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Applied Sciences

Improving Continuous Variable Quantum Secret Sharing with Weak Coherent States

Yijun Wang, Bing Jia, Yun Jie Mao, Xuelin Wu, Ying Guo

Published Apr 1, 2020• 4 citations
Publisher

Abstract

Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.

DOI
10.3390/app10072411

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Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.
Secret sharing allows a trusted party (the dealer) to distribute a secret to a group of players, who can only access the secret cooperatively. Quantum secret sharing (QSS) protocols could provide unconditional security based on fundamental laws in physics. While the general security proof has been established recently in an entanglement-based QSS protocol, the tolerable channel loss is unfortunately rather small. Here we propose a continuous variable QSS protocol using conventional laser sources and homodyne detectors. In this protocol, a Gaussian-modulated coherent state (GMCS) prepared by one player passes through the secure stations of the other players sequentially, and each of the other players injects a locally prepared, independent GMCS into the circulating optical mode. Finally, the dealer measures both the amplitude and the phase quadratures of the receiving optical mode using double homodyne detectors. Collectively, the players can use their encoded random numbers to estimate the measurement results of the dealer and further generate a shared key. We prove the unconditional security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss, and discuss various practical issues.
Continuous variable quantum secret sharing (CV-QSS) technologies are described that use laser sources and homodyne detectors. Here, a Gaussian-modulated coherent state (GMCS) prepared by one device passes through secure stations of other devices sequentially on its way to a trusted device, and each of the other devices coherently adds a locally prepared, independent GMCS to the group of propagating GMCSs. Finally, the trusted device measures both the amplitude and the phase quadratures of the received group of coherent GMCSs using double homodyne detectors. The trusted device suitably uses the measurement results to establish a secure key for encoding secret messages to be broadcast to the other devices. The devices cooperatively estimate, based on signals corresponding to their respective Gaussian modulations, the trusted device's secure key, so that the cooperative devices can decode the broadcast secret messages with the secure key.
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.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes against eavesdroppers and dishonest participants remained unproven. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players, by utilizing ideas from the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate the practical feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes still remains unproven almost two decades after their original conception. Here we establish an unconditional security proof for entanglement-based continuous-variable quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players. We tackle the problem by resorting to the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate theoretically the feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results contribute to validating quantum secret sharing as a viable primitive for quantum technologies.
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.