FlexRay is a hybrid communication protocol tailored to the requirements of safety-critical distributed real-time automotive systems, providing support for the transmission of time-critical periodic frames in a static segment and event-triggered frames in a dynamic segment. With the development of intelligence and networking of vehicles, such systems are becoming increasingly connected to external environments; thus, security has become a pressing issue in system design. However, FlexRay-based architecture does not have direct support for secure communication. When deploying the security mechanisms on these architectures, a primary challenge is to guarantee the schedulability of systems, given the tight resource constraints and strict timing constraints. In this paper, we apply an authentication mechanism based on the delayed exposure of one-way key chains to protect the authenticity of messages on FlexRay and make a slight modification to reduce the authentication delay. On that basis, we propose a mixed integer linear programming formulation for solving the scheduling problem of FlexRay-based real-time automotive systems subject to both authentication mechanism constraints and other traditional design constraints. Experimental results demonstrate the effectiveness and efficiency of the proposed method in system design and indicate the necessity of collaborative design between security and other functionalities.