We propose a new artificial-noise aided hybrid time-switching/power-splitting scheme for orthogonal frequency-division multiplexing (OFDM) systems to securely transmit data and transfer energy to a legitimate receiving node. In our proposed scheme, the cyclic prefix has two more benefits in addition to the cancellation of the inter-symbol interference between the OFDM blocks. Firstly, it enables the legitimate transmitter to send artificial-noise (AN) vectors in a way such that the interference can be canceled at the legitimate receiver prior to information decoding. Secondly, its power is used to energize the legitimate receiver. We optimize the cyclic prefix length, the time-switching and power-splitting parameters, and the power allocation ratio between the data and AN signals at the legitimate transmitter to maximize the average secrecy rate subject to a constraint on the average energy transfer rate at the legitimate receiver. Our numerical results demonstrate that our proposed scheme can achieve up to 23% average secrecy rate gain relative to a pure power-splitting scheme.