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Voprosy kiberbezopasnosti

NEW APPROACHES TO EAVESDROPPER INFORMATION BOUNDS IN QUANTUM CRYPTOGRAPHY PROBLEMS

Dmitry Anatolevich Kronberg, Alexander Semenovich Holevo

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.

DOI
10.21681/2311-3456-2025-3-110-117

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Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.
Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation 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.
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.
Entanglement-measurement attack is one of the most famous attacks against quantum cryptography. In quantum cryptography protocols, eavesdropping checking is an effective means to resist this attack. There are currently two commonly used eavesdropping checking methods: one is to prepare two sets of non-orthogonal single-particle states as decoy states, and determine whether there are eavesdroppers in the quantum channel by comparing the states obtained by measurements with the original states; The other is to prepare two sets of non-orthogonal entangled states and use their entanglement correlations to judge whether there are eavesdroppers in the quantum channel. In this paper, we theoretically demonstrate how quantum cryptography can utilize these two eavesdropping checking methods to resist entanglement-measurement attacks. We take the quantum cryptography protocols based on maximally entangled states as examples to demonstrate the proof process, transitioning from qubit-based protocols to qudit-based ones.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
Quantum information theory is a modern branch of theoretical physics. One of its main goals is to interpret concepts of quantum physics. This leads to a deeper understanding of quantum theory. The most common examples of practical applications of basic quantum theory are quantum computation and quantum cryptography. Quantum cryptography provides secure communication between legitimate users even in the presence of an adversary by making possible the distribution of a secret key. It then allows error correction and privacy amplification, which is elimination of adversary information, through classical communication. In this thesis two important aspects of quantum key distribution are covered, namely robustness bounds with respect to provable entanglement for ideal protocols and practical quantum key distribution using two-way classical communication. In part one of the thesis, ideal quantum key distribution protocols and their robustness in terms of provable entanglement are discussed. The robustness bounds are proved for most general coherent attacks. These bounds for provable entanglement are already known to be 25% for the four-state protocol and 33% for the six-state protocol. We anticipate to provide a region in which the legitimate users share entanglement. This region is large for the four-state protocol and is reduced to a smaller region for the six-state protocol because of additional constraint on it. We also investigate the information cost which the adversary has to pay in order to reach these bounds. In part two we adopt a more practical approach. We investigate the limitation on distance of secure communication because of practical restrictions. In particular we investigate the restrictions due to the lack of single photon sources, the lossy channel and faulty detectors. These practical limitations have already been observed using one-way classical communication between legitimate users. It has been observed that it is actually the dark count rate that limit the distance up to which legitimate users can share a secret key. We have used two-way classical communication to postpone the effect of dark counts and increase the distance to considerable amount. For the purpose we have considered an optimal attack with respect to the disturbance that an eavesdropper creates while attacking. Any other format of attacking will increase the disturbance. We show that using two-way classical communication for post processing we can increase the distance of secure communication considerably.