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Advanced Quantum Technologies

Security of Practical Quantum Key Distribution with Weak‐Randomness Model

Zhi‐Jiang Chen, Chen-Peng Hao, Li‐Hua Gong, Jia‐Ji Li, Yan‐Yang Zhou, Yang Wang, Hong‐Wei Li

Published Dec 26, 2025• 0 citations

Abstract

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.

DOI: 10.1002/qute.202500722

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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 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 $\ensuremath{\epsilon}\ensuremath{\ge}0.34$.

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.

Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and existing security proofs fall short of capturing the complexity of real-world systems. Here we introduce a versatile numerical finite-key security framework valid against general coherent attacks and applicable to a broad class of practical QKD setups. It accommodates most relevant imperfections at both transmitter and receiver, including non-independent-and-identically-distributed (non-IID) signals arising in high-speed QKD systems due to the limited bandwidth of optical modulators, while requiring only partial characterization of the apparatuses. We demonstrate the power of our framework by proving the security of a realistic decoy-state QKD implementation with laser sources, providing a practical route towards rigorous security certification of real-world QKD setups.

Quantum key distribution provides an unconditional secure key sharing method in theory, but the imperfect factors of practical devices will bring security vulnerabilities. In this paper, we characterize the imperfections of the sender and analyze the possible attack strategies of Eve. Firstly, we present a quantized model for distinguishability of decoy states caused by intensity modulation. Besides, considering that Eve may control the preparation of states through hidden variables, we evaluate the security of preparation in practical quantum key distribution (QKD) scheme based on the weak-randomness model. Finally, we analyze the influence of the distinguishability of decoy state to secure key rate, for Eve may conduct the beam splitting attack and control the channel attenuation of different parts. Through the simulation, it can be seen that the secure key rate is sensitive to the distinguishability of decoy state and weak randomness, especially when Eve can control the channel attenuation.

Quantum secure direct communication (QSDC) enables the user to directly transmit secret messages through quantum channels without pre-shared keys. However, the imperfection of devices brings a security loophole to QSDC. The weak-random basis selection attack is a strong attack mode, where the eavesdropper can manipulate users’ basis selection probability distribution, and thus reduce the error rate caused by her eavesdropping. In this paper, we propose the first, to the best of our knowledge, general quantitative security analysis model for the practical QSDC system under the weak-randomness basis selection attack. We characterize the imperfect basis selection by the parameter ε . The simulation results show that when ε increases from 0 to 0.1, the maximal secure communication distance reduces from 34 km to 24 km. When ε > 0.32, the maximal secure communication distance reduces to 0. Our work indicates the importance of inspecting the QSDC system’s security loopholes from the weak-randomness basis selection attack and contributes to enhancing its practical security under real experimental conditions.

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.