# Secure and Efficient High Throughput Medium Access Control for Vehicular Ad-Hoc Network
## 3 Secure VANET Communication (SVC) Using Commutative RSA Technique
Hop-based communication is adopted for data transmission among vehicles. Each vehicle encrypts the data using its own public key. The receiver performs decryption operations based on the number of times it is encrypted using its commutative keys of participating vehicles. The proposed model preserves data and user's privacy, and an intruder can be tracked using the user's commutative keys. First, once established the key management, the key management center will distribute two prime numbers \(A\) and \(B\) to all VANETs which are the same. Then, it will calculate \(L\) and \(M\) at each VANET node. Based on these two, each vehicular node will compute the encryption and decryption keys. Second, once established the key exchange and once all the vehicles do their encryption and decryption keys, they will inform the key management that it is over. For example (Figure 6):  
1. Key setup: 1. The same values of \(A\) and \(B\) are considered in all VANETs distributed by the key management center. 2. \(L\) and \(M\) are calculated at each VANET node. In the normal RSA or Elliptical Curve Cryptography (ECC) [48], when you encrypt encrypted data again, data get corrupted. Therefore, on decryption, the data cannot be recovered. Therefore, in our mechanism, the user does not need to decrypt the data; the user can just encrypt using his key and forward it. The normal RSA implementation might not be very fruitful, and it remains unexplored even with recent and optimized encryption techniques. Hence, approaches like commutative characteristics, which means that the order in which encryption takes place does not affect the decryption process if it is done in the same way and avoids security breaching, can be implemented. The unique characteristic of commutative RSA cryptosystem is that it can facilitate the reorder decryption which is unique and effective itself. On the other hand, in most existing approaches, the public key cryptosystems employ a key exchange approach that ultimately causes the increase in computational overheads for key exchange, and alternatively, in individual transceiver, the encryption and decryption are a must, and thus somewhere, the efficiency as well as security would be compromised. Therefore, the consideration of commutative RSA (CRSA) might be an optimum solution for accomplishing an efficient and most secure communication for multi-channel V2V vehicular ad hoc smart infotainment applications. Computation of contention window:  
To reduce the overhead probability between contending V vehicles considering security provisioning, contention window \(\mathcal{A}\) is computed (example of contention window: a vehicle that wants to transmit a packet must first request a channel) [37]. Indeed, there is a tradeoff between collision probability and overhead of MAC protocol that is influenced by \(\mathcal{A}\) (i.e., decreasing the \(\mathcal{A}\) value increases the probability of the collision, in the cost of MAC lower overhead (lower MAC overhead: overhead incurred in defining contention window size)) and vice versa. However, each vehicle chooses some equal back-off time. However, the higher the probability of a collision, the higher the probability of a first collision because the number of vehicles involved decreases. (For example, firstly, 10 vehicles contend, and out of those, 5 get contention, so the collision likelihood is higher (20%). Then,  
\[\sum_{x}^{R}e_{xy}=1\ \forall y \tag{4}\]1 Example for CRSA. only the remaining 5 vehicles contend for the channel. Therefore, the likelihood of collision comes down.) Let \(\mathcal{L}_{u}\) be the probability of the first collision. Consider constraint \(\mathcal{L}_{u}\leq eL\), where \(eL\) is the tradeoff between collision probability and management overhead to determine \(\mathcal{A}\) contention window. For \(r\) vehicles in the window contention stage, \(\mathcal{L}_{u}\) is evaluated as a function of \(\mathcal{A}\).