A Quantum Money Solution to the Blockchain Scalability Problem

Andrea Coladangelo1 and Or Sattath2

1Computing and Mathematical Sciences, Caltech
2Computer Science Department, Ben-Gurion University

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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.

Circa 1969, Wiesner proposed the idea of using the principles of quantum mechanics to construct “money that is physically impossible to counterfeit”.

40 years later, Nakamoto invented Bitcoin — a decentralized and censorship resistant form of money. Unlike other modern forms of money, here, no central party has control over the minting process (the issuance, or the printing of the money), users can make payments without permission from a central party, and the system is designed so that it is extremely hard to censor some transactions (for example, of a specific user), or the system as a whole.

Traditionally, quantum money and cryptocurrencies offer different trade-offs. One of the most serious limitations of Bitcoin and other crypto currencies is in terms of throughput: all the transactions need to be recorded in a shared ledger, and reaching consensus on that ledger is a slow process. Bitcoin supports less than 10 transactions per second, which is several orders of magnitude less than needed for a global currency.
Quantum money, on the other hand, is similar to cash, in which the throughput is essentially unbounded, as transactions only involve a payer and a payee; on the other hand, the minting is done by a central party, such as a central bank.

Is there a way to enjoy the benefits of both worlds – the decentralization and censorship resistance of a system such as Bitcoin, as well as the unlimited throughput that quantum money provides? In this work, we show that the answer is affirmative. We achieve this using a recent construction of a certain form of quantum money, called quantum lighting (Zhandry, Eurocrypt’19). Users can transform their “digital” cryptocurrency to quantum money, and use it much like cash. Users can also transform their quantum money back to its digital form, using a new cryptographic primitive which we introduce in this work, called bolt to signature capability.

For our design to be practical, the coherence time of quantum memory needs to increase from milliseconds to years. We expect that this increase would take decades to fruition. Additionally, the security of existing quantum lightning schemes is not satisfying: none of the existing schemes is provably secure based on standard assumptions.

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