## 4 Security Analysis and Performance Assessment
### Passive Attacks  
In the category of passive attacks, this paper examines a typical non-invasive passive attacker, [PERSON], who attempts to eavesdrop on the data packets transmitted over the legitimate channel within the communication range to decipher the symmetric key, all while [PERSON] and [PERSON] remain unaware of [PERSON]'s presence. [PERSON] is equipped with the same AIS equipment and has the ability to monitor all ongoing AIS communications within the communication range. Additionally, [PERSON] possesses complete knowledge of the communication system, including the cryptographic algorithms used by [PERSON] and [PERSON]. If [PERSON] succeeds in obtaining the shared key, the security of the system is compromised. To evaluate this, let us analyze the scenario from an information-theoretic perspective.  
The maximum number of bits of shared information between [PERSON] and [PERSON], \(Info_{max}\), can be represented by the mutual information \(I\) between the nodes, expressed as  
\[Info_{max}=I(\hat{h}_{AB},\hat{h}_{BA})=H(\hat{h}_{AB})+H(\hat{h}_{BA})-H(\hat{h }_{AB},\hat{h}_{BA}) \tag{14}\]  
where \(H\) represents the information entropy. Similarly, when [PERSON] monitors the legitimate channel and obtains the channel estimation values \(\hat{h}_{AE}\) and \(\hat{h}_{BE}\), the number of bits of information shared between [PERSON] and [PERSON] \(info_{secure}\) can be expressed as  
\[Info_{secure}=I(\hat{h}_{AB},\hat{h}_{BA}|\hat{h}_{AE},\hat{h}_{BE})=H(\hat{h}_ {BA}|\hat{h}_{AE},\hat{h}_{BE})-H(\hat{h}_{BA}|\hat{h}_{AE},\hat{h}_{BE},\hat{ h}_{AB}) \tag{15}\]  
Based on this, the number of bits of information that [PERSON] can eavesdrop on from the information shared by the legitimate communication parties \(Info_{E}\) can be expressed as  
\[Info_{E}=Info_{max}-Info_{secure} \tag{16}\]  
Now, let us discuss a situation. In Section 1, we mentioned that when the distance between the eavesdropper and the legitimate communication node is greater than half a wavelength, the eavesdropping channel and the legitimate channel can be considered independent of each other. In other words, \(\hat{h}_{AE}\) and \(\hat{h}_{BE}\) are independent of \(\hat{h}_{AB}\) and \(\hat{h}_{BA}\). Based on this premise, Equation (15) can be further written as  
\[Info_{secure} =H(\hat{h}_{BA})-H(\hat{h}_{BA}|\hat{h}_{AB})\] \[=H(\hat{h}_{BA})-\left[H(\hat{h}_{AB},\hat{h}_{BA})-H(\hat{h}_{AB })\right]\] \[=H(\hat{h}_{AB})+H(\hat{h}_{BA})-H(\hat{h}_{AB},\hat{h}_{BA}) \tag{17}\]  
This result is identical to \(info_{max}\), meaning that \(Info_{E}=0\). This indicates that all shared bits between [PERSON] and [PERSON] are secure. Thus, we can conclude that, in theory, when [PERSON]'s received signal is uncorrelated with the legitimate signals of [PERSON] and [PERSON], all shared information between [PERSON] and [PERSON] remains impervious to eavesdropping.  
For the scheme proposed in this paper, knowledge about [PERSON] is generally not required. This is because the eavesdropper is typically located farther than half a wavelength (approximately 1.852 m for the AIS frequency band), which is negligible in marine communication scenarios. In practical situations, the distance between ships is often thousands of times the wavelength or more. Additionally, this paper does not consider scenarios where an attacker infiltrates the interior of a ship. The simulation results for the CIR estimation values of the received signals from [PERSON], [PERSON], and [PERSON] are presented in Figure 6.