# Secure and Efficient High Throughput Medium Access Control for Vehicular Ad-Hoc Network
## 3 Secure VANET Communication (SVC) Using Commutative RSA Technique
Therefore, ENCCMA does not consider user privacy, nor does it provide message authentication security. The proposed security model is presented in the next subsection. (c) RSA with commutative key:  
Generally, with encrypting, we first encrypt with [PERSON]'s key, then encrypt with [PERSON]'s key, and then decrypt with [PERSON]'s key and [PERSON]'s key. The exchange cipher allows decoding in any order. An important factor is that [PERSON] and [PERSON] need to share the values of \(p\) and \(q\). For example, Figure 5 shows the encryption in the correct order and then in the incorrect order with the use of Prime size 128 (bits). However, we propose a safe and effective CRSA algorithm for data authentication between participant's vehicles/devices in a V2V environment. To enable safe data communication among the corresponding vehicle in the V2V environment, it is a noble commutative RSA method which indicates that in order encryption can be performed in the same manner without affecting the results of encryption and decryption technique. A secure communication model can be realized only when message transmitted over the communication channel is protected and cannot be collided. To achieve this, cryptography mechanisms are generally considered. Therefore, the S - PECA proposed here adopts CRSA algorithm. The S - PECA considers two prime param \(A_{u}^{\mathcal{C}}\) and \(B_{b}^{\mathcal{C}}\) initialized amongst all the vehicles of the region. Let \(\mathcal{R}_{X}\) and \(\mathcal{R}_{Y}\) represent the region member required to securely communicate over the secure channel. To compute the encryption keys and decryptions key pairs of the CRSA algorithm, the property \(L^{\mathcal{C}}\) and \(M^{\mathcal{C}}\) are evaluated using the following:  
\[L^{\mathcal{C}}=\left[\left(A_{a}^{\mathcal{C}}\right)\times\left(B_{b}^{ \mathcal{C}}\right)\right] \tag{7}\]  
\[M^{\mathcal{C}}=\left[\left(A_{a}^{\mathcal{C}}-1\right)\times\left(B_{b}^{ \mathcal{C}}-1\right)\right] \tag{8}\]  
From the above expression, it can be seen that \(L_{X}^{\mathcal{C}}=L_{Y}^{\mathcal{C}}\) and \(M_{X}^{\mathcal{C}}=M_{Y}^{\mathcal{C}}\) for \(X\) and \(Y\). The key pair for encryption of \(X\) and \(Y\) are signified as follows:  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]0  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]1 Encryption in the correct order and then in the incorrect order. The parameter \(\mathcal{E}^{\mathcal{C}}\) has obtained by arbitrarily selecting the parameter like it is a co-prime of \(M^{\mathcal{C}}\), in another expression  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]2  
where \(\mathbb{F}_{\mathcal{G}}(u,v)\) denotes the largest common factor function between \(u\) and \(v\). The decryption pair key of \(X\) and \(Y\) is described by \(\big{(}L_{X}^{\mathcal{C}},\mathcal{D}_{X}^{\mathcal{C}}\big{)}\) and \(\big{(}L_{Y}^{\mathcal{C}},\mathcal{D}_{Y}^{\mathcal{C}}\big{)}\). The \(\mathcal{D}^{\mathcal{C}}\)property is evaluated as follows:  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]3  
Let \(\mathbb{E}_{\text{U}}\) indicate the encrypted U message. The encryption process is as follows  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]4  
The CRSA decryption process is expressed on \(\mathcal{Y}\) encrypted message as  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]5  
(d) Proof of commutative RSA model:  
If the \(U\) message is encrypted with \(X\) and then encrypted with \(Y\), the commutative RSA can be demonstrated by the SVC model. As for the encryption performed with \(Y\), if it is encrypted at \(X\), the message result is the same and can be expressed as follows:  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]6 \[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]7 (15) \[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]8  
As \(L_{X}^{\mathcal{C}}=L_{Y}^{\mathcal{C}}\), it can be said that  
\[\underset{E}{max}\sum_{x}^{R}C_{x}. \tag{3}\]9  
and therefore,  
\[\sum_{x}^{R}e_{xy}=1\ \forall y \tag{4}\]0  
Each vehicle computes its public and private key using the proposed commutative RSA algorithm.