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Safety-critical embedded systems such as autonomous vehicles typically have only very limited computational capabilities on board that must be carefully managed to provide required enhanced functionalities. As these systems become more complex and inter-connected, some parts may need to be secured to prevent unauthorized access, or isolated to ensure correctness. We propose the multi-phase secure (MPS) task model as a natural extension of the widely used sporadic task model for modeling both the timing and the security (and isolation) requirements for such systems. Under MPS, task phases reflect execution using different security mechanisms which each have associated execution time costs for startup and teardown. We develop corresponding limited-preemption EDF scheduling algorithms and associated pseudo-polynomial schedulability tests for constrained-deadline MPS tasks. In doing so, we provide a correction to a long-standing schedulability condition for EDF under limited-preemption. Evaluation shows that the proposed tests are efficient to compute for bounded utilizations. We empirically demonstrate that the MPS model successfully schedules more task sets compared to non-preemptive approaches.