Abstract Although continuous-variable quantum secret sharing (CVQSS) has been theoretically proven to be secure, it may still be vulnerable to various local oscillator (LO) attacks. To close this loophole, here we propose a practical CVQSS scheme using local LO (LLO-CVQSS), where LO is no longer generated by each user but is locally generated by the legitimate dealer. This waives the necessity that all LOs have to be transmitted through untrusted channels, making CVQSS system naturally immune to all LO-aimed attacks and enhancing its practical security. We also develop a dedicated phase compensation method for LLO-CVQSS to control the phase noise, and construct a noise model that derives its security bound against both eavesdroppers and dishonest users. Finally, numerical simulation shows that LLO-CVQSS can support 30 users at the same time and the maximal transmission distance reaches 112 km, revealing its potential for building large-scale practical quantum communication networks.
Abstract Although continuous-variable quantum secret sharing (CVQSS) has been theoretically proven to be secure, it may still be vulnerable to various local oscillator (LO) attacks. To close this loophole, here we propose a practical CVQSS scheme using local LO (LLO-CVQSS), where LO is no longer generated by each user but is locally generated by the legitimate dealer. This waives the necessity that all LOs have to be transmitted through untrusted channels, making CVQSS system naturally immune to all LO-aimed attacks and enhancing its practical security. We also develop a dedicated phase compensation method for LLO-CVQSS to control the phase noise, and construct a noise model that derives its security bound against both eavesdroppers and dishonest users. Finally, numerical simulation shows that LLO-CVQSS can support 30 users at the same time and the maximal transmission distance reaches 112 km, revealing its potential for building large-scale practical quantum communication networks.
Quantum communications can be conveniently implemented by two participants, but quantum secret key sharing (QSS) through multi-participant communication seems difficult in practice. In this paper, we propose a multi-participant QSS scheme with the local local oscillator (LLO) in continuous variable (CV) quantum communications. It allows an honest participant called a dealer to share a secret key with the others, making it possible to establish a secret key if and only if all participants gather together. The LLO scheme, which eliminates the need for the local oscillator (LO) to be propagated in insecure channels, can be used to avoid the potential LO attack in the traditional CVQSS scheme. Numerical simulation shows that the performance of the LLO-based CVQSS can be improved in terms of the maximal transmission distance even if it is performed with the partially trusted noise.
In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subjected to security threats due to various targeted attacks. To solve this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local intrinsic oscillator, in which the intrinsic oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection by using the local intrinsic oscillator and reference phases; post-processing, which involves parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter (KF) is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar KF and vector KF are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even at lower levels, minimizing interference with quantum signals. These results highlight that the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.
Continuous-variable quantum secret sharing (CVQSS) allows a legitimate user, i.e., the dealer, to share a string of secret keys with multiple distant users. These users cannot individually recover the dealer's secret key unless they work cooperatively. Although the theoretical security proof of CVQSS has been well established, its practical security and implementation still face challenges. In this paper, we suggest a practical scheme for CVQSS using plug-and-play (P&P) configuration and dual-phase-modulated coherent state (DPMCS). The proposed scheme, called P&P DPM-based CVQSS, waives the necessity that each user has to prepare respective coherent states with their own lasers, thereby eliminating synchronous loopholes caused by different lasers and reducing the complexity of deployment of the user's stations. Moreover, the local oscillator (LO) can be generated locally by the dealer so that the whole CVQSS system could be naturally immune to all LO-aimed attacks. We derive the security bounds for P&P DPM-based CVQSS by properly making most of the existing security analysis techniques of continuous-variable quantum key distribution (CVQKD). In addition, an experimental concept of P&P DPM-based CVQSS is also presented, which can be deemed a guideline for future implementation.
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.
