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. The trend of outsourcing design and fabrication strongly questions the assumption that 3PIP components are trustworthy. However, the complexity of an MPSoC makes it expensive and time consuming to fully analyze and test it during the design stage.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 securitydriven 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 securityconstrained 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 within minimum impact on the other design goals such as performance and hardware. Experimental results show that without any extra cores, security constraints can be fulfilled within 4 vendors and 81% overhead in schedule length. We believe that this extra cost is acceptable for building a trustworthy MPSoCs for critical infrastructures.