In the operation 314, the processing circuit 117 may establish a connection with the second member device 130 through the host-side communication circuit 111, and may decide a second parameter P2 and generate a second privileged pairing notice. In one embodiment, the processing circuit 117 may generate a second predetermined value, a second random value, a second predetermined address, a second random address, a second predetermined string, a second random string, a second predetermined token, a second random token, or a second access address corresponding to the second member device 130 to be the second parameter P2. In another embodiment, the processing circuit 117 may opt to use the content of a predetermined field in a certain Bluetooth packet transmitted from the second member device 130 to the Bluetooth host device 110 to be the second parameter P2, or may instead opt to use the content of a predetermined field in a certain Bluetooth packet transmitted from the Bluetooth host device 110 to the second member device 130 to be the second parameter P2. For example, the processing circuit 117 may opt to use an initial value of a cyclic redundancy check (CRCInit), a window size (WinSize), a window offset (WinOffset), a connection event interval (Connection Interval), a slave latency, a timeout value, a channel map, a hop, or a sleep clock accuracy (SCA) in a connection indication (Connect_IND) packet or in an auxiliary connection request (AUX_Connect_REQ) packet generated by the processing circuit 117 to be the second parameter P2. For another example, the processing circuit 117 may opt to use the value of the cyclic redundancy check (CRC) in the aforementioned connection indication (Connect_IND) packet or auxiliary connection request (AUX_Connect_REQ) packet to be the second parameter P2. For another example, the processing circuit 117 may opt to use the value of the cyclic redundancy check (CRC) in an auxiliary connection response (AUX_Connect_RSP) packet or in a specific Bluetooth advertising packet generated by the second member device 130 to be the second parameter P2. The processing circuit 117 may also transmit the second privileged pairing notice to the second member device 130 through the host-side communication circuit 111 in the operation 314. Additionally, in the operation 314, the processing circuit 117 may also transmit the second parameter P2 or a second field indication to the second member device 130 through the host-side communication circuit 111, wherein the second field indication is utilized for indicating a specific packet field whose content is to be utilized as the second parameter P2. In practice, the second parameter P2 may be identical to the first parameter P1, or may be different from the first parameter P1.