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Implementing a Quantum Coin Scheme

Hazel Murray, Jerry Horgan, Joao F. Santos, David Malone, Harun Šiljak

Published Jan 1, 2020• 3 citations
OpenAlex

Abstract

Quantum computing has the power to break current cryptographic systems, disrupting online banking, shopping, data storage and communications. Quantum computing also has the power to support stronger more resistant technologies. In this paper, we describe a digital cash scheme created by Dmitry Gavinsky, which utilises the capability of quantum computing. We contribute by setting out the methods for implementing this scheme. For both the creation and verification of quantum coins we convert the algebraic steps into computing steps. As part of this, we describe the methods used to convert information stored on classical bits to information stored on quantum bits.

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Implementing a Quantum Coin Scheme

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Quantum computing has the power to break current cryptographic systems, disrupting online banking, shopping, data storage and communications. Quantum computing also has the power to support stronger more resistant technologies. In this paper, we describe a digital cash scheme created by Dmitry Gavinsky, which utilises the capability of quantum computing. We contribute by setting out the methods for implementing this scheme. For both the creation and verification of quantum coins we convert the algebraic steps into computing steps. As part of this, we describe the methods used to convert information stored on classical bits to information stored on quantum bits.

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We propose an information theoretically secure secret-key quantum money scheme in which the verification of a coin is classical and consists of only one round; namely, a classical query from the user to the bank and an accept/reject answer from the bank to the user. A coin can be verified polynomially (on the number of its qubits) many times before it expires. Our scheme is an improvement on Gavinsky's scheme [Gavinsky, Computational Complexity, 2012], where three rounds of interaction are needed and is based on the notion of quantum retrieval games. Moreover, we propose a public-key quantum money scheme which uses one-time memories as a building block and is computationally secure in the random oracle model. This construction is derived naturally from our secret-key scheme using the fact that one-time memories are a special case of quantum retrieval games.

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The rapid advancement of quantum computing presents a significant challenge to classical cryptographic systems that underpin modern digital security infrastructures. In particular, RSA-2048 encryption, widely deployed in banking and financial institutions for secure transactions, relies on the computational hardness of integer factorization. However, the emergence of quantum algorithms—especially Shor’s algorithm—poses a fundamental threat to RSA security by enabling polynomial-time factorization of large integers on sufficiently powerful quantum computers. This case study investigates the vulnerability of RSA-2048 within a banking environment, analyzing the mathematical foundations of the threat, potential timelines for quantum feasibility, and associated cybersecurity risks. The study further examines the implications for financial data protection, digital signatures, and secure communication channels. In response to these emerging risks, the paper explores post-quantum cryptographic alternatives, including lattice-based, hash-based, and code-based schemes, and evaluates their suitability for banking applications. The findings emphasize the urgency of transitioning toward quantum-resistant cryptographic frameworks and propose strategic recommendations for proactive cryptographic migration to ensure long-term data confidentiality and system resilience.

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Quantum computing has the power to break current cryptographic systems, disrupting online banking, shopping, data storage and communications. Quantum computing also has the power to support stronger more resistant technologies. In this paper, we describe a digital cash scheme created by Dmitry Gavinsky, which utilises the capability of quantum computing. We contribute by setting out the methods for implementing this scheme. For both the creation and verification of quantum coins we convert the algebraic steps into computing steps. As part of this, we describe the methods used to convert information stored on classical bits to information stored on quantum bits.
Quantum computing has the power to break current cryptographic systems, disrupting online banking, shopping, data storage and communications. Quantum computing also has the power to support stronger more resistant technologies. In this paper, we describe a digital cash scheme created by Dmitry Gavinsky, which utilises the capability of quantum computing. We contribute by setting out the methods for implementing this scheme. For both the creation and verification of quantum coins we convert the algebraic steps into computing steps. As part of this, we describe the methods used to convert information stored on classical bits to information stored on quantum bits.
Harnessing the laws of quantum theory can drastically boost the security of modern communication networks, from public key encryption to electronic voting and online banking. In this thesis, we bridge the gap between theory and experiment regarding two quantum-cryptographic tasks: quantum money and quantum weak coin flipping. Quantum money exploits the no-cloning property of quantum physics to generate unforgeable tokens, banknotes, and credit cards. We provide the first proof-of-principle implementation of this task, using photonic systems at telecom wavelengths. We then develop a practical security proof for quantum credit card schemes, in which the bank can remotely verify a card even in the presence of a malicious payment terminal. We finally propose a setup for secure quantum storage of the credit card, using electromagnetically-induced transparency in a cloud of cold cesium atoms. Quantum weak coin flipping is a fundamental cryptographic primitive, which helps construct more complex tasks such as bit commitment and multiparty computation. It allows two distant parties to flip a coin when they both desire opposite outcomes. Using quantum entanglement then prevents any party from biasing the outcome of the flip beyond a certain probability. We propose the first implementation for quantum weak coin flipping, which requires a single photon and linear optics only. We provide the complete security analysis in the presence of noise and losses, and show that the protocol is implementable on the scale of a small city with current technology. We finally propose a linear-optical extension of the protocol to lower the coin bias.
We propose an information theoretically secure secret-key quantum money scheme in which the verification of a coin is classical and consists of only one round; namely, a classical query from the user to the bank and an accept/reject answer from the bank to the user. A coin can be verified polynomially (on the number of its qubits) many times before it expires. Our scheme is an improvement on Gavinsky's scheme [Gavinsky, Computational Complexity, 2012], where three rounds of interaction are needed and is based on the notion of quantum retrieval games. Moreover, we propose a public-key quantum money scheme which uses one-time memories as a building block and is computationally secure in the random oracle model. This construction is derived naturally from our secret-key scheme using the fact that one-time memories are a special case of quantum retrieval games.
The rapid advancement of quantum computing presents a significant challenge to classical cryptographic systems that underpin modern digital security infrastructures. In particular, RSA-2048 encryption, widely deployed in banking and financial institutions for secure transactions, relies on the computational hardness of integer factorization. However, the emergence of quantum algorithms—especially Shor’s algorithm—poses a fundamental threat to RSA security by enabling polynomial-time factorization of large integers on sufficiently powerful quantum computers. This case study investigates the vulnerability of RSA-2048 within a banking environment, analyzing the mathematical foundations of the threat, potential timelines for quantum feasibility, and associated cybersecurity risks. The study further examines the implications for financial data protection, digital signatures, and secure communication channels. In response to these emerging risks, the paper explores post-quantum cryptographic alternatives, including lattice-based, hash-based, and code-based schemes, and evaluates their suitability for banking applications. The findings emphasize the urgency of transitioning toward quantum-resistant cryptographic frameworks and propose strategic recommendations for proactive cryptographic migration to ensure long-term data confidentiality and system resilience.