RSA from the Perspective of Modular Analysis of Prime Gaps

In this paper, we develop an analysis of the multiplication of two prime numbers, particularly with respect to parity, based on whether the difference between the prime numbers is a multiple of six. Using this analysis, we make it possible to obtain information about the difference between the prime numbers by using the multiplication of two prime numbers. We also examine their impact on the RSA cryptographic system. Using the algebraic regularities identified, we propose two new algorithms, SMFA and SMFA-P, to identify potential vulnerabilities in the factorization problem, on which RSA relies for security. Thus, we provide a new perspective connecting prime number difference distributions to modern public-key cryptography.