Outsourcing of the various aspects of IC design and fabri cation flow strongl y questions the classic assumption that "hardware is trustworth y ". Multiprocessor S y stem-on-Chip (MPSoC) platforms face some of the most demanding securit y concerns, as they process, store, and communicate sensitive information using third-part y intellectual property (3PIP) cores that ma y be untrustworth y . The complexit y of an MPSoC makes it expensive and time consuming to full y anal y ze 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 b y revising the task scheduling step of the MPSoC design process. We impose a set of securit y -driven diversit y constraints into the scheduling process, enabling the s y stem to detect the presence of malicious modifications or to mute their effects during application execution. Furthermore, we pose the securit y -constrained MPSoC task scheduling as a multi-dimensional optimization problem, and propose a set of heuristics to ensure that the introduced securit y constraints can be fulfilled with minimum performance and hardware overhead.