# An ECC-Based Anonymous and Fast Handover Authentication Protocol for Internet of Vehicles
## 6 Performance Analysis
### Communication Cost  
In this section, we analyze the communication overhead of our proposed scheme by combining the schemes of [PERSON] et al. [28], [PERSON] et al. [29], and [PERSON] et al. [30]. For the sake of comparison, this section assumes that \(|G|,|ID|,|h|,|Ts|\) are the length of the elliptic curve point, the length of the vehicle or server identity, the output length of the hash function, and the length of the timestamp, respectively. In the implementation, it is assumed that the elliptic curve point is 320 bits, the output length of the hash function is 256 bits, the length of the vehicle or server identity (including the real identity and the disguised identity) is 160 bits, and the length of the timestamp is 32 bits. In the protocol of [PERSON] et al. [29], in the initial authentication phase, two messages \(\{M_{0},M_{2},M_{3},M_{4},Y,T_{1}\}\) and \(\{Z_{2},M_{4},VERI_{SKij},T_{2}\}\) are transmitted between \(velk_{j}^{k}\) and \(rsu_{i}^{k}\), requiring \(|ID|+|G|+3|h|+|Ts|=1280\) bits and \(|G|+2|h|+|Ts|=864\) bits, respectively, so the total communication cost of sending these two messages is 2144 bits; in the handover authentication phase, four messages \(\{M_{00},M_{22},M_{33},M_{44},B,T_{3}\}\), \(\{R_{2},F,T_{5}\}\), \(\{H,R_{4},VERI_{SKii},T_{6}\}\) and \(\{Z_{22},M_{44},VERI_{SKii},T_{4}\}\) are exchanged among \(velk_{j}^{k}\),\(rsu_{m}^{k}\) and \(velk_{i}^{k}\), requiring \(|ID|+|G|+3|h|+|Ts|=1280\) bits, \(|G|+|h|+|Ts|=608\) bits, \(|G|+2|h|+|Ts|=864\) bits and \(|G|+2|h|+|Ts|=864\) bits, respectively, so the total communication cost of sending these four messages is 3616 bits. In summary, the total communication cost of this scheme is 5760 bits. In the protocol proposed by [PERSON] et al. [30], the initial authentication phase requires 512 bits in total, comprising \(|ID|+|G|+|Ts|\), while the handover authentication phase  
Figure 3: Comparison of the computational cost [28; 29; 30]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Protocols** & **Initial Authentication Phase (ms)** & **Handover Authentication Phase (ms)** \\ \hline
[28] & \(4T_{h}+4T_{bp}+6T_{ex}+3T_{mm}+2T_{mi}\) & 292.84 & \(2T_{h}+2T_{bp}+6T_{ex}+5T_{mm}\) & 204.46 \\
[29] & \(12T_{h}+6T_{m}\) & 211.92 & \(21T_{h}+12T_{m}\) & 211.92 \\
[30] & \(4T_{h}+2T_{m}+2T_{bp}+6T_{ex}\) & 253.78 & \(3T_{h}+2T_{m}+2T_{bp}+7T_{ex}\) & 253.78 \\ Ours & \(13T_{h}+16T_{m}\) & 277.76 & \(9T_{h}+4T_{m}\) & 71.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of computational costs of protocols. requires 1280 bits (\(4|G|\)). This results in an overall communication overhead of 1792 bits. However, the protocol does not support multi-domain authentication for vehicles, limiting its applicability in large-scale vehicular networks. Additionally, the messages \(HK_{1}\) and \(HK_{2}\) are transmitted over public channels without integrity verification at the receiving RSU, leaving the protocol unable to guarantee the confidentiality of public messages or the integrity of the handover process. Building on this, [PERSON] et al. [28] later introduced a protocol that incurs 1056 bits of overhead during initial authentication and 3072 bits during handover authentication, amounting to a total of 4128 bits. Despite the increased communication cost, this scheme does not offer mutual authentication and fails to address the risk of privileged insider attacks. In the protocol proposed in this paper, in the initial authentication phase, two messages \(\{PID_{i},R_{1},V_{v},T_{1}\}\) and \(\{ID_{RSU_{j}},R_{2},H_{1},V_{r},T_{2}\}\) are transmitted, requiring \(|ID|+2|G|+|Ts|=832\) bits and \(2|ID|+2|G|+|Ts|=992\) bits, respectively, so the total communication cost of sending these two messages is 1824 bits; in the handover authentication phase, two messages \(\{PID_{i},V_{i},R_{i},T_{3}\}\) and \(\{ID_{RSU_{j}},V_{j},H_{2},R_{j},T_{4}\}\) are exchanged, requiring \(2|ID|+|G|+|Ts|=672\) bits and \(2|ID|+|G|+|h|+|Ts|=928\) bits, so the total communication cost of sending these messages is 1600 bits.