# Practical V2I Secure Communication Schemes for Heterogeneous VANETs
## 6 Performance Analysis  
Figure 2 gives a specific application scenario of the proposed schemes. If vehicle \(V_{\text{A}}\) collides with vehicle \(V_{\text{B}}\), \(V_{\text{A}}\), \(V_{\text{B}}\), and \(V_{\text{C}}\) signcrypt the traffic information including collision messages to  
a nearby RSU by our many-to-one signcryption schemes (MOHSC-I or MOHSC-II) just in order to avoid traffic jams, and these steps are repeated in a short time interval according to DSRC protocol [1]. Then, the nearby RSU unsigncrypted the messages from \(V_{A}\), \(V_{B}\), and \(V_{C}\) after authenticating the messages integrity and vehicles' identities, which is just to ensure that the vehicles will be responsible for messages. Further, by using our one-to-many signcryption schemes (OMHSC-I or OMHSC-II), the RSU signcrypts and broadcasts the integrated information to other adjacent vehicles in time and makes them go around early. As a result, other cars can avoid joining this traffic congestion and make traffic management more convenient. Compared with the other current broadcast technology, our schemes can guarantee the integrity and tamper-resistance of message and the authentication of message sources, which can improve the credibility of message. To guarantee the authenticity and confidentiality of message, the sender signcrypts message in our schemes. Upon receiving messages from many vehicles, the RSU first verifies the authenticity of these messages and then discards the error or distorted messages. Although some methods in [21; 22; 23; 24; 25; 26] achieve heterogeneous communication, they have different disadvantages, which are given in **Related Work**. The function comparisons of all the schemes are depicted in Table 1. In addition, Tables 2 and 3 and Figures 3 and 4 mainly focus on the comparison  
Figure 4: Comparisons of the computational time (IBC\(\rightarrow\)PKI). Figure 5: Comparisons of total energy consumption (PKI\(\rightarrow\)IBC). Figure 3: Comparisons of the computational time (PKI\(\rightarrow\)IBC). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheme** & **PKI Setup** & **IBC Setup** & **Signcryption** & **Unsigncryption** & **Total** \\ \hline HOOSC [23] & \(n(2l_{m}+l_{im})\) & \(n(l_{m}+l_{im})\) & \(n(l_{e}+2l_{m}+l_{im})\) & \(n(2l_{p}+l_{e}+2l_{m}+l_{im})\) & \(2 nt_{p}+2 nt_{e}+4 nt_{im}+7 nt_{m}\) \\ \hline HSC-II [25] & \(n(t_{m}+t_{im})\) & \(n(2t_{m}+t_{im})\) & \(n(t_{e}+2t_{m})\) & \(n(2l_{p}+l_{e}+l_{m}+l_{im})\) & \(2 nt_{p}+2 nt_{e}+3 nt_{im}+6 nt_{m}\) \\ \hline MOHSC-II & \(nt_{m}\) & \(nt_{m}\) & \(n(l_{p}+3t_{m})\) & \((n+2)l_{p}+nt_{m}\) & \((2n+2)l_{p}+6 nt_{m}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computation comparisons (IBC\(\rightarrow\) PKI). From Table 1, we see only the schemes from [25] and our schemes can achieve bi-directional heterogeneous communication. Since our MOHSC-I and MOHSC-II schemes simultaneously send \(n\) messages but the schemes in [23; 24; 25] send one message to the receiver, their ciphertexts length should be multiplied by \(n\) just to ensure the fairness of comparisons. Obviously the aggregate ciphertext length from \(n\) messages in our MOHSC-I and MOHSC-II schemes is the shortest, regardless of the size of \(m\) and \(G_{1}\) that are selected. So, the communication costs and storage in our schemes have also been reduced. In Tables 2 and 3, \(t_{m}\), \(t_{p}\), \(t_{inv}\), and \(t_{e}\), respectively, represent the time of performing a scalar multiplication, one pairing calculation in \(G_{1}\), an inverse operation in \(Z_{q}^{*}\), and an exponent operation in \(G_{2}\) individually. We do not consider other less time-consuming operations, such as the XOR operation. For the fairness of comparison, we extend schemes in [23; 25; 26] to \(n\) senders sending \(n\) messages to a receiver in Tables 2 and 3.