Applications of Modular Arithmetic and Recursion to the RSA Cipher

Abstract

Regarding cryptography, one of the most popular forms of encoding information today is the RSA Cipher, used to convert one integer into another. The workings of the RSA Cipher can be described through the lens of modular arithmetic, a branch of number theory focused on remainders when dividing positive integers. This paper will explain the mathematics of the RSA Cipher, methods of decryption, and justifications as to why it is such an effective tool for encoding data.