As Hugh Williams looks back on his career, he recognizes that there have been many people and conversations that have set and sometimes changed the direction of his career.
“There are a lot of people who influence you in different ways,” says Williams. “You don’t even think of it at the time, but they all make a difference in your life.”
Williams became fascinated with number theory as a teenager and set his sights on pursuing a math degree at nearby McMaster University. When a former math teacher, Mr. Watts, offered to take him on a tour of the University of Waterloo, he realized it was a better fit.
“I got an interview with the great Ralph Stanton. He and I had a lengthy chat. He was impressed enough that he provided me with a scholarship that would pay for my first year,” says Williams. “I liked Waterloo. I liked the newness of the place.”
In 1967, Waterloo converted their math department into a mathematics faculty and created five separate departments, one of which was called Applied Analysis and Computer Science. Don Cowan suggested that Williams pursue his PhD degree in computer science. This move set his career in motion.
“Computer science interested me because I wanted to understand how you can solve problems that arise in number theory,” says Williams. “Some problems can be quite complicated. Wesley Graham was very helpful to three of us: Gus German, Bob Zarnke and I, who were working on the Cattle Problem of Archimedes, an unsolved problem dating back to about 220 BCE. In particular, he got us time on the IBM 7040, which was the fastest computer around. Once we solved the cattle problem, he advertised our achievement extensively, and we became ambassadors for the university’s computing program.
After completing his PhD under the supervision of Ron Mullin, Williams accepted a faculty position at the University of Manitoba where Ralph Stanton was building a new department of Computer Science. His research continued to focus on computational number theory, but things changed again in 1976 with the publication of the Diffie-Hellman paper, New Directions in Cryptography.
“At that time, cryptography was practiced as a dark art not as an academic subject,” says Williams. “But grant money was readily available. I was right there when all this stuff started to happen around me. There were things that we discovered – real surprises. Ideas that seemed so very theoretical with no practical applications turned out to have practical applications. It was always amazing.”
In 1980, during a visit to Stanford University, an opportunity to attend a lecture by Martin Hellman led Williams to write his most cited paper by far on public key cryptography. The paper was published in IEEE Transactions on Information Theory and was recognized in the ISO/IEC 9796, ANSI X9.31 and the IEEE1363 standards for public-key cryptography and digital signatures.
“At the time, I didn’t think much of it at all,” says Williams. “After the class, I had a chance to talk with Ralph Merkel, one of Hellman’s students, for a few minutes. He told me about a result that came out of Harvard. I started thinking about it and prepared the paper. It was all because of a chance conversation.”
In 2001, after 31 years at the University of Manitoba, Williams was invited to join the University of Calgary’s Department of Mathematics and Statistics as the Alberta Informatics Circle of Research Excellence (iCORE) Chair in Algorithmic Number Theory and Cryptography. He was instrumental in establishing one of Canada’s leading research centres in cryptography and information security.
Although he officially retired in 2016, he continues his research and collaborates with students and other researchers. He considers the students he has taught and mentored to be the most important part of his career.
“The students were the most important thing,” he says. “I could teach them and watch their interest flourish. It was kind of like being a parent. My favourite time was when a student would come in with some computer output and plop it down on my desk and work to figure out what was going on.”
His students, his research, and his many accomplishments are all sources of pride for Williams.
“Naming a particular accomplishment is like trying to choose a favourite child,” says Williams. “They’re from different times and different parts of life. As you get older, one of the pleasures is to have the ability to look back and see the impact.”