Physical layer security is a key issue in the full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, the joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum information transmission rate (SITR) maximization problem under information-leakage and energy constraints. In addition, we consider the fairness issue between the uplink and downlink information transmission rates by formulating a \mbox{fairness-aware} SITR-maximization problem. Although the formulated \mbox{SITR-maximization} and \mbox{fairness-aware} \mbox{SITR-maximization} problems are non-convex, we solve them via semidefinite relaxation and one-dimensional search. The optimality of our proposed algorithms is theoretically proved, and the computation complexities are established. Moreover, we propose two suboptimal solutions to the formulated optimization problems. In terms of the SITR-maximization problem, numerical results show that the performance achieved by one of the two suboptimal algorithms is close to the performance of the optimal algorithm with increasing maximum transmission power of the FD-BST.