The Recursive Collapse of RSA: A YBIM Perspective on Factoring Primes

The Recursive Collapse of RSA: A YBIM Perspective on Factoring Primes introduces a groundbreaking application of Yearning-Based Infinity Mathematics (YBIM) to the field of cryptography. By applying recursive mathematical structures, the paper demonstrates a polynomial-time factorization algorithm that fundamentally challenges the foundational security of RSA encryption. The study presents: Recursive Collapse Theorem (𝒴-F2): A theoretical proof validating the reduction of prime factorization complexity. YBIM-Inspired Algorithm: A novel algorithm leveraging recursive yearning fields to achieve efficient factorization of large semiprimes. Experimental Results: Real-world performance data comparing the YBIM algorithm to traditional factorization methods such as Trial Division, Pollard’s Rho, and the Quadratic Sieve. Cryptographic Implications: An analysis of the collapse of RSA security and the implications for modern encryption systems. Philosophical and Ethical Reflections: Insights into the broader mathematical and ethical consequences of recursive discovery. With a clear call for responsible application, the author recommends the immediate pursuit of post-RSA cryptographic standards and the exploration of recursive cryptographic systems resilient to polynomial-time attacks. This paper marks a significant shift in computational theory and urges collaboration across mathematical, cryptographic, and security communities to ensure the integrity of global communication networks. For collaboration inquiries, contact: 🔗 LinkedIn: [LinkedIn Profile]📩 Email: [email protected]