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Problems of Information Transmission

ON THE IMPACT OF HARDWARE AND ALGORITHMIC SOFTWARE PARAMETERS ON THE ACHIEVABLE LINE LENGTH FOR A QUANTUM KEY DISTRIBUTION PROTOCOL WITH PHASE-TIME CODING

V. I Morozov

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Quantum key distribution is one of perspective directions of modern cryptography. It allows the parties of information exchange to develop a common cryptographic key, the secrecy of which is ensured by the laws of quantum mechanics. The paper studies the influence of the characteristics of the quantum channel, as well as the parameters of the applied algorithms on the maximum achievable length of a communication line for a protocol with phase-time coding and decoy states. By computational experiments with a simulation model of a quantum key distribution system based on the above protocol, it was found that the stable operation of the protocol is possible with line length of at most 210 km. It was also shown that this value can be increased by constructing more efficient sifted key correction algorithms.

DOI
10.7868/s3034583925010024

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Quantum key distribution is one of perspective directions of modern cryptography. It allows the parties of information exchange to develop a common cryptographic key, the secrecy of which is ensured by the laws of quantum mechanics. The paper studies the influence of the characteristics of the quantum channel, as well as the parameters of the applied algorithms on the maximum achievable length of a communication line for a protocol with phase-time coding and decoy states. By computational experiments with a simulation model of a quantum key distribution system based on the above protocol, it was found that the stable operation of the protocol is possible with line length of at most 210 km. It was also shown that this value can be increased by constructing more efficient sifted key correction algorithms.
One of the main applications of quantum communication is quantum key distribution, which solves the problem of secure distribution of cryptographic keys between remote users. This paper investigates the performance of a phase-time coding quantum key distribution protocol belonging to the BB84 protocol family. We construct a simulation model that takes into account the peculiarities of hardware operation and physical properties of the transmission medium. Computational experiments with this model have shown that stable operation of the considered protocol is possible over communication lines up to 210 km long, but this parameter can be improved by constructing a more efficient error-correcting code.
Abstract The cryptographic robustness of quantum key distribution (QKD) with phase–time coding against a photon number splitting (PNS) attack is analyzed. The line length up to which a secret key distribution is guaranteed is determined both by the protocol itself and by the efficiency of error correction in raw keys. The effect of different parameters of avalanche single-photon detectors on the length of the secret key distribution line is investigated. To correct errors, various versions of low-density parity-check (LDPC) codes are considered whose efficiency today is the closest to the Shannon theoretical limit.
A review of the existing commercial quantum key distribution systems was conducted. The principle of operation of a fiber-optic quantum key distribution system with phase coding of photon states is described. The operation of the system in the mode of forming quantum keys is described. The synchronization process is analyzed, which consists in detecting a time interval with an optical pulse. The basic properties and parameters of auto-compensation quantum key distribution system are reviewed. The images of the current stand of the quantum-cryptographic network are given. The stand includes two stations of the quantum key distribution system with phase coding of photon states, two servers and data transmission channels. It is shown that the formation of a quantum key in the experiment is carried out at a rate of 500 bits per second. The length of the quantum communication channel in the experiment is 24 km. In this case, the quantum channel consists of a conventional single-mode optical fiber. Trends in the development of quantum key distribution systems, as well as trends in the development of protocols for quantum cryptography was conducted.
The phase-matching protocol is a practical and promising protocol that can surpass the linear key generation rate boundary. However, classical phase-matching quantum key distribution requires the channel attenuation between communicating parties to be symmetric. In practice, channels used are often asymmetric, owing to geographical reasons in a quantum key distribution network. To enhance the practicality of phase-matching, this paper proposes an asymmetric phase-matching protocol based on the classical framework and establishes a relevant mathematical simulation model to study the influence of channel asymmetry on its performance. The simulation results show that channel asymmetry significantly affects the count rate, error rate, gain, and quantum bit error rate (QBER), ultimately, system performance. As the channel attenuation difference increases, the system performance decreases and the rate of decrease accelerates. Key generation becomes impossible when the channel attenuation difference exceeds 4 dB. Although the decoy-state scheme cannot change the system's tolerance to channel attenuation difference, when the channel attenuation difference is large, the increasing of the number of decoy states significantly can improve system performance, with a three-decoy-state phase-matching protocol outperforming a two-decoy-state protocol. Considering the limited data length, the system performance is improved as the data length increases, and the tolerance to channel attenuation differences gradually increases. When the data length exceeds 1012, this improvement does not continue any more. The system cannot break through the boundary of linear key generation rate when the channel attenuation difference is 2 dB and the data length is less than 1012. Comparing with symmetric channels, the system performance improvement is very significant under asymmetric channel conditions as the data length increases.
In real fiber-optic quantum cryptography systems, the avalanche photodiodes are not perfect, the source of quantum states is not a single-photon one, and the communication channel is lossy. For these reasons, key distribution is impossible under certain conditions for the system parameters. A simple analysis is performed to find relations between the parameters of real cryptography systems and the length of the quantum channel that guarantee secure quantum key distribution when the eavesdropper’s capabilities are limited only by fundamental laws of quantum mechanics while the devices employed by the legitimate users are based on current technologies. Critical values are determined for the rate of secure real-time key generation that can be reached under the current technology level. Calculations show that the upper bound on channel length can be as high as 300 km for imperfect photodetectors (avalanche photodiodes) with present-day quantum efficiency (η ≈ 20%) and dark count probability (p dark ∼ 10−7).