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To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here the efficient integration of confidential services in the three-node bidirectional relay channel is studied. A relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol, which is also known as two-way relaying. In the broadcast phase, the relay transmits not only the two bidirectional messages it received in the previous multiple access phase, but also an additional confidential message to one node while keeping the other node completely ignorant of it. The concept of strong information theoretic secrecy is used to ensure that the nonlegitimate node cannot decode the confidential message no matter what its computational resources are. Moreover, this implies that the average decoding error at the nonlegitimate node goes exponentially fast to one for any decoding strategy it may use. This results in the study of the bidirectional broadcast channel with confidential messages for which the strong secrecy capacity region is established. Furthermore, it is shown that the efficient integration of confidential messages with strong secrecy extends to such scenarios, where the relay further transmits an additional common message to both nodes.