Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

McMurran, Shawnee


We live in an age where we willingly provide our social security number, credit card information, home address and countless other sensitive information over the Internet. Whether you are buying a phone case from Amazon, sending in an on-line job application, or logging into your on-line bank account, you trust that the sensitive data you enter is secure. As our technology and computing power become more sophisticated, so do the tools used by potential hackers to our information. In this paper, the underlying mathematics within ciphers will be looked at to understand the security of modern ciphers.

An extremely important algorithm in today's practice is the Advanced Encryption Standard (AES), which is used by our very own National Security Agency (NSA) for data up to TOP SECRET. Another frequently used cipher is the RSA cryptosystem. Its security is based on the concept of prime factorization, and the fact that it is a hard problem to prime factorize huge numbers, numbers on the scale of 2^{2048} or larger. Cryptanalysis, the study of breaking ciphers, will also be studied in this paper. Understanding effective attacks leads to understanding the construction of these very secure ciphers.