A Novel Approach to Integer Factorization: A Paradigm in Cryptography

Abstract

This article proposes a solution to the factorization problem in cryptographic systems by leveraging the steps of the Toom-Cook algorithm for large-number multiplication. This approach can factor a 200-bit number, with performance varying depending on memory and processing power. Experiments demonstrate that the factorization problem in cryptography can be solved more efficiently by employing algorithms designed for fast and straightforward multiplication of large numbers. Examples include the Schönhage–Strassen algorithm, which is based on polynomials and Fourier transforms, the Fürer algorithm, the second Schönhage–Strassen algorithm using modular arithmetic, and Karatsuba's algorithm. This advancement significantly impacts modern computing and cryptography, enhancing both security and reliability. The proposed technique was extensively tested through simulations using the MATLAB simulator. Experimental results indicate improvements of 91% in efficiency and 95% in accuracy compared to state-of-the-art techniques.