Integer factorization.

Abstract

The aim of this study is to discuss some of the old integer factoring methods, as well as some of the more recent methods that utilize the Kraitchik scheme. In the first chapter, the statement of the factoring problem is presented. A review of some concepts of elementary number theory and some details about continued fractions that are needed in later chapters are given. In chapter two, some of the old factoring methods, Trial Division, Legendre's, Gauss' and Fermat's factoring methods, are discussed. In chapter three, the continued Fraction method is presented. In chapter four, the Quadratic Sieve method with some of its improvements are presented. In chapter five, the Number Field Sieve method is presented.