## 3 The Proposed Protocol
### Three Proposed Authentication Methods
#### 3.3.3 Receiver Centric Authentication (RCA)  
Next, we present the third method, Receiver Centric Authentication (RCA). It is a light-weight authentication method that allows vehicles in different zones to communicate using a short aggregated single signature that can be verified by any receiver vehicle that belongs to multiple neighbor zones. In this method, the transmitter vehicle aggregates the generator values of neighbor zones to generate aggregated public keys that allow the receivers to verify the message. In this method, receivers aggregate the neighboring zone's generators to verify the message. For example, \(V_{1}\) in zone 1 received messages from \(V_{2}\) in zone 1 and \(V_{3}\) in zone 2. Instead of broadcasting one message carrying two signatures for the receivers in the two zones like in the conventional method, RCA generates one message with a single signature to be verified by all vehicles in both zones. Vehicles generate a new aggregated secret key from their original zone's secret keys to hide the original secrets and increase the security level. The transmitter vehicle searches the security parameters in its pre-stored table for the required \((g_{2 ZID})\). If the parameter cannot be found, it requests the possible combinations of \(\big{(}g_{2 ZID}\big{)}\) from the nearest BS. It generates an aggregated public key corresponding to the secret keys {\(sk_{1}+sk_{2}+\ldots sk_{N}\)} for the \(N\) neighboring zones that have receivers. The generation of an aggregated public key and aggregated generators for the neighboring zones can be done offline, to reduce the computation time in the vehicles for every transmission. In the RCA method, the transmitter vehicles generate an aggregated secret key \(sk_{aggr}=sk_{1}+sk_{2}+\ldots sk_{N}\) using the pre-stored vehicle secret keys for the neighboring zones and their corresponding aggregated public key \(pk_{aggr}=sk_{aggr}\). \(g_{2 aggr}\), where \(g_{2 aggr}=g_{1}+g_{2}+\ldots+g_{2N}\) represents the aggregated generators. The transmitter generates message m = {\(L_{ZID},\;pid_{i},m_{i},T_{s}\)}, and signs it using the aggregated secret key for the neighboring zones. It then generates a single signature \(\sigma_{aggr}=sk_{aggr}\).\(H(m)\). The transmitter broadcasts {\(L_{ZID},\;pid_{i},m_{i},T_{s},pk_{aggr},\sigma_{aggr}\)} to all receivers in the neighboring zones. The receivers aggregate the required generators of the neighboring zones as the start of the verification process. Given \(g_{2 aggr}\), \(pk_{aggr}\in G_{2}\), and \(\sigma_{aggr}\in G_{1}\), the receivers verify the message by checking if Equation (8) holds. \[e\big{(}g_{2 aggr},\sigma_{aggr}\;\big{)}=e\big{(}\;pk_{aggr},\;H(m)\big{)} \tag{8}\]If Equation (8) is satisfied, the receiver accepts the message, else it rejects the message. Equations (9)-(11) define \(g_{2 aggr},\ pk_{aggr},\) and \(sk_{aggr}.\)  
\[g_{2 aggr}=\ g_{21}+\ g_{22}\ldots+\ g_{2N} \tag{9}\]  
\[pk_{aggr}=sk_{aggr}\cdot g_{2 aggr} \tag{10}\]  
where  
\[sk_{aggr}=\ sk_{1}+sk_{2}+\ldots+sk_{N} \tag{11}\]  
\[\sigma_{aggr}=sk_{aggr}\cdot H(m) \tag{12}\]  
Algorithm 3 summarizes the signature generation and verification procedure of the proposed RCA method. Figure 9 illustrates an example of the RCA authentication method for the two zones. In Figure 7, the vehicles in orange belong to zone 1, the vehicles in green belong to zone 2, and the vehicles in blue belong to zone 1 and 2. Transmitter \(V_{1}\) broadcasts a message m to the orange and green receivers, simultaneously. \(V_{1}\) signs a message m in the following steps. \(V_{1}\) calculates \(sk_{aggr}=sk_{1}+sk_{2}\) followed by \(pk_{aggr}=sk_{aggr}\cdot g_{2 aggr}\). \(V_{1}\) attaches an aggregated signature \(\sigma_{aggr}=\sigma_{1}+\sigma_{2}=sk_{aggr}\cdot H(m)\) to the message. Then, the receivers in zone 1 and zone 2 can verify \(\sigma_{aggr}\). The proof of the verification can be proved as follows, in Equation (13):  
\[