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Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 protocol in fully quantum cryptography into SQKD. In this protocol, the sender Alice just sends one quantum state to the classical Bob and Bob just prepares a fixed state in the preparation process. It is much simpler than the existing SQKD and potentially much easier to be implemented. It can be seen as a semi-quantum version of B92 protocol, compared to the protocol BKM07 as the semi-quantum version of BB84 in fully quantum cryptography. We verify that it is more efficient than the existing single-state SQKD protocols by introducing an efficiency parameter. Specifically, we prove it is secure against a restricted collective attack by computing a lower bound of the key rate in the asymptotic scenario. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be definitely established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case the reverse channel is a depolarizing one with parameter $p$. Though the threshold value is a little smaller than those of some existing SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.

During free-space quantum key distribution, the rotation and fluctuation of reference frame degrades the performance of quantum key distribution (QKD). Reference-frame-independent QKD (RFI-QKD) overcomes this issue effectively. To date, much theoretical and experimental research has been conducted on the performance of free-space RFI-QKD. However, these studies are all based on free-space air and satellite ground, and none have investigated the performance of RFI-QKD in an underwater channel. Therefore, this paper constructed a channel model that considered both scattering and optical attenuation to obtain an RFI-QKD secret key rate in an underwater channel. The simulation results confirm that even in a relatively harsh underwater scenario, RFI-QKD maintains good performance.