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Physical Review A

Small imperfect randomness restricts security of quantum key distribution

Hongwei Li, Zheng-Mao Xu, Qing-yu Cai

Published Dec 20, 2018• 21 citations
Publisher

Abstract

Quantum key distribution protocol requires true random numbers to prepare and measure quantum states, but the randomness may be weakened by applying the imperfect input random numbers or imperfect quantum devices. In this work, we propose the randomness attack model in the practical quantum key distribution system, and we analyze the final secret key rate under the randomness attack. The security analysis result demonstrates that the imperfect randomness can be amplified by considering the signal loss, thus the quantum key distribution system may be attacked even if the randomness has very small part of imperfection. Combining the practical experimental parameters with the small nonrandom probability parameters $0.1%$ and $1%$, we prove that the maximal transmission distance will be sharply reduced from 140 km to 60 and 12 km, respectively.

DOI
10.1103/physreva.98.062325

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Quantum key distribution protocol requires true random numbers to prepare and measure quantum states, but the randomness may be weakened by applying the imperfect input random numbers or imperfect quantum devices. In this work, we propose the randomness attack model in the practical quantum key distribution system, and we analyze the final secret key rate under the randomness attack. The security analysis result demonstrates that the imperfect randomness can be amplified by considering the signal loss, thus the quantum key distribution system may be attacked even if the randomness has very small part of imperfection. Combining the practical experimental parameters with the small nonrandom probability parameters 0.10.1%0.1 and 11%1, we prove that the maximal transmission distance will be sharply reduced from 140 km to 60 and 12 km, respectively.
The security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing imperfect state preparation and measurement devices. In this work, we analyze the security of the practical quantum key distribution system with weak-randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $\ensuremath{\epsilon}$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $\ensuremath{\epsilon}$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from 142 to 139 km if $\ensuremath{\epsilon}\ensuremath{\le}0.1$, but no secret key can be generated in the case of $\ensuremath{\epsilon}\ensuremath{\ge}0.34$.
Abstract Ideal randomness is one of most important conditions for the implementation of continuous-variable quantum key distribution (CVQKD). However, imperfect randomness may exist in a practical CVQKD system due to imperfections in Gaussian modulation or in random-number generators. Here we propose a weak randomness attack model in practical CVQKD systems to investigate the practical performance of the systems with imperfect randomness, where the prepared coherent states based on nonrandom state modulation are assumed to be known by Eve. Then, we perform parameter estimation and calculate the secret key rate of the system based on the proposed attack model. The simulation results demonstrate that a small imperfect randomness can dramatically reduce the secret key rate of the system, which may seriously limit the practical performance of the system. Therefore, true random numbers and perfect Gaussian modulation are key for practical CVQKD systems.
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system.
Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number N=1012N=10^{12}N=1012 and the SKR closely approaches the asymptotic limit up to 250 km with N=1014N=10^{14}N=1014. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.
ABSTRACT Quantum key distribution (QKD) enables long‐distance secret keys transmission with information‐theoretic security. However, weak‐randomness obviously limits the security of practical QKD systems. This may leak the key information by considering the imperfect devices. In this work, we proposed a practical security analysis model that simultaneously considers the bit‐weak‐randomness and the basis‐weak‐randomness parameters, which we refer to as the weak‐randomness model. First, we establish a novel bit‐weak‐randomness model based on the virtual mutually unbiased bases method. Subsequently, under the framework of information‐theoretic security proof, we proposed a comprehensive weak‐randomness model by incorporating the basis‐weak‐randomness model. Then, we characterize the relationship between typical quantum attacking strategies and weak‐randomness parameters. Based on our proposed weak‐randomness model, we perform a security analysis against these attacks. Finally, we perform numerical simulations of the weak‐randomness model based on the advantage distillation method, considering both single photon sources and weak coherent sources. Our results can provide a model capable of characterizing security parameters to simultaneously account for the impacts of both imperfect devices and quantum hacking. This enables a unified standard for evaluating the security levels of practical QKD systems and offers a theoretical foundation for QKD system testing and assessment.
The ideal quantum key distribution (QKD) protocol requires perfect random numbers for bit encoding and basis selecting. Perfect randomness is of great significance to the practical QKD system. However, due to the imperfection of practical quantum devices, an eavesdropper (Eve) may acquire some random numbers, thus affecting the security of practical systems. In this paper, we analyze the effects of the weak randomness in the measurement-device-independent QKD (MDI-QKD) with finite resources. We analytically derive concise formulas for estimating the lower bound of the single-photon yield and the upper bound of the phase error rate in the case of the weak randomness. The simulation demonstrates that the final secret key rate of MDI-QKD with finite resources is sensitive to state preparation, even with a small proportion of weak randomness, the secure key rate has a noticeable fluctuation. Therefore, the weak randomness of the state preparation may bring additional security risks. In order to ensure the practical security of the QKD system, we are supposed to strengthen the protection of state preparation devices.