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 complexity of MPSoC makes it expensive and time consuming to fully analyze and test during the design stage. This has given rise to the trend of outsourcing design and fabrication of 3PIP components, that may not be trustworthy. To protect MPSoCs against malicious modifications, we impose a set of security-driven diversity constraints into the task scheduling step of the MPSoC design process, enabling the system to detect the presence of malicious modifications or to mute their effects during application execution. We pose the security-constrained MPSoC task scheduling as a multidimensional optimization problem, and propose a set of heuristics to ensure that the introduced security constraints can be fulfilled with a 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 four vendors and 81% overhead in schedule length.