# Secure and Efficient High Throughput Medium Access Control for Vehicular Ad-Hoc Network
## 3 Secure VANET Communication (SVC) Using Commutative RSA Technique
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notations** & **Abbreviation** \\ \hline \(\wedge_{R}\) & Set of all \(R\) vehicles \((\{1,2,3,\ldots,R\})\) \\ \hline \(\wedge_{t}\) & A specific set of \(r\) user \\ \hline \(h\) & Mean value of the back-off parameter \\ \hline \(\mathcal{D}(\mathcal{A})\) & Mean Overhead \\ \hline \(s_{CTS}\) & Corresponding time of CTS \\ \hline \(s_{STS}\) & Corresponding time of RTS \\ \hline \(s_{SIFS}\) & Corresponding time of SIFS \\ \hline \(s_{SYNC}\) & Size of synchronization packets \\ \hline \(s_{SEN}\) & Time of sensing \\ \hline \(\varphi\) & A time that corresponds to one back off param \\ \hline \(S_{\mathcal{I}}\) & Cycle Time \\ \hline \(A_{a}^{c}\) & Prime Number \\ \hline \(B_{b}^{c}\) & Prime Number \\ \hline \(\mathcal{E}^{c}\) & Public Key \\ \hline \(\mathcal{D}^{c}\) & Secret Key \\ \hline \(U\) & Data \\ \hline \(\mathcal{Y}\) & EncData \\ \hline \(\mathbb{D}_{V}\) & Decryption EncData \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._Note: we run flow diagram 1, to get channels set assigned to each device/vehicle, and according to these channels, Equation (5) can be utilized to calculate the throughput. Therefore, this work's goal is to achieve maximum throughput in the network to obtain channel allocation performance. However, we consider the throughput gained by \(x\) vehicle/device where \(C_{x}\) and \(e_{xy}\) represent the channel allocation decision. However, if the \(y\) channel is set for \(x\) vehicle, \(e_{xy}\) is set 1, else \(e_{xy}\) is set to 0. However, the gain throughput issue is shown as follows:  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]  
We have the following commitment to allocate the non-shared channel as  
\[\sum_{x}^{R}e_{xy}=1\ \forall y \tag{4}\]  
Now, we can calculate the throughput gained by \(x\) vehicle on non-shared channel assignment according to the following formula: \(T_{x}\) is the \(x\) vehicle/device assigned channel group, and \(l_{xy}\) is \(x\) vehicle channel \(y\) accessibility. However, \(C_{x}\) is calculated as follows:  
\[C_{x}=1-\prod_{y\in T_{x}}l_{xy}^{\prime}=1-\prod_{y=1}^{K}\left(l_{xy}^{ \prime}\right)^{e_{xy}} \tag{5}\]  
where \(l_{xy}^{\prime}=1-l_{xy}\) is the probability of \(x\) vehicle/device not accessing the \(y\) channel, and \(1-\prod\limits_{y\in T_{x}}l_{xy}^{\prime}\) is the probability of \(x\) vehicle accessing the channel. However, each vehicle can use one channel utmost, so the highest throughput is 1. The bound in Equation (4) is not required in the channel assignment technique. Moreover, solving Equations (3) and (4) are NP - hard problems because this is a nonlinear integer program. (b) Shared channel allocation \((\text{SCA})\):  
A shared channel (If the channel is shared between neighboring vehicles, then each vehicle has a specific time to do the transmission. However, the time required to reach  
Figure 3: Flow diagram of proposed non-shared channel allocation. the channel is determined by two factors, maximum throughput, and reduced collision for multi-user vehicle grid in the duct help improve throughput performance. However, they create MAC overhead due to multi-user allocation access channel conflict. Therefore, an optimized channel allocation method is needed to overhead for redundant design and balance throughput. The channel allocation model includes two steps. In the first as shown in Figure 2, single-vehicle channel assignment information is computed using flowchart 1. The following deals with multi-user channel allocation by assigning channels assigned to specific vehicles to other vehicles. Here, we model the SCA algorithm as shown in flow chart 2 in Figure 4.  
First, assigned accessible channels for all vehicles. Execute algorithm to obtain channel assigned to single vehicle then consider a group of channels which are shared by set vehicles/device and set of vehicles that shares channel among vehicles in the network. Figure 4: Flow diagram of proposed channel shared allocation. Update overhead to zero and set process to 1.