The improvement of initial value closer to the target for Fermat’s factorization algorithm

Abstract

Integer Factorization Algorithm is one of the hard problems for breaking RSA. Fermat’s Factorization Algorithm (FFA) factoring the modulus very fast whenever the difference between two large prime factors is very small is a type of integer factorization algorithms. Generally, the initial values are far from the targets which are perfect square numbers. Although the new initial values closer to the targets in comparison to the originals were proposed, the method is called Estimated Prime Factor (EPF), they can be applied with only unbalanced modulus. In this paper, the new methodology for estimating one of initial values is proposed. In deep, it is closer to the target when it is compared with the original and it can be applied with all values of the modulus. The experimental results show that the new initial value can be larger when the size of the modulus is higher. In fact, it is based on the size of the modulus and also the distance between the original initial value and the possible target which is the closest to the original initial value. Furthermore, it implies that loops computation can be decreased especially the large size of the modulus because the new initial value is always very larger than the traditional.