The probabilistic combinatorial attacks on atmospheric continuous-variable quantum secret sharing

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 under moderate intensity turbulence, but still enable secure QSS at a distance of 8 km on a scale of hundreds. However, 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.