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In low-earth-orbit (LEO) satellite-to-ground communication, the size of satellite antennae is limited and the satellite motion trajectory is predictable, which makes the channel state information (CSI) of the satellite-to-ground channel easy to leak and impossible to use to generate a physical layer key. To solve these problems, we propose a key generation method based on multi-satellite cooperation and random perturbation. On the one hand, we use multi-satellite cooperation to form a constellation that services users, in order to increase the equivalent aperture of satellite antennae and reduce the correlation between the legal channel and the wiretap channel. On the other hand, according to the endogenous characteristics of satellite motion, a random perturbation factor is proposed, which reflects the randomness of the actual channel and ensures that the CSI of the legal channel is not leaked due to the predictability of satellite motion trajectory. Simulation results show that the proposed method can effectively reduce the leakage of the legal channel's CSI, which makes the method of physical layer key generation safe and feasible in the LEO satellite-to-ground communication scene. [ABSTRACT FROM AUTHOR]