# Practical V2I Secure Communication Schemes for Heterogeneous VANETs
## 6 Performance Analysis
Since other schemes in [23; 26] only provide one-way heterogeneous communication, the comparisons are divided into PKI\(\rightarrow\)IBC in Table 2 and IBC\(\rightarrow\)PKI in Table 3 just for more scientific and elaborate results. From Tables 2 and 3, we can see our MOHSC-I and MOHSC-II schemes require a smaller total computation time (the sum of PKI setup, IBC setup, signcryption, and unsig encryption) when \(n\) messages are involved. The more intuitive analyses are given in Figures 3 and 4 for schemes in [23; 25; 26] and our schemes. We implement the experiment on MICA2 platform (same as [24]). We can get \(t_{p}\), \(t_{e}\), and \(t_{m}\) takes 1.9 s, 0.9 s, and 0.81 s, respectively [24]. Note that a \(t_{inv}\) operation needs roughly 0.9 s, although, theoretically, a \(t_{inv}\) operation is more time-consuming than a \(t_{e}\) operation. Finally, according to Tables 2 and 3, we can compute the total computation time of HSC-I, MHSC, MOHSC-I, HOOSC, HSC-II, and MOHSC-II are \(2n\times 1.9+(2n+3n)\times 0.9+6n\times 0.81=13.16 ns\), \((n+2)\times 1.9+2n\times 0.9+7n\times 0.81=9.37n+3.8s\), \((2n+2)\times 1.9+6n\times 0.81=8.66n+3.8s\), \(2n\times 1.9+(2n+4n)\times 0.9+7n\times 0.81=14.87 ns\), \(2n\times 1.9+(2n+3n)\times 0.9+6n\times 0.81=13.16 ns\), and \((2n+2)\times 1.9+6n\times 0.81=8.66n+3.8s\), respectively. The comparisons of total computational time are shown in Figures 3 and 4. Since vehicles and RSUs are both energy-constrained devices, we must consider the energy consumption. According to [24], a \(t_{p}\) operation consumes 45.6 mJ, a \(t_{e}\) operation consumes 21.6 mJ, and a \(t_{m}\) operation consumes 19.44 mJ; here, we suppose \(t_{inv}\) also consumes 21.6 mJ. So, the computational energy consumption of HSC-I, MHSC, HMOSC-I, HOOSC, HSC-II, and HMOSC-II schemes are \(2n\times 45.6+(2n+3n)\times 21.6+6n\times 19.44=315.84n\) mJ, \((n+2)\times 45.6+2n\times 21.6+7n\times 19.44=224.88n\) + 91.2 mJ, \((2n+2)\times 45.6+6n\times 19.44=207.84n+91.2\) mJ, \(2n\times 45.6+(2n+4n)\times 21.6+7n\times 19.44=356.88n\) mJ, \(2n\times 45.6+(2n+3n)\times 21.6+6n\times 19.44=315.84n\) mJ, and \((2n+2)\times 45.6+6n\times 19.44=207.84n+91.2\) mJ, respectively. For the communication energy consumption, as in [24], a sensor consumes 0.052 mJ and 0.019 mJ to transmit and receive a 1-byte message (namely the total energy consumption of communicating a one-byte message is 0.071 mJ). Combined with the ciphertext length in Table 1 and the common assumptions that \(|G_{1}|=160\) bits and \(|m|=160\) bits, which can be reduced to  
Figure 6: Comparisons of total energy consumption (IBC\(\rightarrow\)PKI). 20 bytes, the communication energy consumption of HSC-I, MHSC, OMHSC-I, HOOSC, HSC-II, and MOHSC-II schemes are \((20+2\times 20)\times 0.071\times n=4.26n\) mJ, \(20\times 0.071\times n+(n+1)\times 20\times 0.071=2.84n+1.42\) mJ, \(20\times 0.071\times n+(n+1)\times 20\times 0.071=2.84n+1.42\) mJ, \((20+3\times 20)\times 0.071\times n=5.68n\) mJ, \((20+2\times 20)\times 0.071\times n=4.26n\) mJ, and \(20\times 0.071\times n+(n+1)\times 20\times 0.071=2.84n+1.42\) mJ, respectively. In a word, the total energy consumption of HSC-I, MHSC, MOHSC-I, HOOSC, HSC-II, and MOHSC-II schemes are \(315.84n+4.26n=320.1n\) mJ, \(224.88n+91.2+2.84n+1.42=227.72n+92.62\) mJ, \(207.84n+91.2+2.84n+1.42=210.68n+92.62\) mJ, \(356.88n+5.68n=362.56n\) mJ, \(315.84n+4.26n=320.1n\), and \(207.84n+91.2+2.84n+1.42=210.68n+92.62\) mJ, respectively. The comparisons of total energy consumption are shown in Figures 5 and 6. As can be seen from the Tables 1-3 and Figures 3-6, our schemes have the minimum aggregate ciphertext length, total computation costs, and total energy consumption among these schemes. It is very viable and sound for the practical application of VANETs.