Exploring the Cryptographic Potential of the Riemann Zeta Function and Prime Number Distribution

Implications for Modern Cryptographic Protocols and Security

Abstract

Understanding the Riemann hypothesis is integral for the continuation of math into the future and potentially the security of cyberspace. The Riemann hypothesis is one of the Millennium Problems, a set of 7 famous unsolved problems in mathematics.  It is a hypothesis that scientists and mathematicians alike have tried to prove for decades but have not yet been successful. It is hypothesized that it may have applications in various mathematics and scientific fields, such as quantum mechanics. Beyond that, the applications of the Zeta function and Riemann hypothesis are relatively unknown.

One way the hypothesis can potentially be used is in cryptography. Using the implications of the hypothesis and the distribution of prime numbers, algorithms can be created through the primes to send and receive messages with dependable security. In this project, the hypothesis was used to create an algorithm that can generate long alphabetical phrases to relay classified information in a unique way that might be difficult to identify for an adversary. These results indicate that there are applications of the hypothesis in cryptography and that one could algorithmically create prime number sequences that could be used for encryption and decryption. This finding is significant as it provides supplemental evidence for the Riemann hypothesis, while also opening a pathway to explore unfamiliar connections between number theory and cryptography.