If I may steal some thunder from Peter Shor, his paper, Quantum money from knots (with Edward Farhi, David Gosset, Avinatan Hassidim, and Andrew Lutomirski) relies for the security of its "quantum money scheme" on
the assumption that given two different looking but equivalent knots, it is difficult to explicitly find a transformation that takes one to the other.
The Alexander polynomial plays a prominent role in the paper.
