## 3 The Proposed Key Generation Protocol
### Channel Probing
To address this, [PERSON] and [PERSON] opt to transmit short probing sequences of pre-agreed lengths instead of standard AIS messages when sending probing signals. Let the probing signal length be \(d\), the AIS data rate be \(R\), and the time slot length be \(t_{slot}\). The time required for a round of probing can then be expressed as follows:  
\[t_{\text{probe}}=t_{slot}+\frac{d}{R} \tag{9}\]  
If the probing signal is very short, \(t_{probe}\) can be approximated by the duration of a single time slot (see Figure 5). For instance, if the 24-bit preamble sequence of a standard AIS message is used as the probing signal, a single round of probing requires approximately 29.17 ms, representing a significant reduction in time. This approach not only shortens the probing time but also reuses the existing preamble sequence, thereby reducing implementation complexity and conserving channel bandwidth. Figure 4: Correlation time at different relative speeds. Based on the above discussion, during the probing phase, [PERSON] and [PERSON] must exchange \(n\) sets of probing signals to gather sufficient key generation material. The time required for each set of probing signals, \(t_{\text{probe}}\), must be less than \(t_{c}\) at the corresponding relative speed \(\Delta v\). Additionally, it is essential to ensure that the time interval between the \(n\) sets of probing signals, \(t_{\text{interval}}\), is not shorter than \(t_{c}\). Otherwise, the correlation within the probing signals may reduce the entropy of the final key. Before initiating channel probing, [PERSON] and [PERSON] must agree on several key parameters through a handshake process. These parameters include the number of probing rounds, probing intervals, and the start time for each probing round. The start time of each probing round can be determined using the frame map and the SOTDMA (Self-Organized Time Division Multiple Access) time slot reservation mechanism. The frame map serves as a critical tool for managing time slot allocation and coordinating communication in the AIS. It represents the occupancy status of each time slot within an AIS frame. During the handshake process, [PERSON] and [PERSON] can evaluate the availability of the time slots in the frame map and reserve suitable slots accordingly. Issues related to data packet loss and retransmission are managed by the existing AIS standard and are not considered within the scope of this protocol. The estimation of the probing interval is given in Equation (10), while the estimation of the number of probing rounds is provided in Equation (11). \[t_{interval}=\left\lceil\frac{t_{c}}{t_{\text{slot}}}\right\rceil\cdot t_{slot} \tag{10}\]  
\[n=\left\lceil\frac{L_{k}}{\eta dP_{s}}\right\rceil \tag{11}\]  
Here, \(L_{k}\) represents the required key length; \(\eta\) denotes the key generation efficiency, which is the product of the quantization efficiency and the information reconciliation efficiency; \(\bar{\gamma}\) represents the average SNR; and \(P_{s}\) is the probing success rate. The value of \(P_{s}\) can be obtained by estimating the bit error rate of the Rayleigh fading channel, as shown in Equation (12). \[P_{s}=\frac{1}{2}\bigg{(}1+\sqrt{\frac{\bar{\gamma}}{1+\bar{\gamma}}}\bigg{)} \tag{12}\]  
\[f_{d}=\frac{\Delta v}{c}f_{VHF}\cos\theta \tag{7}\]0 Channel probing.