Quantum money from knots

TL;DR

This paper introduces a quantum money scheme utilizing superpositions of knot diagrams with identical Alexander polynomials, aiming for security against computational adversaries.

Contribution

It presents a novel quantum money protocol based on topological knot invariants, specifically Alexander polynomials, which is a new approach in quantum cryptography.

Findings

Scheme is based on superpositions of oriented links with same Alexander polynomial

Expected to be secure against computationally bounded adversaries

Provides a concrete implementation of quantum money using knot theory

Abstract

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.