#### Faculty Advisor

Beezer, Rob

#### Area of Study

Science and Mathematics

#### Publication Date

Summer 2015

#### Abstract

First developed in 2001, the Advanced Encryption Standard (AES) cipher is now one of the most commonly used encryption algorithms worldwide. However, the algebraically simple description of the AES leads some cryptographers to question whether an algebraic weakness in the cipher exists, which would be fatal to the security of the AES. This summer, I studied the algebraic properties of the AES with the goal of designing a computational tool for researchers and algebraic cryptanalysts of the AES which would allow more rigorous study of the algebraic qualities of the AES. I accomplished this by implementing an algebraic representation of the cipher in the open source mathematical software system Sage.

Over the course of this project, my examination of the algebraic properties of the cipher allowed me to create a generalized system of algebraic equations which behaved analogously to the entire cipher. I then used this system of equations as an underlying mathematical framework for an implementation of the AES cipher in Sage, which allowed this implementation to perform the cipher's functions through strictly algebraic means. This allows the implementation to be used for close study of the algebraic properties of the individual steps of the cipher as well as the cipher as a whole in a powerful computing environment, making this tool a valuable addition to the Sage cryptography library.

#### Recommended Citation

Gagne, Thomas, "Building an Algebraic Representation of the AES in Sage" (2015). *Summer Research*. 243.

http://soundideas.pugetsound.edu/summer_research/243

#### Rights

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License

#### Publisher

University of Puget Sound