## 4 Proposed ECC-GA-PASR Approach
### ECC-Based Authentication for the Trusted Authority (TA)  
In the research, the trusted authority (TA) is used as the main source for the authentication process, which secures the network using the public-private key pair using ECC. The work of TA is that it is accountable for SVs management through a pair of cryptographic keys as well as it controls the verification process that the SVs contain any kind of misbehavior reports that are not using the trust values of SVs. Subsequently, the TA creates a certificate that upholds key pairs for every SVs; it is called the initial registration within a network. The proper utilization of this process is verified by the RSU, which will check whether the SVs hold their valid certificates issued by the TA. RSU is highly secured to preserve the privacy of the network. In the part of ECC key generation, it is applied to the dynamic network with high speed and huge mobility because it reduces the complexity by using data with decreasing key size with high security. To provide secure vehicular communication, ECC is modified with a top-secret key which is shown in Figure 8. The generated public-private key pairs are used during the process of communication between the SVs. The messages maintain a speed of SV, location, direction, and authenticated and private key that gets broadcasted at each instance of time during transmission. The \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline Genetic Code & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 \\ Road Division & 1 & 2 & 2 & 3 & 4 & 4 & 5 & \(\dots\) & \(n\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Genetic code illustration using GA.  
transmitted message is encrypted with SV's private key, and then at the time of decryption, the SV's uses the public key for verification. The mathematical expression for the typical elective curve for ECC is expressed as  
\[y^{2}=x^{3}+ax+b\ (mod\ p) \tag{8}\]  
In Equation (8), a and b represent the integer values that assure the properties of ECC \(4a^{3}+27b^{2}\
eq 0\). The public-private key pairs for SVs and the secret shared key of any two SVs are generated using the following process. For example, if \(SV_{1}\) wants to communicate with \(SV_{2}\), at the initial condition, these SVs need to secure the legitimacy of the message. \(SV_{1}\) choose the private key such as secret key \(\delta_{1}\) and private key (\(Pr_{s}\)). In the same way, \(SV_{2}\) chooses the private key such as secret key \(\delta_{2}\) and private key (\(Pr_{s}\)). Then the private keys of the \(SV_{1}\) and \(SV_{2}\) are expressed below. \[SV_{1}=\delta_{1}.Pr_{s} \tag{9}\]  
\[SV_{2}=\delta_{2}.Pr_{s} \tag{10}\]  
In Equations (9) and (10) \(\delta_{1}\) and \(\delta_{2}\) are the secret keys, and \(Pr_{s}\) is the private key. The vehicle which initiates malfunction that fails to identify the values of the secret keys \(\delta_{1}\) and \(\delta_{2}\). At this condition \(SV_{1}\) maintain the secret key \(\delta_{1}\) and the top-secret key \(TS_{1}\). Similarly, \(SV_{2}\) maintain the secret key \(\delta_{2}\) and the top-secret key \(TS_{2}\). The expression for the top-secret keys is given below. \[TS_{1}=t_{1}\ *\ t_{1} \tag{11}\]  
\[TS_{2}=t_{2}\ *\ t_{2} \tag{12}\]  
In Equations (11) and (12) \(t_{1}\) and \(t_{2}\) are the random values and the \(ts_{1}\) and \(ts_{2}\) are top-secret keys. So, the public key of \(SV_{1}=\delta_{1}.P_{s}\). Similarly, for \(SV_{2}=\delta_{2}.P_{s}\). After that, the \(SV_{2}\) transmits the public key \(SV_{2}\) to \(SV_{1}\). Then, \(SV_{1}\) receives the message that \(SV_{2}=\left(X_{SV_{2}},Y_{SV_{2}}\right)\) as well as the \(SV_{1}\) transmits the public key \(SV_{1}\) to \(SV_{2}\). Then, \(SV_{2}\) receives the message that \(SV_{1}=\left(X_{SV_{1}},Y_{SV_{1}}\right)\). In this way, the create key is shared between two SVs. In the next stage, a two-way hash function and addition operation is performed. \[M=P_{s}+HF(TS_{1})+HF(TS_{2}) \tag{13}\]  
At the final stage, the top-secret key of \(SV_{1}\) and \(SV_{2}\) are given below.