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This article investigates physical layer security (PLS) in reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) channels. Existing researches ignore the problem that secrecy rate can not be calculated if the eavesdropper's instantaneous channel state information (CSI) is unknown. Furthermore, without the secrecy rate expression, beamforming and phase shifter optimization with the purpose of PLS enhancement is not available. To address these problems, we first give the expression of secrecy outage probability for any beamforming vector and phase shifter matrix as the RIS-assisted PLS metric, which is measured based on the eavesdropper's statistical CSI. Then, with the aid of the expression, we formulate the minimization problem of secrecy outage probability that is solved via alternately optimizing beamforming vectors and phase shift matrices. In the case of single-antenna transmitter or single-antenna legitimate receiver, the proposed alternating optimization (AO) scheme can be simplified to reduce computational complexity. Finally, it is demonstrated that the secrecy outage probability is significantly reduced with the proposed methods compared to current RIS-assisted PLS systems.