A Study of the Use of Euler Totient Function in RSA Cryptosystem and the Future of RSA Cryptosystem

At the end of the last century, an innovative two-key cryptosystem called RSA was created due to booming demand for secure remote communication. The core for this encryption system is a mathematical function called the Euler totient function (Euler φ function), introduced by Leonhard Euler. This article will first deduce four theorems related to Euler φ function, and then illustrate the correctness of the RSA cryptosystem using Euler’s φ function. The study then starts with well-known RSA attacks such as the Coppersmith attack, assesses some of RSA’s vulnerabilities, and measures the impact of quantum technologies on RSA. Finally, this study provides projections and recommendations for the future development of RSA based on all evaluation studies completed during the entire research program.