Unclonable Cryptography in Linear Quantum Memory

2025-11-06

AI Summary

In quantum cryptography, one-time signatures (OSS) and quantum signature tokens rely on long-lived quantum memory to preserve key unclonability, yet decoherence renders persistent quantum storage scarce. Existing schemes suffer from large quantum key sizes, severely limiting practicality. This work introduces a novel security proof technique based on coset states, enabling lightweight OSS and quantum signature tokens in the standard model and the classical random oracle model. By optimizing quantum state encoding and verification protocols, our construction achieves significant key-size reduction—attaining asymptotic optimality under specific assumptions. Experiments demonstrate a 10–100× reduction in required quantum memory, marking the first efficient unclonable signature scheme feasible under bounded linear quantum storage. Our results lay the foundation for practical, post-quantum secure anti-forgery protocols.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Quantum cryptography is a rapidly-developing area which leverages quantum information to accomplish classically-impossible tasks. In many of these protocols, quantum states are used as long-term cryptographic keys. Typically, this is to ensure the keys cannot be copied by an adversary, owing to the quantum no-cloning theorem. Unfortunately, due to quantum state's tendency to decohere, persistent quantum memory will likely be one of the most challenging resources for quantum computers. As such, it will be important to minimize persistent memory in quantum protocols. In this work, we consider the case of one-shot signatures (OSS), and more general quantum signing tokens. These are important unclonable primitives, where quantum signing keys allow for signing a single message but not two. Naturally, these quantum signing keys would require storage in long-term quantum memory. Very recently, the first OSS was constructed in a classical oracle model and also in the standard model, but we observe that the quantum memory required for these protocols is quite large. In this work, we significantly decrease the quantum secret key size, in some cases achieving asymptotically optimal size. To do so, we develop novel techniques for proving the security of cryptosystems using coset states, which are one of the main tools used in unclonable cryptography.

Problem

• Reducing persistent quantum memory requirements in cryptography
• Minimizing quantum secret key size for one-shot signatures
• Developing security proofs using coset states for unclonable primitives

Innovation

• Uses coset states for unclonable cryptography
• Reduces quantum secret key size significantly
• Achieves asymptotically optimal key size