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.
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.
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.
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.
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.
Abstract Continuous-variable source-independent quantum random number generator (CV-SI-QRNG) can produce random numbers with an untrusted source. However, the material properties of trusted measurement devices may lead to potential security risks, such as Lithium niobate (LiNbO3, LN) devices, which must be accurately characterized and considered in security analysis. The performances of LN devices are sensitive to photorefractive effect (PE) in LN, which has been shown to be exploited for malicious attacks on quantum key distribution. However, the research on the security problems associated with loopholes induced by PE has not been carried out in the practical security of CV-SI-QRNG. In this paper, we give a light-induced photorefraction attack against homodyne-based CV-SI-QRNG as well as the corresponding security analysis. Simulation results show that eavesdroppers can use very weak irradiation beam to change the splitting ratio of directional coupler and the phase shift of phase modulator, which leads to an overestimation on the number of extractable random bits. Our work reveals that PE-related security issues should be carefully considered in the LN-based QRNG.
Abstract A quantum random number generator (QRNG) as a genuine source of randomness is essential in many applications, such as number simulation and cryptography. Recently, a source-independent quantum random number generator (SI-QRNG), which can generate secure random numbers with untrusted sources, has been realized. However, the measurement loopholes of the trusted but imperfect devices used in SI-QRNGs have not yet been fully explored, which will cause security problems, especially in high-speed systems. Here, we point out and evaluate the security loopholes of practical imperfect measurement devices in SI-QRNGs. We also provide corresponding countermeasures to prevent these information leakages by recalculating the conditional minimum entropy and adding a monitor. Furthermore, by taking into account the finite-size effect, we show that the influence of the afterpulse can exceed that of the finite-size effect with the large number of sampled rounds. Our protocol is simple and effective, and it promotes the security of SI-QRNG in practice as well as the compatibility with high-speed measurement devices, thus paving the way for constructing ultrafast and security-certified commercial SI-QRNG systems.
Quantum random number generators (QRNGs) harness quantum mechanical unpredictability to produce true randomness, which is crucial for cryptography and secure communications. Among various QRNGs, source-independent QRNGs (SI-QRNGs) relax the trust on the quantum source, allowing for flexible use of advanced detectors to achieve high randomness generation rates. Continuous-variable (CV) SI-QRNGs, in particular, hold promise for practical deployment due to their simplicity and randomness generation rates comparable to trusted-device QRNGs. In this work, we propose a novel CV-SI-QRNG scheme based on phase-insensitive detections, and provide security proof based on semi-definite programming (SDP). We introduce a dimension reduction technique, which rigorously reduces an infinite-dimensional SDP problem to a finite-dimensional one, enabling efficient computation while maintaining valid randomness lower bound. We further validate our method through simulations. These results demonstrate the feasibility of our framework, paving the way for practical and simple SI-QRNG implementations.