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arXiv:2002.11998 · Quantum

A Quantum Money Solution to the Blockchain Scalability Problem

Andrea Coladangelo, Or Sattath

Published Jul 16, 2020• 42 citations
arXivHTMLPDF

Abstract

We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry [55]. Our hybrid payment system employs quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.

DOI
10.22331/q-2020-07-16-297

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We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry [55]. Our hybrid payment system employs quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.
We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry [Eurocrypt 2019]. Our hybrid payment system uses quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.
Smart contracts are cryptographic protocols that are enforced without a judiciary. Smart contracts are used occasionally in Bitcoin and are prevalent in Ethereum. Public quantum money improves upon cash we use today, yet the current constructions do not enable smart contracts. In this work, we define and introduce quantum payment schemes, and show how to implement prudent contracts -- a non-trivial subset of the functionality that a network such as Ethereum provides. Examples discussed include: multi-signature wallets in which funds can be spent by any 2-out-of-3 owners; restricted accounts that can send funds only to designated destinations; and "colored coins" that can represent stocks that can be freely traded, and their owner would receive dividends. Our approach is not as universal as the one used in Ethereum since we do not reach a consensus regarding the state of a ledger. We call our proposal prudent contracts to reflect this. The main building block is either quantum tokens for digital signatures (Ben-David and Sattath QCrypt'17, Coladangelo et al. Crypto'21), semi-quantum tokens for digital signatures (Shmueli'22) or one-shot signatures (Amos et al. STOC'20). The solution has all the benefits of public quantum money: no mining is necessary, and the security model is standard (e.g., it is not susceptible to 51\% attacks, as in Bitcoin). Our one-shot signature construction can be used to upgrade the Bitcoin network to a quantum payment scheme. Notable advantages of this approach are: transactions are locally verifiable and without latency, the throughput is unbounded, and most importantly, it would remove the need for Bitcoin mining. Our approach requires a universal large-scale quantum computer and long-term quantum memory; hence we do not expect it to be implementable in the next few years.
Quantum money is a main primitive in quantum cryptography, that enables a bank to distribute to parties in the network, called wallets, unclonable quantum banknotes that serve as a medium of exchange between wallets. While quantum money suggests a theoretical solution to some of the fundamental problems in currency systems, it still requires a strong model to be implemented; quantum computation and a quantum communication infrastructure. A central open question in this context is whether we can have a quantum money scheme that uses "minimal quantumness", namely, local quantum computation and only classical communication.
Decentralized finance (DeFi) uses smart contracts to automate payments, lending, and asset management, but current blockchains often suffer from slow, expensive, and energy-hungry execution. In this project, I explore a quantum-enhanced optimization framework for smart contract–based financial services. The main idea is to treat gas use, transaction ordering, and resource allocation as optimization problems that can be tackled by hybrid quantum–classical algorithms. Using a conceptual model, I map smart contract execution to cost functions suitable for the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE). I then compare, at a qualitative level, how these quantum-inspired approaches differ from classical heuristics in terms of expected throughput, latency, and cost. A focused literature review on quantum computing, blockchain scalability, and quantum-safe cryptography provides context for these ideas. The results suggest that quantum-enhanced optimization could reduce gas fees, improve transaction scheduling, and support more efficient consensus under heavy load. The project also discusses the need for post-quantum security so that future quantum computers do not undermine blockchain trust. Overall, the work outlines how quantum computing might contribute to faster, safer, and more sustainable automated financial systems.
The convergence of Quantum Computing and Blockchain marks a transformative step in secure distributed systems, offering immense potential and serious security challenges. Quantum algorithms like Shor’s and Grover’s threaten classical cryptographic foundations such as ECC and symmetric key systems, making current blockchains vulnerable. This study explores these vulnerabilities and proposes a hybrid quantum-secure blockchain architecture that integrates post-quantum cryptography such as lattice-based and hash-based algorithms with traditional methods for backward compatibility and efficiency. It also highlights how quantum technologies can enhance blockchain performance through faster consensus and smart contract optimization. The paper concludes that adopting hybrid quantum-resistant mechanisms is vital for ensuring blockchain security, scalability, and resilience in the post-quantum era.
Quantum computing's development poses a significant threat to the cryptographic security of current blockchain technologies, potentially undermining the integrity of digital transactions. Quantum computers can break the complex mathematical problems that algorithms like RSA and ECC rely on, which could lead to vulnerabilities such as double-spending and fraud. To address these risks, the blockchain community is exploring quantum-resistant protocols that employ post-quantum cryptographic algorithms, which are designed to withstand quantum computing attacks. Quantum-secure blockchain protocols integrate quantum key distribution (QKD) and post-quantum cryptography (PQC) to enhance security. QKD uses quantum mechanics principles to secure communication channels, ensuring that any attempt to intercept the key introduces detectable anomalies. PQC involves algorithms like lattice-based, hash-based, or multivariate polynomial-based algorithms that are believed to be secure against quantum attacks. These protocols aim to maintain the confidentiality, integrity, and security of data transmitted over the blockchain, ensuring the longevity and reliability of blockchain systems in the face of evolving computational advancements. A quantum-secure blockchain scheme (QSB) utilizes a consensus mechanism, QPoA, and IQS. The QPoA is leveraged for block generation while the IQS is deployed in transaction verification1. Furthermore, the integration of quantum computing with blockchain can address current limitations, such as slow transaction speeds and lack of scalability, by optimizing calculations and enabling smarter, more sophisticated smart contracts. The development and implementation of quantum-resistant blockchains are essential for future-proofing digital transactions and maintaining trust in decentralized systems