Finite Field |
| Degree |
Master of Science |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Brown, Ezra A. |
Committee Chair |
| Parry, Charles J. |
Committee Member |
| Williams, Michael |
Committee Member |
|
| Keywords |
- Elliptic Curve
- Schoof
- Cryptography
|
| Date of Defense |
2006-04-25 |
| Availability |
unrestricted |
Abstract
Elliptic curves have a rich mathematical history dating back to Diophantus (c. 250 C.E.), who used a form of these cubic equations to find right triangles of integer area with rational sides. In more recent times the deep mathematics of elliptic curves was used by Andrew Wiles et. al., to construct a proof of Fermat's last theorem, a problem which challenged mathematicians for more than 300 years. In addition, elliptic curves over finite fields find practical application in the areas of cryptography and coding theory. For such problems, knowing the order of the group of points satisfying the elliptic curve equation is important to the security of these applications. In 1985 René Schoof published a paper [5] describing a polynomial time algorithm for solving this problem. In this thesis we explain some of the key mathematical principles that provide the basis for Schoof's method. We also present an implementation of Schoof's algorithm as a collection of Mathematica functions. The operation of each algorithm is illustrated by way of numerical examples.
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| Files |
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Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
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SchoofsAlgorithmThesisMcGee.pdf |
1.04 Mb |
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ThesisMcGee06June2006.nb |
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