# An ECC-Based Anonymous and Fast Handover Authentication Protocol for Internet of Vehicles
## 5 Security Analysis  
In this section, we show that our protocol satisfies the security requirements mentioned in Section 3. 1. Untraceability: In the process of authentication, the protocol proposed in this paper changes the parameters of each authentication randomly and contains dynamic timestamps. The adversary cannot effectively link related vehicles based on some random numbers. Therefore, this protocol is untraceable. 2. Anonymity of vehicle identity: When a vehicle attempts to communicate with an RSU or other vehicles, it will use a temporary pseudonym \(PID_{i}=ID_{V_{i}}\oplus h(r_{1}\cdot D_{r})\) instead of its real identity to transmit on a public channel. Without the master private key of the TA or RSU, the attacker cannot obtain the real identity of the vehicle. Only the TA or RSU can reveal the real information of the vehicle. The vehicle can update \(PID_{i}\) autonomously every time it communicates (rather than being generated by a trusted third party like other protocols). 3. Perfect forward secrecy: Even if an adversary intercepts messages such as \(R_{1}\) and \(R_{2}\), deriving the session key (SK) remains infeasible. This is because SK is computed using a secret random value generated by the client. Recovering the SK from the intercepted data would require solving the elliptic curve discrete logarithm problem (ECDLP), which is widely regarded as computationally intractable. As a result, the protocol \begin{table}
\begin{tabular}{c c} \hline \(V_{i}\) & \(TA\) \\ \hline Randomly choose \(r_{i}\) & \\ Compute \(R_{i}=r_{i}\cdot P\) & \\ \(V_{i}=PID_{i}\oplus h(T_{3}||R_{i}||C)\) & \\ send \(\{PID_{i},V_{i},R_{i},T_{3}\}\) & \\ \hline \end{tabular} Check \(|T_{3}-T_{c}|<\Delta T\) & \\ Retrieve \(\{C,ID_{i}\}\) & \\ Verify \(TTL\stackrel{{?}}{{>}}0\) & \\ Check \(V_{i}\stackrel{{?}}{{=}}PID_{i}\oplus h(T_{3}||R_{i}||C)\) & \\ Randomly choose \(r_{j}\) & \\ Compute \(R=r_{j}\cdot R_{i},R_{j}=r_{j}\cdot P\) & \\ \(PID_{i}^{+}=h(d_{RSU_{j}}||ID_{V_{i}}||C||T_{4})\) & \\ \(H_{2}=PID_{i}^{+}\oplus h(C||T_{4})\) & \\ \(V_{j}=h(H_{2}||ID_{V_{i}}||C||R_{j})\) & \\ Generate \(SK_{ij}=h(R||C)\) & \\ Update \(PID_{i}^{+},TTL-1\) & \\ send \(\{ID_{RSU_{j}},V_{2},H_{2},R_{j},T_{4}\}\) & \\ \(\longleftarrow\) & \\ Check \(|T_{4}-T_{c}|<\Delta T\) & \\ Verify \(V_{j}\stackrel{{?}}{{=}}h(H_{2}||ID_{V_{i}}||C||R_{j})\) & \\ Compute \(R=r_{i}\cdot R_{j}\) & \\ Generate \(SK_{ij}=h(R||C)\) & \\ Update \(PID_{i}^{+}=H_{2}\oplus h(C||T_{4})\) & \\ \hline \end{tabular}
\end{table} 
Table 6: The handover authentication between vehicles and \(RSUs\) and the generation of cryptographic keys. achieves perfect forward secrecy, ensuring that past session keys remain secure even if long-term private keys are compromised. * Resistance to DDoS attacks: The system architecture employs multiple registration servers, which improves fault tolerance and enhances overall availability. Due to the protocol's low transmission and processing overhead, the system remains responsive even when subjected to a high volume of incoming requests. This design allows it to effectively absorb and mitigate the impact of distributed denial-of-service (DDoS) attacks, ensuring continued service for legitimate users. * Resistance to replay attacks: The protocol prevents adversaries from reusing previously intercepted messages to gain unauthorized access. Each message carries a timestamp T, allowing the server to verify its timeliness. Messages with outdated or invalid timestamps are recognized as replays and are subsequently rejected, thereby mitigating the risk of replay attacks. * Resistance to man-in-the-middle attacks: As mentioned above, this protocol can prevent \(V_{i}\)'s identity \(ID_{i}\), random number \(r_{i}\), and secret parameter \(C\) from being recovered by malicious opponents. And this protocol is based on the mutual authentication feature and can resist man-in-the-middle attacks.