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Relay assisted communication helps to extend the transmission coverage area. In more realistic scenarios, the available relays are untrusted, which try to decode the confidential signals during their main relaying function. Thus, these untrusted relays are regarded as potential eavesdroppers, and the confidential signals are vulnerable. A positive secrecy rate can be achieved at the physical layer without any cryptography, in particular, the mutual interference achieved from two-way relaying network can be used to secure the confidential signals against eavesdroppers attack. In this paper, the relay selection of two-way untrusted relays network is presented, and a directed beamforming is aligned to zero force the transmission at all other non-selected relays. Particularly, we propose a selection scheme based on max-min criterion, which requires an exhaustive search. Then, the lower bound (LB) of the secrecy rate is …