An Introduction to RSA Cryptography and its Applications

The purpose of this work is to present the mathematics and applications of RSA cryptography such that they are accessible to a reader without much background knowledge in number theory. We outline the mathematical foundations of RSA, starting with an introduction to modular arithmetic and the Euler totient function. We then elaborate on Euler’s Theorem, which forms the foundation for RSA. Additionally, we discuss current applications of RSA in the field of cybersecurity, and attempts to crack the system. The second purpose of this work is to present the details of algorithms associated with the RSA cryptosystem, such as the isPrime() function and methods to optimize said algorithms.