Quantum Money from Abelian Group Actions

TL;DR

This paper introduces a new method for creating public key quantum money and quantum lightning using abelian group actions derived from elliptic curve isogenies, with security proofs and analysis of underlying assumptions.

Contribution

It presents a novel construction of quantum money schemes from abelian group actions and develops a framework for proving their security in the generic group model.

Findings

Security proven in the generic group model under plausible assumptions

Developed a toolkit for quantum security proofs in group action settings

Identified limitations of knowledge assumptions in quantum algebraic group actions

Abstract

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.