Quantum Money from Abelian Group Actions

2023-07-22

IACR Cryptology ePrint Archive

AI Summary

Addressing the long-standing challenge of constructing quantum-secure public-key quantum money and quantum lightning resilient against quantum forgery, this paper introduces the first provably secure public-key quantum money scheme and an enhanced quantum lightning scheme by integrating abelian group actions—based on elliptic-curve isogenies—with quantum lightning. Methodologically, we formulate a generic algebraic group action model, develop security reductions in the quantum random oracle model, and construct a quantum-safe proof toolkit tailored to group actions. Our main contributions are threefold: (1) the first integration of abelian group actions with quantum lightning; (2) the first general quantum-security proof framework specifically designed for group actions; and (3) a fundamental characterization of the inherent limitations of knowledge assumptions for algebraic group actions in quantum settings. All schemes achieve rigorous security proofs under standard computational assumptions, establishing a new provably secure paradigm for post-quantum cryptographic currencies.

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.

Problem

• Constructing quantum money from abelian group actions
• Proving security under computational assumptions
• Exploring limitations of quantum knowledge assumptions

Innovation

• Quantum money from abelian group actions
• Security proof in generic group model
• Toolkit for quantum security proofs