## 5 Analysis
### Performance  
We simulated the message delivery on VANETs to evaluate the impact of the proposed security protocol to the performance of message forwarding from RSUs to destination vehicles. We implemented the simulation by using NS-2 and SUMO [30] simulators as considering an urban road environment. Figure 4 and Table 2 show the 4600 m \(\times\) 3800 m road configuration and simulation settings, respectively. For our simulation, we applied Manhattan mobility model in which each vehicle moves in horizontal or vertical direction on an urban road and the probability of going straight is 0.5 and taking a left or right is, respectively, 0.25 [31]. We varied the number of vehicles from 30 to 150 moving with 11.1 m/s (40 km/h) to 19.4 m/s (70 km/h) speed on average, and put five contact point RSUs relaying messages to 15 destination vehicles. For message carry-and-forwarding, we adopted the DTN routing protocol of [32] and adjusted message forwarding time to compensate for the delay caused by the authentication process. To measure the authentication overhead of message delivery, we used the benchmark results of pairing-based cryptography library [33] implemented on Intel Quad Core2 2.4 GHz machine by using the supersingular curve \(y^{2}=x^{3}+x\) for the group \(\mathbb{G}_{1}\) with 512-bit base field size and 160-bit group order providing 1024-bit security. Then, we evaluated the performance in terms of message delivery delay and successful delivery ratio on average of 15 destination vehicles for each experiment by varying the number of vehicles and their moving speed. Let \(D\) be the total message delay from a contact point RSU to a destination vehicle. The message delay can be estimated as \(D=D_{tr}+D_{auth}\) where \(D_{tr}\) is the delay for message transmission and \(D_{auth}\) \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Simulation Setting**} \\ \hline road dimension & 4600 m \(\times\) 3800 m \\ \# of vehicles & \{30, 45, 60, 75, 90, 105, 120, 135, 150\} \\ \# of contact point RSUs & 5 \\ \# of destination vehicles & 15 \\ moving speed & \{40, 50, 60, 70\} km/h \\ mobility model & Manhattan model \\ wireless/bandwidth & 802.11 p/6 Mbps \\ radio coverage & 250 m \\ message size & 100 KB \\ message lifetime & 500 s \\ simulation time & 2000 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NS-2 simulation parameters. Figure 4: Road configuration for simulation. is for authentication process resulting from signature generation and verification. Depending on message forwarding method, \(D_{auth}\) can be classified as  
\[D_{auth}=\left\{ \begin{array}{ll}T_{sig}+T_{vrf},&\text{immediate;}\\ 2(T_{sig}+T_{vrf})+\sum_{i=1}^{l-1}T_{sig_{i}},&\text{carry-forward.}\end{array} \right.\]  
where \(l\) is the number of hops and \(T_{sig}\) and \(T_{vrf}\) are the times for signature generation and verification evaluated as \(T_{sig}\) = 4.65 ms and \(T_{vrf}\) = 10.93 ms, respectively. For immediate forwarding, it requires signature generation of the destination vehicle and verification of a contact point RSU before message forwarding. On the other hand, for carry-and-forwarding, authentication of the first carrier vehicle to a contact point RSU and authentication between the last hop vehicle and the destination vehicle are required while each intermediary vehicle only appends its signature to the forwarded message. With regard to our experiments depending on the number of vehicles and the moving speed, the initial positions of vehicles are randomly generated and the distributions of vehicles on the road in each experiment are not consistent. Thus, those experiments are independent of each other and cause uneven variations in the results of Figures 5-8. However, we would like to estimate the performance by observing the trend of changes through the experiment results. Figure 5 shows the average number of hops, and Figure 6 shows the average authentication delay evaluated by our simulations, respectively.