RSA Encryption and Number Theory
Alice Flarend, Robert Hilborn · 2026
Abstract This chapter sets the background for the famous Shor algorithm that can allow a sufficiently powerful quantum computer to easily break the current classical RSA encryption method. The RSA algorithm relies on the impossibility of even the most powerful classical computers to factor large numbers in any practical length of time. Before going through the details of the RSA encryption method, the number theory of the modulus or mod function is explained with many examples including exponential ones. The connection between factoring and the periodicity of mod functions is emphasized because it is needed for the RSA and Shor algorithms. The in-depth explanation of the RSA algorithm makes use of number theory to explain how the encryption key can be made public while other information is kept secret to ensure secure communication.