Class of 2021: Clayton Bollinger

Clayton Bollinger is a Mathematics and Computer Science double major from Westminster, Maryland.

Aha moment: Group Theory. The course Abstract Algebra is mostly a study of group theory; the whole concept of group theory provided the vocabulary to describe, in general, math I have been doing my whole life with integers and real numbers and apply those concepts that to (arguably) more interesting groups of numbers.

Took me totally by surprise: During my freshman year, I took an ASL First Year Seminar. I was anxious to learn a new, signed language, and was not expecting to be able to connect with the class very well. I ended up loving my First Year Seminar and decided to minor in ASL and Deaf Studies while at McDaniel. My time in the ASL department was some of my favorite while at McDaniel and I am thankful for the community fostered by, and education I received from, my ASL professors.

My favorite spot on campus: Hoover Library on the second quiet floor. I love going to the very back of the floor and sitting by a window to study. The quiet environment, full of shelves of books overlooking the football fields and the Carroll County landscape is so relaxing and calming for me. 

My capstone: My Mathematics Capstone is: “Elliptic Curve Cryptology Through the Diffie-Hellman Key-Exchange.” My Honors Mathematics Capstone is: “The Post-Quantum Future of the Diffie-Hellman Key-Exchange.” My Computer Science capstone is: “Sudoku! The Multi-Player Sudoku App.”

What it’s about: In my Math capstone, I am studying the growing field of elliptic curve cryptology by studying the Diffie-Hellman key-exchange and its history. I am interested in studying how and why the Diffie-Hellman key-exchange’s original implementation using prime fields and modular arithmetic is becoming a thing-of-the-past, and how and why implementing the Diffie-Hellman key-exchange using elliptic curves on prime fields instead and elliptic curve addition is preferred.

In my Honors Math capstone, I am studying the implications of Shor’s algorithm and quantum computers on the traditional implementations of the Diffie-Hellman key-exchange. I wanted to see how the Diffie-Hellman key-exchange could be used in a post-quantum environment and determine if it would be a good cryptologic tool post-quantum.

In my Computer Science capstone, I am developing a Sudoku app that has various single-player and multi-player games. I am excited to be developing my own app, with its own unique structure.

Capstone translated: My Math capstone is about the field of cryptography which is interested in how to communicate information while keeping it secret from an unintended audience. Ever since the mid-to-late 1900s, the Diffie-Hellman key-exchange has been used to secure information by taking advantage of difficult-to-solve math problems. Classically, the problem used is called the “Discrete Logarithm Problem.” However, in its traditional context, the discrete logarithm problem is becoming easier for a perpetrator to solve. I am interested in how we can develop a new discrete logarithm problem that is more difficult by using a more complicated groups of numbers called elliptic curves.

In my Honors Math capstone, I am interested in how a new type of computer called a quantum computer can make the Diffie-Hellman key exchange obsolete. Quantum computers are unique because they allow a user to compute multiple things simultaneously, whereas a traditional computer only allows one computation to be computed at a time. In this extension to my first capstone, I am studying how we can make a protocol like the Diffie-Hellman key-exchange (again using elliptic curves) that is useful in quantum computers.

In my Computer Science capstone, I am making an app so I can play Sudoku (one of my favorite puzzles) with my friends and family.

What’s next: Post-graduation, I will be working as a software engineer. I plan on working for a few years as a software engineer, and then going to grad school to study Machine Learning or Cybersecurity.