The Elliptic Curve Method and Other Integer Factorization Algorithms

Graduate Project

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_projects/m326m241m

Descriptions

Attribute Name	Values
Creator	Wright, John
Abstract	The goal of this paper is to describe the Elliptic Curve Method (ECM), an integer factorization algorithm first proposed by Lenstra. Before describing this algorithm, we first discuss some preliminaries. In Chapter 2, we prove some elementary results from number theory and explicitly describe the RSA algorithm. In Chapter 3, we describe several factorization algorithms, including Pollard's Rho algorithm and the Quadratic Sieve. In Chapter 4, we discuss the algebraic properties of elliptic curves and the ECM. In Chapter 5, we discuss how performing the ECM with a curve in Montgomery form reduces computations. We conclude Chapter 5 by discussing some recent developments of the ECM.
Resource Type	Capstone Project
Date Available	2012-05-02T05:01:29+00:00
Date Issued	2012-04-12
Degree Level	Master's
Degree Name	Master of Science (M.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2012
Academic Affiliation	Mathematics
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Replaces	http://hdl.handle.net/1957/28960

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