Advanced Factorization Methods

The RSA cipher is considered secure based on the idea that large composite numbers are difficult to factor. Currently there are several sieves that allow us to factor large integers. However depending on the size of the integer, it could still take many years to factor a number. The goals of this research project are to learn about different sieves, make implementations of them in Mathematica, factor an RSA number, and find ways to make the sieves better. The sieves this project will focus on are the Continued Fraction Method, the Quadratic Sieve, and the General Number field Sieve. This project will enable us to further understand the factorization methods that threaten the security of the RSA cipher.