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IEEE Transactions on Quantum Engineering

Continuous-Variable Quantum Secret Sharing in Fast-Fluctuating Channels

Fangli Yang, Daowen Qiu, Paulo Mateus

Published Jan 1, 2023• 5 citations
Publisher

Abstract

Recently, several continuous-variable quantum secret sharing (CV-QSS) protocols were proposed, while most of them are limited to the fiber channel systems with a relatively stable transmissivity. However, by means of complex channels, the transmissivity fluctuates dramatically in time with a probability distribution, which will lead to a fast-fluctuating attack. Therefore, the security analysis of CV-QSS in fiber channels may not apply to CV-QSS in complex channels. In this paper, we study the CV-QSS protocol in the absence of uniform fast-fluctuating channels whose transmissivity changes with respect to a uniform probability distribution. We give a lower bound of secret key rate to provide security analysis against the fast-fluctuating attack for the CV-QSS protocol. In particular, the realistic highly asymmetric beam splitter (HABS) in CV-QSS protocol is investigated in detail here for the first time, and numerical simulation shows that the security bound is overestimated when the HABS is treated as the perfect device.

DOI
10.1109/tqe.2023.3322171

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Recently, several continuous-variable quantum secret sharing (CV-QSS) protocols were proposed, while most of them are limited to the fiber channel systems with a relatively stable transmissivity. However, by means of complex channels, the transmissivity fluctuates dramatically in time with a probability distribution, which will lead to a fast-fluctuating attack. Therefore, the security analysis of CV-QSS in fiber channels may not apply to CV-QSS in complex channels. In this paper, we study the CV-QSS protocol in the absence of uniform fast-fluctuating channels whose transmissivity changes with respect to a uniform probability distribution. We give a lower bound of secret key rate to provide security analysis against the fast-fluctuating attack for the CV-QSS protocol. In particular, the realistic highly asymmetric beam splitter (HABS) in CV-QSS protocol is investigated in detail here for the first time, and numerical simulation shows that the security bound is overestimated when the HABS is treated as the perfect device.
Quantum secret sharing (QSS) faces inherent limitations in scaling to multi-user networks due to excess noise introduced by highly asymmetric beam splitters (HABSs) in chain-structured topologies. To overcome this challenge, we propose an optical frequency comb-based continuous-variable QSS (OFC CV-QSS) scheme that establishes parallel frequency channels between users and the dealer via OFC-generated multi-wavelength carriers. By replacing the chain-structured links with dedicated frequency channels and integrating the Chinese remainder theorem (CRT) with a decentralized architecture, our design eliminates excess noise from all users using HABS while providing mathematical- and physical-layer security. Simulation results demonstrate that the scheme achieves a more than 50% improvement in maximum transmission distance compared to chain-based QSS, with significantly slower performance degradation as users scale to 20. Numerical simulations confirm the feasibility of this theoretical framework for multi-user quantum networks, offering dual-layer confidentiality without compromising key rates.
Free-space quantum cryptography holds significant potential for enabling global quantum communication networks. This paper proposes a free-space continuous-variable quantum secret sharing (CV-QSS) protocol employing a local local oscillator (LLO). The proposed protocol simplifies the system architecture by requiring only two heterodyne detections at the dealer’s side, thereby eliminating the additional noise and complexity associated with coherent measurements at each participant’s side in conventional schemes. Theoretically, we establish a channel transmittance model that comprehensively incorporates the effects of rain extinction and atmospheric turbulence, and derive the bound of the secret key rate. Experimentally, we systematically evaluate the impact of weather conditions and atmospheric turbulence on protocol performance and conduct comparative evaluations against existing schemes. The results demonstrate that the proposed protocol outperforms the previously proposed free-space LLO-based CV-QSS protocol in terms of key rate, transmission distance, noise tolerance, and participant capacity. Furthermore, this protocol supports secret sharing among 5 participants over 75 km or up to 37 participants within 10 km, outperforming the LLO-based CV-QSS system in a fiber channel. This study validates the potential of free-space CV-QSS as a viable solution for medium-to-long-distance and multi-user quantum secret sharing.
We propose a continuous-variable quantum secret sharing (CV-QSS) protocol in which the quantum states are prepared passively using a thermal source. In our protocol, one player splits the output of a thermal source into two spatial modes with the help of a beam splitter, then he (or she) measures one of the correlated thermal states and sends the others to the secure station of the adjacent player in sequence after using appropriate optical attenuation, which waives the necessity of employment of high extinction ratio modulators with good stability. Therefore, the proposed protocol provides convenient implementation in QSS framework. Moreover, our scheme is immune to Trojan horse attacks. We derive the security bounds for our protocol against both eavesdroppers and dishonest players. Furthermore, we can achieve tighter bound of QSS distance by considering the finite-size effect, which is more practical than that obtained in the asymptotic limit.
The combination of quantum secret sharing (QSS) and continuous-variable quantum key distribution (CV-QKD) has demonstrated clear advantages and has undergone significant development in recent years. However, research on the practical security of CV-QSS remains limited, particularly in the context of free-space channels, which exhibit considerable flexibility. In this paper, we study the practical security of free-space CV-QSS, innovatively propose an attack strategy that probabilistically combines two-point distribution attack (TDA) and uniform distribution attack (UDA). We also establish channel parameter models, especially a channel noise model based on local local oscillators (LLO), to further evaluate the key rate. In principle, the analysis can be extended to any number of probabilistic combinations of channel manipulation attacks. The numerical results demonstrate that the probabilistic combination attacks reduce the real key rate of CV-QSS. Moreover, it should be noted that the probabilistic combination attacks will make the deviation between the estimated key rate and the real key rate, i.e., the key rate is overestimated, which may pose a security risk.
Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system.
We investigate the performance of several continuous-variable quantum key distribution protocols in the presence of uniform fading channels. These are lossy channels whose transmissivity changes according to a uniform probability distribution. We assume the worst-case scenario where an eavesdropper induces a fast-fading process, where she chooses the instantaneous transmissivity while the remote parties may only detect the mean statistical effect. We analyze coherent-state protocols in various configurations, including the one-way switching protocol in reverse reconciliation, the measurement-device-independent protocol in the symmetric configuration, and its extension to a three-party network. We show that, regardless of the advantage given to the eavesdropper (control of the fading), these protocols can still achieve high rates under realistic attacks, within reasonable values for the variance of the probability distribution associated with the fading process.