Modified trial division algorithm using KNJ-factorization method to factorize RSA public key encryption

Abstract

The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the past years. The offered KNJ-Factorization algorithm contributes a deterministic way to factorize RSA N=p*q. The algorithm limits the search by only considering the prime values. Subsequently prime numbers are odd numbers (apart from 2) accordingly it also requires smaller number steps to factorize RSA. In this paper, the anticipated algorithm is very simple besides it is very easy to understand and implement. The main concept of this KNJ-factorization algorithm is, to check only those factors which are odd and prime. The proposed KNJ-Factorization algorithm works very efficiently on those factors; which are adjoining and close to √N. The proposed factorization method can speed up if we can reduce the time for primality testing. It fundamentally decreases the time complexity.