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Journal of Physics B Atomic Molecular and Optical Physics

Eavesdropping attack on a continuous-variable source-independent quantum random number generator with fluctuating local oscillator

Han Zhou, Ziyong Zheng, Luyu Huang, Xiangyu Wang, Ziyang Chen, Song Yu

Published Feb 15, 2022• 9 citations
Publisher

Abstract

Abstract In the practical continuous-variable source-independent quantum random number generator, it is usually necessary to introduce a local oscillator to amplify the received quantum signal due to its weak intensity. However, the intensity fluctuation of the local oscillator itself will lead to a deviation in evaluating the randomness without monitoring the local oscillator in real time and calibrating each output measurement, which will inevitably open a loophole for the eavesdropper to intercept the information of generated random numbers. Here, we present an eavesdropping attack utilizing this loophole. The results of numerical simulation indicate that when the proposed eavesdropping attack is performed, the evaluated extractable randomness value will be compromised severely, which will impact the communication security under the practical conditions. Meanwhile, we analyze the effects of practical imperfections in the presence of local oscillator fluctuation. Taking this as a reference, we may consider how to perfect the experimental system in practice and how to deal with this kind of eavesdropping attack.

DOI
10.1088/1361-6455/ac5581

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Abstract In the practical continuous-variable source-independent quantum random number generator, it is usually necessary to introduce a local oscillator to amplify the received quantum signal due to its weak intensity. However, the intensity fluctuation of the local oscillator itself will lead to a deviation in evaluating the randomness without monitoring the local oscillator in real time and calibrating each output measurement, which will inevitably open a loophole for the eavesdropper to intercept the information of generated random numbers. Here, we present an eavesdropping attack utilizing this loophole. The results of numerical simulation indicate that when the proposed eavesdropping attack is performed, the evaluated extractable randomness value will be compromised severely, which will impact the communication security under the practical conditions. Meanwhile, we analyze the effects of practical imperfections in the presence of local oscillator fluctuation. Taking this as a reference, we may consider how to perfect the experimental system in practice and how to deal with this kind of eavesdropping attack.
A quantum random-number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices and is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loopholes to eavesdroppers. Recently, Thewes et al. experimentally demonstrated a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in many other practical continuous-variable QRNG studies, they always supposed the local oscillator was stable and ignored its fluctuation, which might lead to security threats such as wavelength attack. In this work, based on the theory of the conditional min-entropy, imperfections of the practical security of continuous-variable QRNGs are systematically analyzed, especially the local oscillator fluctuation under imbalanced homodyne detection. Experiments of a practical QRNG based on vacuum fluctuation are demonstrated to show the influence of local oscillator fluctuation on the total measurement noise variances and the practical conditional min-entropy with beam splitters of different transmittances. Moreover, a local oscillator monitoring method is proposed for the practical continuous-variable QRNG, which can be used to calibrate the practical conditional min-entropy.
Heterodyne-based continuous-variable source-independent quantum random number generator (CV-SI-QRNG) can produce true random numbers without any assumptions on source. However, practical implementations always contain imperfections, which will greatly influence the extractable randomness and even open loopholes for eavesdroppers to steal information about the final output. In this work, based on the theoretical model, we systematically analyzed the effects of imperfect implementations on the practical security of heterodyne-based CV-SI-QRNG. The influences of local oscillator (LO) fluctuation under imbalanced heterodyne detection are first analyzed. The simulation results show that the lower bound of extractable randomness will be overestimated without considering the influence of LO fluctuation, which will threaten the practical security of CV-SI-QRNG system. Moreover, we analyze the effects of the degree of imbalance and the magnitude of LO fluctuation on evaluating the extractable randomness. Finally, we investigate the impact of an imperfect phase modulator on the practical security of CV-SI-QRNG and find it will reduce the extractable randomness. Our analysis reveals that one should carefully consider the imperfections in the actual implementations of CV-SI-QRNGs.
Continuous-variable source-independent quantum random-number generators (CV-SI-QRNGs) generate high-speed secure random numbers without any assumptions about source. Recently, Smith et al. [Phys. Rev. A 99, 062326 (2019)] proposed a CV-SI-QRNG with phase-randomized local oscillator (LO) protocol, which does not require additional active optical components, thus reducing the complexity of the CV-SI-QRNG setup and attracting widespread attention. However, the trusted but imperfect sampling device used in CV-SI-QRNG has not yet been fully investigated, which will lead to performance degradation and security problems. In this work, we investigate the influence of imperfect sampling devices on the CV-SI-QRNG with phase-randomized LO, including the finite-sampling bandwidth, finite-sampling precision, and finite-size effect. Simulation results show that practical imperfections in the sampling device will affect the estimation of lower bound on the conditional min-entropy and reduce the extractable randomness. To improve the performance of CV-SI-QRNG and prevent such information leakages, we also provide some corresponding countermeasures. Our work highlights the influences of imperfect sampling devices on the performance and security of practical CV-SI-QRNG systems, which helps to improve their robustness and practicality.
In practical continuous-variable quantum key distribution system using local local oscillator (LLO CV-QKD), the phase noise related to coherent detection and phase-reference pulse intensity that can be locally calibrated at the receiver side is considered to be trusted noise to improve the performance. However, if the intensity of the phase-reference pulse is not monitored precisely in real-time, a security loophole will be opened for the eavesdropper to launch attacks. To this end, we propose two practical phase-reference pulse intensity attack strategies, where Eve can reduce the trusted phase noise by manipulating the intensity of the phase-reference pulse, thereby hiding her attack on the signal pulse if the total excess noise remains unchanged. The performance of the LLO CV-QKD system under these attacks has been analyzed. We show that precisely monitoring the intensity of the phase-reference pulse in real-time is an essential countermeasure to prevent the proposed attacks. Moreover, an intensity-monitoring scheme for the phase-reference pulse is proposed to strengthen the security of the practical LLO CV-QKD system and make the trusted phase noise model more robust.
In continuous-variable quantum key distribution system with a true local oscillator (LLO CV-QKD), part of the phase noise associated with the coherent detector and the phase-reference intensity can be considered as trusted because which can be locally calibrated at the receiver’s side. The trusted phase noise model can significantly improve the noise tolerance of the system since the phase noise is the major excess noise. However, the transmission of the phase-reference pulse through the insecure quantum channel in the LLO CV-QKD system may leave rooms for the eavesdropper to mount attacks. Here, we propose a practical and flexible phase-reference intensity attack scheme using a phaseinsensitive amplifier to amplify the intensity of the phase-reference pulse. In this case, the eavesdropper can compromise the security of the LLO CV-QKD system severely by lowering the trusted part of the phase noise to compensate her increased attack on the signal pulse while the total excess noise is unchanged. We simulate the secure key rate with respect to the transmission distance to show that precisely monitoring the instantaneous intensity of the phase-reference pulse in real time is of great importance to guarantee the security of the LLO CV-QKD system.
We consider the security of practical continuous-variable quantum-key-distribution implementation with the local oscillator (LO) fluctuating in time, which opens a loophole for Eve to intercept the secret key. We show that Eve can simulate this fluctuation to hide her Gaussian collective attack by reducing the intensity of the LO. Numerical simulations demonstrate that if Bob does not monitor the LO intensity and does not scale his measurements with the instantaneous intensity values of LO, the secret key rate will be compromised severely.