Quantum key distribution (QKD) has been proven to promise unconditionally secure data communication between remote legitimate users，based on the fundamental laws of quantum mechanics. QKD has great potential to be commercialized in the market and implemented in securing critical institutions, such as financial infrastructures, smart Grid, and national defence. Most theoretical security analyses of QKD protocols are based on several idealistic assumptions. However, the practical limitations, such as device imperfections, may bring security loopholes and leave QKD systems vulnerable to malicious eavesdropping attacks. Since QKD systems will be used as the practical applications in the real-world, it is of great importance to study the practical security and practical implementations of QKD protocols. Compared with dedicated single-photon based discrete variable (DV) QKD protocols, continuous variable (CV) QKD systems have attracted more attentions in recent years, as they benefit from their compatibility with commercial off-the-shelf (COTS) telecommunication components and high key rate over metropolitan networks. However, the requirement of a co-transmitted local oscillator (LO) brings a number of issues that compromises secure key generation and becomes a major obstacle to the practical implementation of CVQKD. To overcome these problems, a new CVQKD protocol with a locally generated LO (LLO) at Bob has been proposed. Based on previous studies, this thesis presents a novel quantum attack based on a discovered security loophole of the LLO CVQKD protocol, and demonstrates two high performance and low complexity practical LLO CVQKD systems. 1. After exploring the phase recovery scheme and the phase noise model, the first quantum attack on LLO CVQKD system is proposed, that exploits the phase estimation error associated with the amplitude of the phase reference pulses, in a ‘reference pulse attack’. Under this attack, a new system noise model and a refined linear quantum states transmission model have been developed when the phase noise is partially trusted. The attack performance is evaluated in terms of excess noise manipulation and mutual information extraction over both trusted – referred to as realistic, and untrusted – referred to as paranoid, security models of phase noise. Effective countermeasures are also given to improve the practical security and performance of the LLO CVQKD system under the trusted phase noise model. 2. Aside from the practical security analysis, two practical LLO CVQKD implementations developed in the laboratory are demonstrated here. The first practical LLO CVQKD system is featured as high speed (500 MHz) and low complexity, realizing the world’s fastest predicted key rate of 26.9 Mbps over a 15 km optical fibre link. To increase the signal repetition rate, and hence the potential secure key rate, our system is equipped with high-performance, wideband devices and components designed to support high repetition rate operations. To reduce the system complexity and correct for any phase shift during transmission, reference pulses are interleaved with quantum signals at Alice. Customized monitoring software has been developed allowing all parameters to be controlled in real-time without any modification to the physical setup. The system-level noise model analysis is introduced at high bandwidth and a new ‘combined optimisation’ technique is proposed to simultaneously optimize system parameters to high precision. It also has the potential for an even faster implementation. 3. The second demonstrated system presents the feasibility of the first practical LLO CVQKD system. The system comprises integrated real-time data-processing units (DPUs) and commercial off-the-shelf (COTS) telecommunication components. Instead of using conventional expensive, high-specification, standalone laboratory equipment (e.g. oscilloscope and arbitrary waveform generator (AWG) used in most CVQKD systems), each DPU consists of a high-speed, multi-channel data acquisition module, and is embedded in a computer at both Alice and Bob to achieve real-time quantum data generation, acquisition and analysis. In addition, a hardware-based filter unit has been implemented to amplify and stabilise modulation signals, together with a system-level noise model analysis and a combined parameter optimisation method to enhance the system key rate. In laboratory conditions, the system has been shown to run continuously, and the asymptotic secure key rates are estimated as 1.37 Mbps and 509 kbps over 15 km and 25 km optical fibre links, respectively, through stable excess noise measurements for over 10 hours at a 20 MHz repetition rate. The measurement results open up the possibility of building up a commercialized LLO CVQKD system.
Continuous-variable quantum key distribution (CVQKD) with the local local oscillator (LLO) is confronted with new security problems due to the reference pulses transmitted together with quantum signals over the insecure quantum channel. In this paper, we propose a method of phase attack on reference pulses of the LLO-CVQKD with time-multiplexing. Under this phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers, and then the phase compensation error is increased. Consequently, the secret key rate is reduced due to the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, the practical security of LLO-CVQKD under phase attack is analyzed. The simulation results show that the practical security is reduced due to the phase attack, yet it is still tight when system parameters are estimated by training signals.