The adoption of large-scale MPSoCs and the globalization of the IC design flow give rise to two major concerns: high power density due to continuous technology scaling and security due to the untrustworthiness of the third-party intellectual property (3PIP) cores. However, little work has been undertaken to consider these two critical issues jointly during the design stage. In this paper, we propose a design methodology that minimizes the energy consumption while simultaneously protecting the MPSoC against the effects of hardware trojans. The proposed methodology consists of three main stages: 1) Task scheduling to introduce core diversity in the MPSoC in order to detect the presence of malicious modifications in the cores, or mute their effects at runtime, 2) Vendor assignment to the cores using a novel heuristic that chooses vendor-specific cores with operating speed that minimizes the total energy consumption of the MPSoC, and 3) Explore optimization opportunities for further energy savings by minimizing idle periods on the cores, which are caused by the inter-task data dependencies. Experimental results show that our solutions consume only 1/3 energy of existing solutions without increasing schedule length while satisfying the security constraints.