Georgia Institute of Technology College of Sciences

Given a knot diagram, there are certain questions one can ask: Is this a diagram of the unknot? What is the minimal crossing number? Is this knot a connected sum of two smaller knots? These questions are examples of problems in knot theory for which we do not have an efficient algorithm to solve. In this talk, we will see how these computationally hard problems in knot theory can serve as underpinnings for a quantum-secure cryptography system.

We will first cover the basics of quantum computing and quantum money. Then we will closely examine a quantum money scheme based on knot theory. Specifically, the protocol is based on the apparent difficulty of finding a sequence of Reidemeister/Cromwell moves going between two equivalent diagrams of a link. Finally, we will discuss problems in knot theory that are motivated by this protocol for quantum money.