In this paper, we investigate resource allocation algorithm design for secure non-orthogonal multiple access (NOMA) systems empowered by wireless power transfer. With the consideration of an existing eavesdropper, the objective is to obtain secure and energy efficient transmission among multiple users by optimizing time, power and subchannel allocation. Moreover, we also take into consideration for the practical case that the statistics of the channel state information of the eavesdropper is not available. In order to address the optimization problem and its high computational complexity, we propose an iterative algorithm with guaranteed convergence to deliver a suboptimal solution for general cases. For some special cases, the solution ensures the global optimum. Numerical studies demonstrate the competitiveness of the proposed algorithmic solution over conventional orthogonal multiple access systems as well as over other existing NOMA resource allocation schemes.