Modified Trial Division Algorithm Using KNJ-Factorization Method To Factorize RSA Public Key Encryption

TL;DR

This paper introduces a deterministic, efficient factorization algorithm called KNJ-Factorization for RSA that reduces search space by focusing on odd prime factors, potentially speeding up RSA key cracking.

Contribution

The paper presents a new prime-focused factorization method that simplifies and speeds up RSA factorization compared to existing algorithms.

Findings

Efficiently factors RSA modulus by considering only odd prime candidates.

Reduces the number of steps needed to factorize RSA keys.

Decreases time complexity of RSA factorization process.

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. The algorithm limits the search by only considering the prime values. Subsequently prime numbers are odd numbers 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.