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Lobachevskii Journal of Mathematics

On Eavesdropping Strategy for Symmetric Coherent States Quantum Cryptography Using Heterodyne Measurement

Ashot S. Avanesov, Dmitry Anatolevich Kronberg

Published Oct 1, 2021• 5 citations
Publisher

Abstract

Abstract Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users.

DOI
10.1134/s1995080221100048

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Abstract Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users.
Abstract Symmetric coherent states are of interest in quantum cryptography, since for such states there is an upper bound for unambiguous state discrimination (USD) probability, which is used to resist USD attack. But it is not completely clear what an eavesdropper can do for shorter channel length, when USD attack in not available. We consider the task of generalized discrimination between symmetric coherent states and construct an operation which enlarges the information content of the states with fixed failure probability. We apply this transformation to develop a zero-error eavesdropping strategy for quantum cryptography on symmetric coherent states.
It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of S.N. Molotkov [ JETP Lett. , 101 (8), 579 (2015) ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.
Abstract Recent results have shown that the secret-key rate of coherent-one-way (COW) quantum key distribution (QKD) scales quadratically with the system’s transmittance, thus rendering this protocol unsuitable for long-distance transmission. This was proven by using a so-called zero-error attack, which relies on an unambiguous state discrimination (USD) measurement. This type of attack allows the eavesdropper to learn the whole secret key without introducing any error. Here, we investigate the feasibility and effectiveness of zero-error attacks against COW QKD with present-day technology. For this, we introduce two practical USD receivers that can be realized with linear passive optical elements, phase-space displacement operations and threshold single-photon detectors. The first receiver is optimal with respect to its success probability, while the second one can impose stronger restrictions on the protocol’s performance with faulty eavesdropping equipment. Our findings suggest that zero-error attacks could break the security of COW QKD even assuming realistic experimental conditions.
Abstract Quantum cryptography uses non-orthogonal quantum states, and the eavesdropper cannot extract full information without being detected. Nevertheless, losses in fiber channels allow for additional eavesdropping strategies based on postselective measurements. Here, we study the strategy based on unambiguous discrimination between mixed quantum states, and its partial version with higher success probability. We find information available to the eavesdropper for two protocols of quantum key distribution, namely, geometrically uniform states and subcarrier wave protocols.
The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor, to some extent the photon-number statistics of the signals even with todays standard detection schemes. We compare our attack to the beam-splitting attack and show that security against the beam-splitting attack does not necessarily imply security against the attack considered here.
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.