Paper 2021/1294

Quantum Money from Quaternion Algebras

Daniel M. Kane and Shahed Sharif and Alice Silverberg

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.

Note: This paper can be viewed as an extended version of "Quantum Money from Modular Forms" by Daniel M. Kane (arXiv:1809.05925v2).