International Journal of Scientific Research and Engineering Development

Since its inception in 1977, the Rivest Shamir Adleman (RSA) algorithm has functioned as the foundational pillar of modern asymmetric cryptography. This experimental research article presents a comprehensive examination of the RSA algorithm's evolutionary trajectory, analyzing its mathematical underpinnings, historical vulnerabilities, and contemporary applications. Grounded in the computational asymmetry of the integer factorization problem, RSA has undergone continuous adaptation to withstand increasing computational power and algorithmic advancements, notably the transition from Trial Division to the General Number Field Sieve (GNFS). This study critically evaluates the progression of RSA key sizes from the original 426-bit implementations to the modern 2048-bit and 3072-bit standards mandated by NIST. Furthermore, it addresses critical protocol level enhancements, dissecting the failure of PKCS#1 v1.5 padding against Bleichenbacher's chosen cipher text attacks and the subsequent adoption of Optimal Asymmetric Encryption Padding (OAEP). Finally, the research explores RSA's indispensable role in securing modern digital infrastructure, including transport layer security (TLS) in full stack web architectures, while projecting the algorithm's viability against the looming existential threat posed by quantum computing and Shor's algorithm. The findings synthesize structural developments and deployment paradigms, offering insights into the future of hybrid cryptosystems.

R.Rachel, G.Sushma, V.Saravanakumar,"Evolution of RSA Algorithm and its Applications" International Journal of Scientific Research and Engineering Development, V9(4): Page(01-07) May-June 2026. ISSN: 2581-7175. www.ijsred.com. Published by Scientific and Academic Research Publishing.