Abstract
Early proofs of key secrecy in quantum cryptography systems were based on the assumption that the transmitting and receiving stations are completely isolated from the outside world—the eavesdropper. However, this condition cannot be implemented in practice since quantum cryptography systems are open systems in the sense that the eavesdropper may have indirect access, for example, through a fiber communication channel, to the critical elements of the equipment (phase modulators, intensity modulators, etc.) using active probing of the state of these elements. The state of the elements carries information about the transmitted key. In addition, the eavesdropper can use passive detection of side radiation from the receiving and transmitting equipment. Signals in side channels of information leakage may have extremely low intensity and are actually quantum signals. The eavesdropper may use the joint measurement of quantum information states in the communication channel and of states in various side channels of information leakage. The paper considers both passive attacks with measurement of side radiation and active attacks involving the probing of the states of the phase modulator and the intensity modulator, as well as backscattering radiation of single-photon avalanche detectors, which occurs during detecting information states on the receiver side. Combined attacks are also considered. The decoy state method is generalized with regard to active probing attacks, and boundaries for state parameters in side communication channels are obtained that guarantee secret key distribution for a given length of the communication channel.
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Notes
Note that, to obtain the limit as Q → 0 in formula (34), one should apply L’Hospital’s rule to the second order of smallness when expanding the denominator 1 – ε2 and the numerator to the second order of smallness in 1 – 2Q.
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ACKNOWLEDGMENTS
I am grateful to I.M. Arbekov, S.P. Kulik, K.A. Balygin, and A.N. Klimov for numerous interesting discussions, as well as to my colleagues from the Academy of Cryptography of the Russian Federation for discussions and support.
Funding
This work was supported by the Russian Science Foundation, project no. 16-12-00015 (continuation).
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Translated by I. Nikitin
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Molotkov, S.N. Trojan Horse Attacks, Decoy State Method, and Side Channels of Information Leakage in Quantum Cryptography. J. Exp. Theor. Phys. 130, 809–832 (2020). https://doi.org/10.1134/S1063776120050064
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DOI: https://doi.org/10.1134/S1063776120050064