This article is part of a series featuring Centre College’s 2020 John C. Young (JCY) Scholars. Centre’s JCY program, now in its 30th year, is designed to serve highly motivated seniors, allowing them to engage in independent study, research or artistic work in their major discipline or in an interdisciplinary area of their choosing.
Computer science and mathematics double major James Easton ‘20 (Louisville, Kentucky) conducted research on elliptic curve cryptography, as a JCY Scholar, working closely with his faculty mentor John Wilson, H.W. Stodghill, Jr. and Adele H. Stodghill Professor of Mathematics.
“The idea behind our project was that elliptic curve cryptography is the current standard for secure communication over the internet,” Easton explained. “However, quantum computers have the potential to undermine the methods behind this cryptographic method. We wanted to find a new method which used elliptic curves which would be resilient to quantum computers.
“We ended up deciding to move away from elliptic curves because quantum computers do not simply undermine the cryptographic method, which relies on elliptic curves, but it undermines the part of elliptic curves which made them useful for cryptography,” he continued. “Instead, we developed a preliminary cryptographic method which relies on an idea called the largest independent set of a graph from a field of math called Graph Theory that could theoretically be resilient to quantum computers.”
The idea for Easton’s project came from a discussion with Wilson about elliptic curves combined with general interest in quantum computing.
“I love abstract algebra, which is the field of math that elliptic curves tend to fall under,” he said. “Moreover, I love computer science, and I have an interest in physics which meant quantum computing played right into my interests.”
“From his computer science courses, he had developed the programming skills and an understanding of complexity of algorithms,” Wilson said. “He had taken several upper level math courses, including courses in abstract algebra topics, as well as a course in graph theory. The encryption idea for his final paper grew out of the graph theory course he was taking concurrently this past spring.”
Easton’s research experience first began with Wilson and him studying quantum computing in order to understand it.
“We looked at elliptic curves to look for potential cryptographic methods using them,” he added. “Once we decided against using elliptic curves, we found graph theory to be promising and developed a potential cryptographic method using the largest independent set of a graph.”
This was the fourth time Wilson has worked on a project with a JCY Scholar. He said all of the students he’s worked with have been hard working and dedicated to doing what it took to successfully complete the project.
“One primary distinction in this project was the way James took the lead in how we should proceed,” he added. “Most of our weekly meetings were spent with James explaining material and ideas that he had been investigating and thinking about, while I was asking clarification questions. By the end of the year, James was much more the expert on the topic, and I the student. It was a true pleasure working with him.”
Overall, Easton said his research experience has been very fruitful.
“Most significantly, I have learned a lot about the process of grappling with and coming to understanding complex concepts and working with a mentor to come up with potential solutions to a problem,” he shared.
“Dr. Wilson is a pleasure to work with. Neither of us knew much about quantum computing going into the project, and so, we learned about it together. Once we began developing our method, he was very helpful in discussing ideas with to create our final result.”
While Wilson has taught Easton many things during his time at Centre, one thing that stands out is that he taught him to keep an open mind in both his research and throughout his life.
“He is always open and accepting and adopting this mindset in my own life has both made me a better person and allowed me to further my research by solving the problem of quantum cryptography with new notions from Graph Theory,” Easton added.
For Easton, being a JCY Scholar has been a great honor.
“I view the other scholars as people from which I can learn a great amount; I believe them to be some of the wisest students on campus, and I am truly lucky to be associated with them,” he said. “Moreover, the program has given me the opportunity to take my learning into my own hands; it has allowed me to grow my ability to think of the world around me in a more critical manner. The importance of this skill is one that I cannot emphasize enough, and I cannot express how grateful I am to have had this opportunity to expand on it.
“In total, being a JCY Scholar has allowed me to be with some of the wisest minds on campus and given me the ability to explore the most important skills, of which I am capable, and to be given that opportunity is truly incredible,” Easton concluded.
Easton is working as a software engineer at Epic Systems, and he hopes to attend graduate school in a few years.
View James Easton’s project here.
by Kerry Steinhofer
June 26, 2020