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Journal of Experimental and Theoretical Physics

Side Channels of Information Leakage in Quantum Cryptography: Nonstrictly Single-Photon States, Different Quantum Efficiencies of Detectors, and Finite Transmitted Sequences

S. N. Molotkov

Published Sep 1, 2021• 16 citations
Publisher

Abstract

Abstract The implementation of quantum cryptography systems significantly differs from idealized models used to prove the secrecy of distributed keys. Without taking into account the imperfections of real systems, it is impossible to seriously talk about cryptographic strength. The practical use of quantum cryptography systems requires taking into account all the real factors affecting the secrecy of distributed keys. In this paper, in fact an analytical method is proposed that takes into account the nonstrict single-photon nature of information states, different quantum efficiencies of detectors, fluctuations of parameters due to finite transmitted sequences, information leakage through side channels during both passive detection of side radiation and active probing of the components of the system. The states in the side channels may have extremely low intensity; therefore, they are considered in quantum terms. The maximum possible total information leakage to the eavesdropper in all channels is achieved in joint collective measurements of both quantum information states and quantum states in side channels. The method is applicable to any spectral distribution of the number of photons in side channels.

DOI
10.1134/s1063776121080136

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Abstract The implementation of quantum cryptography systems significantly differs from idealized models used to prove the secrecy of distributed keys. Without taking into account the imperfections of real systems, it is impossible to seriously talk about cryptographic strength. The practical use of quantum cryptography systems requires taking into account all the real factors affecting the secrecy of distributed keys. In this paper, in fact an analytical method is proposed that takes into account the nonstrict single-photon nature of information states, different quantum efficiencies of detectors, fluctuations of parameters due to finite transmitted sequences, information leakage through side channels during both passive detection of side radiation and active probing of the components of the system. The states in the side channels may have extremely low intensity; therefore, they are considered in quantum terms. The maximum possible total information leakage to the eavesdropper in all channels is achieved in joint collective measurements of both quantum information states and quantum states in side channels. The method is applicable to any spectral distribution of the number of photons in side channels.
Abstract Quantum key distribution systems are open systems in the sense that in addition to attacking quantum states in the quantum communication channel, the eavesdropper can obtain additional information about the transmitted key using passive radiation detection of the transmitting and receiving stations, as well as active probing of the state of the equipment through a fiber communication line. In this paper, we consider the cryptographic robustness of a quantum cryptography system that uses a protocol with phase coding based on strongly weakened coherent geometrically uniform states. Non-strict single-photon information states, as well as information leakage through side channels, are taken into account by the generalized Decoy State method, taking into account joint collective measurements of information quantum states and quantum states in side channels. An estimate of the secret key length is obtained, which is expressed only in terms of the observed values at the receiving station and the parameters of quantum states in the side channels.
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.
In quantum cryptography, in addition to attacks on transmitted quantum states, states in side channels of information leakage can be detected. The security of keys in real quantum cryptography systems cannot be analyzed without the inclusion of information leakage through side channels. A quantum-mechanical method has been proposed in this work to take into account key information leakage through side channels. This method is based on the detection of side electromagnetic radiation, active probing of a phase modulator at the transmitter station, and re-emission of avalanche detectors at the receiver side. The method takes into account joint collective measurements of quantum states in all channels of information leakage and operates at any intensity and structure of states in side channels. The choice of special prolate spheroidal functions makes it possible to “match” the quantum and classical descriptions of signals in side channels. A relation has been found between information leakage and the fundamental Holevo quantity. A transparent and intuitively clear physical interpretation of the results has been given.
Abstract Various Trojan-horse attacks on quantum cryptography systems are systematically considered: an attack with passive detection of side radiation, an attack with active sensing, as well as joint attacks on states in the quantum channel, side and reflected radiation. It is shown that the most effective attack is an attack with the measurement of the number of photons in the reflected states and further joint measurement of information and reflected quantum states. Explicit estimates are obtained for the intensity of the reflected quantum states at which secret keys can be transmitted to a given length.
Abstract The robustness of a quantum cryptography system is considered that uses a protocol with phase–time coding on attenuated coherent states. This protocol admits an effective fiber optic implementation, which does not require a phase modulator on the receiver side and adjusting the polarization state at the input of the receiver side. The absence of a phase modulator on the receiver side excludes a side channel of information leakage associated with the active probing of the phase modulator at the receiving station, thus making the system more robust against such attacks compared to other systems. The nonstrict single-photon nature of information states, as well as information leakage through side channels, is considered by the generalized decoy state method, which takes into account joint collective measurements of information quantum states and quantum states in side channels. An estimate for the secret key length is obtained that is expressed only in terms of observed quantities at the receiving station and the parameters of quantum states in side channels.
The security of cryptographic keys in quantum cryptography systems is guaranteed by fundamental quantum mechanical exclusion principles. A quantum channel through which quantum states are transferred is not controlled and an eavesdropper can perform any modifications with it. The security of quantum key distribution protocols has already been proved [M. Tomamichel et al., Nature Commun. 3 , 634 (2011); S. N. Molotkov, J. Exp. Theor. Phys. 115 , 969 (2012)], including the realistic case of a finite length of transmitted sequences. It is always assumed that the eavesdropper has neither direct nor indirect access to the transmitting and receiving equipment. The real situation is somewhat different. The preparation and detection of quantum states occur according to random sequences that are generated on the transmitter and receiver sides. Detecting electromagnetic radiation generated in these processes, the eavesdropper can obtain additional information on a key. The upper quantum-mechanical bound on the amount of information of the eavesdropper on the key that can be obtained through a side channel has been determined.