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.
