The joint design of beamforming and artificial noise vectors is proposed for the full-duplex simultaneous wireless information and power transferring (FD-SWIPT) systems when multiple eavesdroppers can wiretap information from FD base station (FD-BST) and FD user equipment (FD-UE). To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum-information-transmission-rate-maximization (SITRM) problem under information-leakage and energy constraints. Besides, we consider the fairness issue between uplink and downlink information-transmission rates by formulating a fairness-aware-SITRM (FA-SITRM) problem. Since the eavesdroppers can receive the information of FD-BST and FD-UE, the information-leakage region becomes non-convex and challenging to handle. Hence, we propose efficient algorithms to solve the SITRM and FA-SITRM problems optimally via semidefinite relaxation (SDR) and a 1-D search. In each search iteration, our proposed algorithms can recover the rank-one constraints when the application of SDR cannot obtain the optimal solutions. Moreover, we analyze the computational complexities and propose two suboptimal solutions to the formulated problems. For the SITRM problem, our numerical results show that the performance achieved by one of two suboptimal algorithms is close to the performance of optimal algorithm with increasing the maximum transmission power of FD-BST.