# 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
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scheme** & \
\begin{tabular}{c} **Broadcast** \\ **Verification** \\ \end{tabular} &
\begin{tabular}{c} **Mutual-** \\ **Healing** \\ **Mechanism** \\ \end{tabular} & **FWS** & **BWS** & **RIA** & **RRA** \\ \hline Scheme in [10] & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & — & \(\times\) \\ Scheme in [12] & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & — & \(\times\) \\ Scheme in [13] & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(mt\) & \(\times\) \\ Scheme in [14] & — & \(\times\) & — & — & — & \(\surd\) \\ Scheme in [15] & — & \(\times\) & \(\surd\) & \(\surd\) & \(any\) & \(\surd\) \\ Our scheme & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(any\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of different UAV swarm key management schemes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition** \\ \hline \(T_{h}\) & Hash operation \\ \(T_{mul}\) & Multiply \\ \(T_{exp}\) & exponentiation \\ \(T_{var}\) & XOR operation \\ \(T_{mod}\) & Mod operation \\ \(T_{e}\) & AES encryption \\ \(T_{d}\) & AES decryption \\ \(T_{bp}\) & Bilinear Pairing \\ \(T_{matrix-m}\) & Matrix calculation time \\ \(T_{so}\) & Asymmetric signature/verification \\ \(T_{l}\) & Solve the system of linear equations \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Definitions of signs of operation. #### 4.3.1 Computing Overhead

In this section, the computing overhead of the swarm head and \(UAV_{ij}\) in the ACPKMS scheme is analyzed. During key establishment, the swarm head node CHN performs the hash operation two times, with the time consumed marked as \(2T_{h}\); the broadcast receiving node \(UAV_{ji}\) performs the hash operation three times, taking \(3T_{h}\). Though theoretically, our scheme has a computing overhead \(3T_{h}\) higher than the scheme proposed in [17], part of the key is updated locally, which reduces the overhead and prevents the \(G_{m\_key}\) from directly engaging in the construction of congruences; the attacker must know all the parameters of \(UAV_{ji}\), i.e., \(p_{i}=\left(K_{0},seed,UAV_{-}SK_{ji},ID_{j},S_{ID},S_{UAV-ID_{ji}},P_{m}\right)\) before it can crack \(G_{m\_key}\), which enhances the key security and cuts the computing overhead during key establishment. Figure 8 shows the computing overhead of the nodes during the key establishment process. In our scheme, the key update process is divided into the local key update and the session key update to reduce the computing workload. For convenient comparison, the data processed in this paper are set to be half that in [17; 18], and the key establishment broadcast message is only one session stage, that is, to solve \(G_{m^{\prime}(t+1)\_key}\) with a given \(G_{m^{\prime}(t-k)\_key}\). Normally, 12 UAVs create a formation. The Visual Studio 2019 is employed to call the MIRACL cryptographic library to measure the computing overhead of different schemes, and the mean value of multiple tests is used for measurement and comparison. Figure 9 shows the key establishment process. In our proposed scheme, the swarm head UAV and the receiver UAV take an average of 1.068 \(\upmu\)s in the key establishment process, which is lower than other schemes, so our scheme is applicable to the fast-moving UAV

Figure 8: Computing overhead of nodes for key establishment in different schemes [16; 17; 18]. #### 4.3.2 Communication Overhead

As UAVGN is a wireless network, the communication overhead is an important indicator in key management. During the key establishment process in the ACPKMS scheme, the requestor node \(UAV_{i}\) needs to send messages including \(Request\) and \(Confirm\), which incurs \(4\log p\) communication overhead; the response node \(UAV_{Neighbor}\) needs to send \(Response\), incurring \(5\log p\) communication overhead. Table 7 displays the communication overhead of various schemes.