Non-orthogonal multiple access (NOMA) is considered as one of the promising techniques for providing high data rates in the fifth generation mobile communication. By applying successive interference cancellation schemes and superposition coding at the NOMA receiver, multiple users can be multiplexed on the same subchannel. In this paper, we investigate resource allocation algorithm design for an OFDM-based NOMA system empowered by wireless power transfer (WPT). In the considered system, users who need to transmit data can only be powered by the WPT. 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 an upper bound and a suboptimal solution in more general cases. For some special cases, we identify the optimality condition that ensures the global optimum in our algorithm. Extensive simulation studies demonstrate the competitiveness and effectiveness of the proposed algorithmic solution over conventional OFDMA systems as well as over other existing NOMA resource allocation schemes.