This letter investigates the ergodic secrecy capacity (ESC) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence of discrete phase shifts and multiple eavesdroppers (Eves). In particular, a closed-form approximation of the ESC is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS $N$ is large. Asymptotic analysis is provided to investigate the impact of $N$ on the ESC, and it is proved that the ESC scales with $\log_2 N$ for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.

中文翻译：

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存在离散相移和多个窃听者的RIS辅助通信系统的遍历保密率

这封信研究了可重构智能表面 (RIS) 辅助通信系统在存在离散相移和多个窃听者 (Eves) 的情况下的遍历保密能力 (ESC)。特别是，对于非共谋和共谋的 Eves，导出了 ESC 的封闭形式近似值。当RIS$N$的反射元素数量较大时，分析结果显示是准确的。提供渐近分析以研究 $N$ 对 ESC 的影响，并证明对于非共谋和共谋 Eves，ESC 以 $\log_2 N$ 缩放。提供了数值结果来验证分析结果和获得的标度定律。