## 3 The Proposed Protocol
### Three Proposed Authentication Methods
#### 3.3.1 Transmitter Centric Authentication (TCA)  
In the TCA authentication method, transmitter vehicles generate signatures using their current zone parameters. The receivers in the transmitter's zone or other zones use the security parameters of the transmitter's zone to verify the signatures. While the receivers in the same transmitter zone use their pre-stored zone parameters to verify messages, the receivers in other zones search their security parameter table for the transmitter's zone parameters. If the transmitter's zone parameters do not exist in the table, the receivers request them from the nearest BS, through a secure channel. The TCA method can also be applied to a single-zone communication, where transmitters and receivers belong to the same zone. In the following, we first describe a single-zone case, followed by a multi-zone case. Single-Zone Case: A sender vehicle \(V_{1}\) authenticates message m by calculating a bilinear pairing signature \(\sigma_{1}\) that can be verified by the receiver vehicle \(V_{2}\). \(V_{1}\) computes a hashed message H(m), where m = \(\{L_{ZID},\ pid_{1},m_{i},T_{s}\}\). In which \(L_{ZID}\) represents a list of zone IDs, \(pid_{i}\) represents the pseudo-identity of \(V_{1}\), \(m_{i}\) represents the message payload, and \(T_{s}\) is a timestamp. Then, the hashed message H(m) is mapped to a point in the bilinear group \(G_{1}\) using its secret key \(sk_{1}\) in zone 1. Then, \(V_{1}\) attaches to each transmitted message the following resulting information--the signature \(\sigma_{1}\), the public key \(pk_{1}\), the sender's pseudo-identity \(pid_{1}\), zone ID (\(z_{1}\)), and the current time stamp \(T_{s}\), which are illustrated in Figure 5. When receiver \(V_{2}\) receives a signed message that contains \(\{L_{ZID},\ pid_{1},m_{i},T_{s},pk_{1},\sigma_{1}\}\), \(V_{2}\) checks the freshness of timestamp Ts. If \(T_{s}\) is invalid, \(V_{2}\) rejects the message; otherwise, \(V_{2}\) checks the list of zone IDs \(L_{ZID}\). If the receiver's zone ID matches the sender's zone ID (\(z_{1}\)), receiver \(V_{2}\) starts verification of the signature using \(pk_{1}\ G_{2},\sigma_{1},\ G_{1}\), and \(g_{21}\). Receivers accept the message if Equation (5) holds. Otherwise, they reject it. For the transmitter and receiver vehicles located in the overlapped area, they are considered as single-zone communication. TCA algorithm allows vehicles to choose the most updated zone parameters to communicate securely. If the security parameters are updated, all vehicles in the overlapped area receive the updates at the same time. Thus, the vehicles are free to choose the zone parameters, they can use zone 1 information or zone 2 information. As shown in Figure 6, \(V_{1}\) and \(V_{2}\) are located in the overlapped area where \(V_{1}\) uses zone 1 security parameters to generate the signature \(\sigma_{1}\) over message m. \(V_{2}\) received m, checks the freshness of \(T_{s}\), if its valid, \(V_{2}\) checks the list of zone IDs \(L_{ZID}\). The zone ID of the transmitter \(V_{1}\) matches the zone ID of the receiver \(V_{2}\), \(V_{2}\) starts verification of the signature using \(pk_{1}\ G_{2},\sigma_{1},\ G_{1}\), and \(g_{21}\). Receivers accept the message if Equation (5) holds. Otherwise, they reject it, as shown in Figure 6.  
Figure 5: Single-zone communication in the TCA method. Figure 6: Overlapped area communication in TCA method. to \(V_{2}\) in zone 1 and \(V_{3}\) in zone 2. In the TCA method, \(V_{1}\) signs the message using zone 1 parameters, while the receivers \(V_{1}\) in zone 1 and \(V_{2}\) in zone 2 verify using the same parameters as the transmitter. Receivers in the same zone as transmitter \(V_{1}\) use their zone information to verify the signature, while receivers in different zones search the zone parameter storage to find the transmitter's zone information. If the information is not found, the receiver requests the transmitter's zone parameters from the nearest BS.