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This paper considered an energy-harvesting based secure two-way relay (EH-STWR) network, where two users exchanged information with the assistance of one buffer-aided relay that harvested energy from two users. To realize the confidential message exchange between two users in the presence of a potential eavesdropper, a secure bidirectional relaying scheme based on time division broadcast (TDBC) was proposed, where one user sent artificial noise to suppress the eavesdropper and another user transmitted data to the relay. A secure sum-rate maximization problem was formulated subject to average and peak transmit power constraints, data buffer and energy storage causality, and transmission mode constraints. By employing the Lyapunov optimization framework, a security-aware adaptive transmission scheme was proposed to jointly adapt transmission mode selection, power allocation, and security rate allocation according to channel/buffer/energy state information (CSI/BSI/ESI). Analysis results showed that the average achievable secrecy rate region can be significantly improved and there exists an inherent tradeoff among transmission delay, requirement of transmit power consumption, and achievable secure sum-rate. Moreover, the channel condition between the energy-constrained relay and the potential eavesdropper is a critical factor on the achievable longterm average secrecy rate performance.