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arXiv:1010.0256

An online attack against Wiesner's quantum money

Andrew Lutomirski

Published Oct 1, 2010• 24 citations
arXivHTMLPDF

Abstract

Wiesner's quantum money [5] is a simple, information-theoretically secure quantum cryptographic protocol. In his protocol, a mint issues quantum bills and anyone can query the mint to authenticate a bill. If the mint returns bogus bills when it is asked to authenticate them, then the protocol can be broken in linear time.
DOI
10.48550/arxiv.1010.0256

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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.
The concept of quantum money (QM) was proposed by Wiesner in the 1970s. Its main advantage is that every attempt to copy QM unavoidably leads to imperfect counterfeits. In the Wiesner's protocol, quantum banknotes need to be delivered to the issuing bank for verification. Thus, QM requires quantum communication which range is limited by noise and losses. Recently, Bozzio et al. (2018) have demonstrated experimentally how to replace challenging quantum verification with a classical channel and a quantum retrieval game (QRG). This brings QM significantly closer to practical realisation, but still thorough analysis of the revised scheme QM is required before it can be considered secure. We address this problem by presenting a proof-of-concept attack on QRG-based QM schemes, where we show that even imperfect quantum cloning can, under some circumstances, provide enough information to break a QRG-based QM scheme.
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