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Quantum Electronics

Vulnerabilities of quantum cryptography on geometrically uniform coherent states

Dmitry Anatolevich Kronberg

Published Sep 27, 2021• 5 citations
Publisher

Abstract

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.

DOI
10.1070/qel17625

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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 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.
In a recent paper, Kravtsov and Molotkov [Phys. Rev. A 100, 042329 (2019)] propose a quantum key distribution protocol and claim ``the protocol security is analyzed by an explicit construction of the most optimal unitary attack'' and ``we provide an extensive security analysis of the proposed protocol by considering a general symmetric unitary attack, and give succinct relations for the asymptotic secret key rate in the case of N=8N=8N=8.'' We show that these claims are erroneous and propose two attacks which are more effective than the attacks considered in the paper of Kravtsov and Molotkov.
Abstract The quantum key distribution protocol utilizing 8 geometrically uniform coherent states is considered. We analyze its security against a generalized photon-number-splitting attack. This protocol allows for several basis configurations, and we demonstrate that one of these configurations is more vulnerable. We also use the previously described methods for attack improvement, namely, modification of observable’s coefficients and using extra photon as assistance for increasing success probability.
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.