Considering the secure communication of the distributed Reconfigurable Intelligent Surfaces(RISs)under imperfect Channel State Information(CSI),a joint optimization problem of the secrecy rate maximization based on the active beamforming,Artificial Noise(AN),and RISs'phase shifts is formulated.Then an efficient algorithm based on alternating optimization and 1-Dimensional linear search is proposed to solve the non-convex optimization problem.Simulation results demonstrate that,compared with the random phase optimization scheme and the secure transmission without AN scheme,the proposed scheme can achieve a higher secrecy rate.The superiority of the proposed scheme over the other transmission schemes becomes more prominent with the increase of the number of distribution units.The proposed scheme has better robustness than the other transmission schemes to the uncertainty of communication channel in our considered network.