Outsourcing of the various aspects of IC design and fabrication flow strongly questions the classic assumption that 'hardware is trustworthy'. Multiprocessor System-on-Chip (MPSoC) platforms face some of the most demanding security concerns, as they process, store, and communicate sensitive information using third-party intellectual property (3PIP) cores that may be untrustworthy. The complexity of an MPSoC makes it expensive and time consuming to fully analyze and test it during the design stage. Consequently, the trustworthiness of the 3PIP components cannot be ensured. To protect MPSoCs against malicious modifications, we propose to incorporate trojan toleration into MPSoC platforms by revising the task scheduling step of the MPSoC design process. We impose a set of security-driven diversity constraints into the scheduling process, enabling the system to detect the presence of malicious modifications or to mute their effects during application execution. Furthermore, we pose the security-constrained MPSoC task scheduling as a multi-dimensional optimization problem, and propose a set of heuristics to ensure that the introduced security constraints can be fulfilled with minimum performance and hardware overhead.