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This brief addresses the security issues of data transmitted in networked control systems (NCSs), especially confidentiality, integrity and authenticity. A secure networked predictive control system (SNPCS) architecture is presented, which integrates the Data Encryption Standard (DES) algorithm, Message Digest (MD5) algorithm, timestamp strategy, and recursive networked predictive control (RNPC) method. The former three parts are used to form a secure transmission mechanism between the controller side and the plant side, which is responsible for enforcing the data confidentiality and checking the data integrity and authenticity. To guarantee the control system performance when suffering from deception attacks, the RNPC method based on round-trip time delays is proposed to compensate for the adverse effects introduced by the deception attacks as well as the network communication constraints, such as time-varying network delay, packet disorder and packet dropout. A theoretical result using the switched system theory is obtained for the closed-loop stability of the RNPC system. Practical experiments are performed to demonstrate the effectiveness of the proposed SNPCS.