## 3 The Proposed Protocol
### System Model
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Descriptions** \\ \hline \(pk_{\text{\tiny{$ZID$}}}\) & An ECC point represents the public key of vehicle \(v_{i}\) in each zone: \(sk_{\text{\tiny{$ZID$}}}\cdot\text{\text{\tiny{$\beta$ZID$}}}\) \\ \hline \(H\) & A cryptographic hash function that maps a message to a point in the group \(G_{1}\) \\ \hline \(pid_{i}\) & \begin{tabular}{c} Represents the pseudo-identity of \(v_{i}\) to hide it’s real identity and allow vehicle to communicate anonymously \\ \end{tabular} \\ \hline \(m_{i}\) & Represents message payload transmitted from vehicle \(v_{i}\) \\ \hline \(T_{s}\) & Is a timestamp to ensure message freshness \\ \hline \(n\) & The number of base stations \\ \hline \(N\) & The number of zones \\ \hline H(m) & Hashed message to a point over the elliptic curve group \(G_{1}\) \\ \hline \(\sigma_{i}\) & Generate a signatureover message m using the secret key of each vehicle \\ \hline \(||\) & Represents the concatenation operation of two elements \\ \hline \(\text{\tiny{$\beta$Z$}}_{\text{\tiny{$ZID$}}}\) & \begin{tabular}{c} Represents the aggregation of zones generators (\(\text{\tiny{$\beta$Z$}}_{\text{\tiny{$ZID$}}}\)) \\ to generate a new value \(\in G_{2}\colon\text{\tiny{$\beta$Z$}}_{1}+\text{\tiny{$\beta$Z$}}_{2}+\ldots+ \text{\tiny{$\beta$Z$}}_{N}\) \\ \end{tabular} \\ \hline \(sk_{\text{\tiny{$\beta$gg$}}}\) & \begin{tabular}{c} Represents the aggregation of vehicle \(v_{i}\) secret keys for different zone destinations \\ \(sk_{1}+sk_{2}+\ldots+sk_{N}\in\text{\tiny{$F$}}_{p}\) \\ \end{tabular} \\ \hline \(pk_{\text{\tiny{$\beta$gg$}}}\) & \begin{tabular}{c} Represents the aggregated public key of \\ vehicle \(v_{i}\colon sk_{\text{\tiny{$gg$}}}\,,\text{\tiny{$\beta$2$}}_{\text{\tiny{$gg$}}}\), where \(pk_{\text{\tiny{$\beta$gg$}}}\in G_{2}\) \\ \end{tabular} \\ \hline \(\sigma_{\text{\tiny{$\beta$gg$}}}\) & \begin{tabular}{c} The aggregated signature over message m using the aggregated secret key \(sk_{\text{\tiny{$\beta$gg$}}}\colon sk_{\text{\tiny{$\beta$gg$}}}\cdot H(m)\), where \(\sigma_{\text{\tiny{$\alpha$gg$}}}\in G_{1}\) \\ \end{tabular} \\ \hline \(\sigma_{\text{\tiny{$\text{C$}}}}\) & \
\begin{tabular}{c} The concatenated signatures that consists of \(N\) signatures \\ generated by vehicle \(v_{i}\) for different zones destinations: \\ \((\sigma_{1}||\text{\tiny{$\rho$}}_{2},\ldots||\text{\tiny{$\rho$}}_{N})\) \\ \end{tabular} \\ \hline \(pk_{\text{\tiny{$\text{C$}}}}\) &
\begin{tabular}{c} The concatenated public keys that consists of \(N\) public keys of \\ vehicle \(v_{i}\) for different zones destinations: \\ \((pk_{1}||\text{\tiny{$pk_{2}}},\ldots||pk_{N})\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._requests the key material and authentication parameters for the current zone. Vehicles can communicate in two modes. The first mode is single-zone communication that allows vehicles to securely communicate with other vehicles in the same zone (e.g., in Figure 2, \(V_{1}\) in zone 1 communicates with \(V_{3}\)). The second mode is the multi-zone communication that allows vehicles in one zone to securely communicate with other vehicles positioned in other neighboring zones (e.g., in Figure 2, \(V_{2}\) in zone 1 communicates with \(V_{4}\) in zone 2). In each zone, all vehicles are configured with common security parameters. However, the vehicles also receive messages from the neighboring zones and thus require the security parameters of the neighboring zones for authentication. Figure 3: BSs registration with CA. Figure 2: Single-zone and multi-zone communication in the 5G-V2X network model time for the three proposed authentication methods, and six previous related methods for single-zone and multi-zone scenarios.