# Cross-Platform UAV Swarm Key Management in Denied Environments
## 3 Cross-Platform Key Management of UAV Swarms in Denied Environments
### Private Key Establishment in the Regrouping and Arrival Stage
\(\forall UAV_{j_{i}}\in U_{m^{\prime}t}\Rightarrow UAV_{j_{i}}\vartriangleleft M _{m^{\prime}t}\Rightarrow\ UAV_{j_{i}}\vartriangleleft M_{m^{\prime}t} \Rightarrow\\ UAV_{j_{i}}\succeq M_{m^{\prime}t}=\left\{\alpha_{m^{\prime}t}^{1},\beta_{m^ {\prime}t}^{2},I_{m^{\prime}t},\varepsilon_{m^{\prime}t},j\right\}\right\}\)_;_
2. \(AT\stackrel{{ M^{\prime}\prime}}{{\rightarrow}}UAV_{j_{i}}:UAV_{j_{i }}\vartriangleleft M^{\prime}_{m^{\prime}t}=\left\{\alpha_{m^{\prime}t}^{1}, \beta_{m^{\prime}t}^{2},I_{m^{\prime}t}^{2},\varepsilon_{m^{\prime}t},j^{ \prime}\right\}\Rightarrow\varepsilon_{m^{\prime}t}=\varepsilon^{\prime}_{m^{ \prime}t}\Rightarrow\\ Replay Attack; Therefore, \(\forall UAV_{j_{i}}\vartriangleleft Um_{m^{\prime}t}\) receives the replayed message \(M_{m^{\prime}t}\) and cannot pass the message legitimacy test. **Lemma 6**. : _The ACPKMS scheme can resist impersonation attacks (RIA)._

_Impersonation node attacks: suppose the attacker forges \(\forall UAV_{j_{i}}\in U_{m^{\prime}t}\ AT\
ot\preceq UAV_{-}SK_{j_{i}}\) to join UAVGN and needs to obtain \(G_{m^{\prime}t_{\cdot}\_key}\) to establish communication, i.e., \(AT\succeq G_{m^{\prime}t_{\cdot}\_key}\Rightarrow AT\succeq\left\{UIAV_{-}ID _{j_{i}},UAV_{-}SK_{j_{i}},h(\cdot),\varsigma_{l}^{NK},M_{m^{\prime}t}\right\}\), which does not hold and conflicts with \(AT\
ot\succeq s_{i}\), as the forged \(UAV_{i}\) needs to obtain the private key of \(UAV_{j_{i}}\) to join UAVGN._

Table 4 shows the performance of different UAV key management schemes. As the table shows, our scheme has forward and backward security, and can resist replay attacks and impersonation attacks. Compared with other schemes, ours uses the hash function for verification, which ensures legitimacy of the requests and responses, and avoids malicious attacks. \"malicious attacks\" Our approach establishes keys by constructing broadcast messages, has good security and efficiency, and hence is applicable to cross-platform UAV swarm key management. ### Efficiency Analysis

Because of the limited communication and computing capacity of UAVs, it is necessary to minimize the computing time and information exchange to reduce the computing and communication overhead [16]. In this study, the efficiency of our scheme is analyzed from the computing overhead, communication overhead, and storage overhead, with focus on the first two aspects. Table 5 shows the definitions of the signs of operations. According to the simulation tests and the efficiency analysis in Section 4.3, the performance of our scheme using the cryptographic library MIRACL is tested in an environment of the following settings: Intel (R) Core (TM), 2 i5-7500 CPU, 3.40 GHz processor, Windows 10. The results are shown in Table 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**256-Bit Data** & **Experiment Data** & **Computing Time (ms)** \\ \hline Time consumed for 1,000,000 & & \\ HASH-256 operations: & 534 & 0.0005340000 \\
534.000000 ms & & \\ Time consumed for 1,000,000 & & \\ times of 256-bit XOR & 3431 & 0.0034310000 \\ operations: 3431.000000 ms & & \\ Time consumed for 1,000,000 & & \\ times of AES 256-digit key & 1215 & 0.0012150000 \\ encryption: 1215.000000 ms & & \\ Time consumed for 1,000,000 & & \\ times of AES 256-digit key & 1219 & 0.0012190000 \\ decryption: 1219.000000 ms & & \\ Time consumed for 10,000 & & \\ times of bilinear pairing & 499,067 & 49.9067000000 \\ operations: 499,067.000000 ms & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computing time on the 256-bit experiment data.