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arXiv:1812.09256 · Physical Review A

Semi-device-independent quantum money with coherent states

Mathieu Bozzio, Eleni Diamanti, Frédéric Grosshans

Published Feb 27, 2019• 28 citations
arXivHTMLPDF

Abstract

The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client, and a payment terminal and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client, and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.

DOI
10.1103/physreva.99.022336

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The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client, and a payment terminal and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client, and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.
Abstract Wiesner’s unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated transactions offering security guarantees impossible to achieve by classical means. However, despite its central role in quantum cryptography, its experimental implementation has remained elusive because of the lack of quantum memories and of practical verification techniques. Here, we experimentally implement a quantum money protocol relying on classical verification that rigorously satisfies the security condition for unforgeability. Our system exploits polarization encoding of weak coherent states of light and operates under conditions that ensure compatibility with state-of-the-art quantum memories. We derive working regimes for our system using a security analysis taking into account all practical imperfections. Our results constitute a major step towards a real-world realization of this milestone protocol.
Wiesner's unforgeable quantum money scheme is widely celebrated as the first quantum information application. Based on the no-cloning property of quantum mechanics, this scheme allows for the creation of credit cards used in authenticated transactions offering security guarantees impossible to achieve by classical means. However, despite its central role in quantum cryptography, its experimental implementation has remained elusive because of the lack of realistic protocols adapted to practical quantum storage devices and verification techniques. Here, we experimentally demonstrate a quantum money protocol that rigorously satisfies the security condition for unforgeability, using a practical system exploiting single-photon polarization encoding of highly attenuated coherent states of light for on-the-fly credit card state generation and readout. Our implementation includes classical verification and is designed to be compatible with state-of-the-art quantum memories, which have been taken into account in the security analysis, together with all system imperfections. Our results constitute a major step towards a real-world realization of this milestone protocol.
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.
Abstract The seminal idea of quantum money, not forgeable due to laws of Quantum Mechanics, proposed by Stephen Wiesner, has laid the foundations for the Quantum Information Theory in the early ’70s. Recently, several other schemes for quantum currencies have been proposed, all, however, relying on the assumption that the quantum source device, acts according to its specification. This makes several known quantum money protocols vulnerable to the so-called hardware Trojan horse attacks. We, therefore, study the following problem: to what extent quantum money schemes can be made independent from the inner working of source and verification-devices used by the honest parties (bank and mint) in creating and processing the quantum money? Drawing inspirations from the semi-device-independent quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its unforgeability. Finally, we formulate and discuss a quantum analog of the Oresme–Copernicus–Gresham’s law of economy, that may hold in the future.
This thesis is concerned with the study and analysis of two quantum cryptographic protocols: quantum key distribution (QKD) and unforgeable quantum money in the continuous-variable (CV) framework. The main advantage of CV protocols is that their implementation only requires standard telecom components. QKD allows two distant parties, Alice and Bob, to establish a secure key, even in the presence of an eavesdropper, Eve. The remarkable property of QKD is that its security can be established in the information-theoretic setting, without appealing to any computational assumptions. Proving the security of CV-QKD protocols is challenging since the protocols are described in an infinite-dimensional Fock space. One of the open questions in CV-QKD was establishing security for two-way QKD protocols against general attacks. We exploit the invariance of Unitary group U(n) of the protocol to establish composable security against general attacks. We answer another pressing question in the field of CV-QKD with a discrete modulation by establishing the asymptotic security of such protocols against collective attacks. We provide a general technique to derive a lower bound on the secret key rate by formulating the problem as a semidefinite program. Quantum money exploits the no-cloning property of quantum mechanics to generate unforgeable tokens, banknotes, and credit cards. We propose a CV private-key quantum money scheme with classical verification. The motivation behind this protocol is to facilitate the process of practical implementation. Previous classical verification money schemes use single-photon detectors for verification, while our protocols use coherent detection.
A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report a proof-of-principle experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6\ifmmode\times\else\texttimes\fi{}{10}^{6}$ states in one verification round, limiting the forging probability to ${10}^{\ensuremath{-}7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.