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Chinese Physics B

Effect of weak randomness flaws on security evaluation of practical quantum key distribution with distinguishable decoy states

Yu Zhi Zhou, Hong-Wei Li, Chun Hua Zhou, Yang Wang, Yifei Lu, Mu-Sheng Jiang, Xiao-Xu Zhang, Wan-Su Bao

Published Aug 5, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ac8730

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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.
Decoy-state quantum key distribution (QKD) has become the most efficient method to resist the photon-number-splitting (PNS) attack and estimate the secure key rate. The decoy-state method has many assumptions, among which a critical one is that an eavesdropper (Eve) cannot distinguish between the signal and decoy states. However, a rigorous proof of the rationality about this assumption is not yet available so far. In fact, due to the difference of photon-number probability distribution between the signal and decoy states, Eve is able to distinguish the two states with a certain probability. In this work, we adopt the Bayesian decision to distinguish the signal and decoy states in one-decoy-state QKD, and perform different PNS attack strategies for the two states according to the previous decision. The numerical simulations indicate that the attack effect is not obvious or even failed. Thus, it is reasonable to assume that the signal and decoy states are indistinguishable in decoy-state QKD. In addition, we also provide the method to set the intensities of signal and decoy states properly, which can not only reduce the preparation cost and improve the communication efficiency, but also avoid the attack from Eve using the intensity difference between the signal and decoy states.
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.
Quantum key distribution (QKD) can share an unconditional secure key between two remote parties, but the deviation between theory and practice will break the security of the generated key. In this paper, we evaluate the security of QKD with weak basis-choice flaws, in which the random bits used by Alice and Bob are weakly controlled by Eve. Based on the definition of Li et al. (Sci Rep 5:16200, 2015) and GLLP's analysis, we obtain a tight and analytical bound to estimate the phase error and key rate for both the single photon source and the weak coherent source. Our approach largely increases the key rate from that of the original approach. Finally, we investigate and confirm the security of BB84-QKD with a practical commercial devices.
The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the receiver (Bob's) unit. We apply our method to three QKD systems and estimate their secure key rates.
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.
Passive decoy-state quantum key distribution is more desirable than the active one in some scenarios. It is also affected by the imperfections of the devices. In this paper, the influence of modulator attenuation on the passive decoy-state method is considered. We introduce and analyze the unbalanced Mach–Zehnder interferometer, briefly, and combining with the virtual source and imaginary unitary transformation, we characterize the passive decoy-state method using a weak coherent photon source with modulator attenuation. According to the attenuation parameter δ , the pass efficiencies are given. Then, the key generation rate can be acquired. From numerical simulations, it can be seen that modulator attenuation has a nonnegligible influence on the performance of passive-state QKD protocol. Based on the research, the analysis method of virtual source and imaginary unitary transformation are preferred in analyzing passive decoy state protocol, and the passive decoy-state method is better than the active one and is close to the active vacuum + weak decoy state under the condition of having the same modulator attenuation.