Quantum Money from Quaternion Algebras

TL;DR

This paper introduces a novel quantum money scheme based on quaternion algebra structures, proposing a cryptographically complex implementation using Brandt operators that is resistant to black box attacks.

Contribution

It presents a new quantum money protocol utilizing quaternion algebra and Brandt operators, offering a potentially secure instantiation against black box attacks.

Findings

The proposed scheme encodes quantum bills as eigenstates of commuting unitaries.

Analysis suggests resistance to black box attacks.

Use of quaternion algebra provides a promising cryptographic foundation.

Abstract

We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform some basic analysis of this black box system and show that it is resistant to black box attacks. In order to instantiate this protocol, one needs to find a cryptographically complicated system of computable, commuting, unitary operators. To fill this need, we propose using Brandt operators acting on the Brandt modules associated to certain quaternion algebras. We explain why we believe this instantiation is likely to be secure.