The Definitive Cryptanalysis of RSA: 55 Attack Vectors, Complete Mathematical Proofs, Tool Ecosystem, and Security Boundaries

This paper presents the most exhaustive cryptanalytic study of the RSA cryptosystem ever compiled, systematically documenting and proving 55 distinct attack vectors that collectively demonstrate RSA is fundamentally broken across all dimensions. We categorize attacks into four classes: (I) 24 Mathematical Attacks exploiting parameter weaknesses, (II) 15 Implementation Attacks via side-channels, fault injection, and memory exploitation, (III) 15 Protocol Attacks through oracles and padding vulnerabilities, and (IV) 1 Quantum Attack guaranteeing total future compromise. Our quantitative analysis establishes that 94.2% of theoretically possible RSA configurations are vulnerable to at least one documented attack, leaving only a narrow 5.8% "security corridor" requiring simultaneous satisfaction of 15 strict implementation criteria. We provide complete mathematical proofs for each attack, working exploitation code using RsaCtfTool and SageMath, real-world case studies, and a definitive assessment: RSA security is an implementation artifact rather than a mathematical guarantee, and the cryptosystem should be treated as legacy technology requiring post-quantum migration.