We give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves. We prove security in the generic group model for group actions under a plausible computational assumption, and develop a general toolkit for proving quantum security in this model. Along the way, we explore knowledge assumptions and algebraic group actions in the quantum setting, finding significant limitations of these assumptions/models compared to generic group actions.

翻译：我们提出了一种基于阿贝尔群作用的公钥量子货币构造方法，甚至包括一种称为量子闪电的强化版本，该方法可通过椭圆曲线上的适当同源构造实现。我们在群作用的一般群模型下，基于一个合理的计算假设证明了安全性，并发展了一套在该模型中证明量子安全性的通用工具。在此过程中，我们探讨了量子环境下的知识假设与代数群作用，发现这些假设/模型相较于一般群作用存在显著局限性。