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.

中文翻译：

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来自四元数代数的量子货币

我们提出了公钥量子货币的新想法。在抽象意义上，我们的账单被编码为一个固定的通勤单一运营商系统的联合本征态。我们对该黑盒系统进行了一些基本分析，并表明它可以抵抗黑盒攻击。为了实例化这个协议，人们需要找到一个密码复杂的可计算、通勤、酉算子系统。为了满足这一需求，我们建议使用 Brandt 算子作用于与某些四元数代数相关的 Brandt 模块。我们解释了为什么我们认为这种实例化可能是安全的。