# University of Vermont

### John Voight

#### Professor of mathematics, cryptography researcher

It used to be just generals, presidents and criminals who wanted to encrypt secrets. Now it's a necessity for anyone who wants some privacy on their phone, and math theorist John Voight is advancing today's science of secrecy.

For his insights into some of these patterns, including his work on elliptical curves (another mathematical principle at the backbone of today's cutting edge cryptography), Voight won the prestigious Selfridge Prize in 2010 given out by the Number Theory Foundation; he has received support for his research from the National Security Agency; and, in July of this year, he was the winner of a \$400,000 CAREER grant from the National Science Foundation, one the government's highest honors for young scientists.

To get a glimpse into how Voight's research might protect privacy in coming decades try this easy problem: Multiply the prime numbers 6,451 and 7,307. Simple. But now reverse the problem. Take this 47,137,457 result and find the prime factors. Now increase your two prime numbers to something large, in the neighborhood of, say, 200 or 300 digits.

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Fnding the prime factors that made this large product "would take longer than the lifetime of the universe," Voight says, "using all the computing resources in the world."

#### That one-way street, in essence, is the heart of modern cryptography and online security

It's that same basic mathematical tool used by the CIA or your smartphone to take plain words or credit card numbers -- and hide them within impregnable codes.   Or, at least today, codes made this way seem impregnable.

But, Voight is quick to point out:   "We don't have any proof yet that these systems are secure," and the possible arrival of unfathomably fast quantum computers might also change the security equation.

"John has a rare combination of computational wizardry with deep theoretical insight," says Matthew Greenberg, a professor at the University of Calgary and Voight's collaborator.

Voight's research gets to the mathematical heart of these cyber security concerns. While his work is removed from applied cryptography, he is doing basic research that is expanding the mathematical toolbox that could improve current cryptography or give rise to the next generation of systems.