MVFactor: A method to decrease processing time for factorization algorithm

Abstract

RSA is the most well-known public key cryptosystem. The security of RSA is based on the difficulty of factoring the modulus which is the product of the two large prime numbers. If the modulus is factorized, RSA is broken. VFactor is a new factorization algorithm which can factorize the modulus faster than Fermat's Factorization algorithm (FFM) and Trial Division algorithm (TDM). The runtime of VFactor depends on the difference between the two large prime numbers but not on the size of the modulus. In this paper, we propose implementing Modified VFactor (MVFactor) modified from VFactor in order to decrease the processing time in computation. Key to MVFactor is the decrease of computation time of computing the product of two integers. Experiments have shown that when using MVFactor, the computation speed increases in comparison to VFactor. However, if the difference between the two prime numbers is large, then the computation time of MVFactor is more decreased than the computation time of VFactor.