# Cross-Platform UAV Swarm Key Management in Denied Environments
## 2 Preliminaries and Definitions
### Division of Task Stages  
The denied environment is characterized by long-distance combat, fierce confrontation in the electromagnetic and physical fields, and high risks to manned equipment, making it impossible for most UAVs to fulfill tasks. According to DARPA's Collaborative Operations in Denied Environment (CODE) program [11], the UAV swarm's task execution in a denied environment is divided into three stages: the transport and delivery stage, the UAV arrival and regrouping stage, and the collaboration stage. Stage 1 starts as the delivery platform departs from the base and ends as the platform arrives at the safe region and finishes the delivery of the UAV; Stage 2 starts as the new UAV swarm is constructed and ends as the UAV arrives at the target region; Stage 3 starts as the UAV arrives at the target region and ends as the UAV completes the automatic collaboration tasks, as shown in Figure 1.  
In denied environments, the UAV swarms often face both geographic and physical denial. The major denial conditions and denial intensity in different stages of a task (as shown in Figure 1) are analyzed, and the specifics are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(KMC_{j}\) & Key management center of the \(j\)-th delivery platform (\(1\leq j\leq m\)) \\ \(K_{0}\) & Global key \\ \(K_{G}\) & \(\{KMC_{1},KMC_{2},\cdots KMC_{m}\}/\) the set of the delivery platforms (KMCs) \\ \(P_{m}\) & \(\{ID_{1},ID_{2},\ldots ID_{m}\}/\)the set of identity labels of delivery platforms \\ \(C_{k}\) & \(\{s_{k1},s_{k2},s_{k3}\cdots s_{km}\}/\)the set of private keys of delivery platforms \\ \(s_{kj}\) & Private key of the \(j\)-th delivery platform (\(1\leq j\leq m\)) \\ \(UAV_{j}\) & The UAV \(i\) launched from the \(j\)-th delivery platform (\(1\leq i\leq n\)) \\ \(UAV\_{j}ID_{j}\) & The identity label of UAV \(i\) launched from the \(j\)-th platform \\ \(UAV\_{SK_{j}}\) & Private key of UAV node \(i\) launched from the \(j\)-th platform \\ \(p_{i}\) & Private key parameter of \(UAV_{j_{i}}\) \\ \(G_{m}\_key\) & Group key of UAV nodes launched from the \(j\)-th platform \\ \(G_{m^{\prime}}\_key\) & The intra-group session key of the \(m^{\prime}\) group after regrouping/\(\left(m^{\prime}\in Z^{*}\right)\) \\ \(m^{\prime\prime}\) & The \(m^{\prime}\) group after regrouping \\ \(t\) & The \(t\)-th stage of the task \\ \(U_{t}\) & The set of UAVs at the \(t\)-th stage of the task (\(1\leq t\leq n\)) \\ \(M_{t}\) & Broadcast message of the \(t\)-th stage of the task \\ \(l_{t}\) & Identity verification factor at the \(t\)-th stage of the task \\ _seed_ & Private key update seed \\ \(S_{UAV\_{ID_{i}}},S_{ID}\) & Present parameter validation factor \\ \(\mathrm{a}_{1}^{1},\hat{P}_{1}^{2}\), & Key creation factor \\ \(B\) & \(\left\{\sum\limits_{j_{i}}b_{j_{i}}\right\}\) prime number set \\ \(h(\cdot)\) & Hash function \\ \hline \hline \end{tabular}
\end{table}
Table 1: Definitions of symbols used in this study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Task Stages** & **Deial Disturbances** & **Geographic** & **Communication** & **Neapon Denial** \\ \hline Stage 1 & +++ & & + \\ \hline Stage 2 & + & ++ & ++ \\ \hline Stage 3 & & +++ & ++ \\ \hline \hline \end{tabular} + indicates weak denial, ++ indicates medium denial, and ++ indicates strong denial. Weak denial represents common denied environments, medium denial represents conventional antagonism, and strong denial represents strong antagonism in the electromagnetic and physical fields.  
Figure 1: Division of task stages of UAV swarms in denied environments.