ABSTRACT
This chapter discusses the various factorization methods such as Fermat’s factorization method, Pollard’s p-1 method, and Quadratic sieve (QS) and number field sieve (NFS) methods. The integer factorization problem is a core of many public key cryptosystems, and it is a challenging problem to find the factors of a large composite number. The chapter provides the list of some integers that are factored in between 1990 and 2017. Pollard proposed a factoring algorithm, which is more efficient than the trial division method. The NFS method is considered as the fastest method for factoring a large number. J. Zalaket and J. Hajj-Boutros proposed a new integer factorization method based on the square root approximation. Pomerance developed a new factoring algorithm called QS method. General-purpose algorithm is used for the cryptographic application.
