My disclaimer: I don't know what any of this means, but it might give you a direction to start your research.

First thing he came up with is Number Theory, and how they've been working on that for centuries, but they never would have imagined that it would be the basis of modern encryption. Multiplying a HUGE prime number with any other numbers is incredibly easy, but factoring the result into those same numbers is near impossible (within reasonable time constraints.)

He said something about knot theory and bacterial proteins, but it was too far above my head to even try to relay how that's relevant.