Quantum Money from Quaternion Algebras
This addresses the challenge of developing practical and secure quantum money systems for cryptographic applications, representing a novel approach rather than an incremental improvement.
The paper tackles the problem of creating secure public key quantum money by proposing a new encoding scheme based on joint eigenstates of commuting unitary operators, and it suggests using Brandt operators on quaternion algebras as a likely secure instantiation.
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.