# EAIA: An Efficient and Anonymous Identity-Authentication Scheme in 5G-V2V
## 6 Security Evaluation
### Security Analysis  
In this section, we will discuss and analyze the security properties of the main component of our proposed EIA protocol, which is the mutual authentication between vehicles.  
1. Mutual authentication: For two vehicles requiring mutual authentication, \(OBU_{i}\) encrypts its identity using \(OBU_{i}\)'s public key, ensuring that only \(OBU_{j}\) can extract \(OBU_{i}\)'s identity. To validate the signature and verify the validity of \(OBU_{i}\), \(OBU_{j}\) uses its private key to compute \(M^{\prime}\). Only the target vehicle \(OBU_{j}\) can obtain the correct identity and random number \(A\) of \(OBU_{i}\) and verify \(OBU_{i}\)'s identity. Therefore, \(OBU_{i}\) can also validate the validity of \(OBU_{j}\).
2. Secure session key agreement: The integrity and confidentiality of the session key are ensured by the principles of ECCDH. If an adversary could forge a session key between vehicles, it would imply that the adversary could solve the computational Diffie-Hellman problem, which is known to be difficult, as discussed in Section 3.2.
3. Anonymity and privacy protection: In the proposed protocol, real identities are anonymized by generating pseudonyms, which are then obscured by hash functions. During the authentication process, the messages \(\{B,N,\sigma,T_{a}\}\) and \(\{D,\eta,T_{b}\}\) do not directly transmit identities. Instead, identities are linked with random numbers, preventing the sender's identity from being disclosed. Thus, the proposed protocol satisfies user anonymity and privacy protection requirements.
4. Resistance to man-in-the-middle attacks: During authentication, authenticated OBUs can verify the requesting OBU by generating its signature \(\sigma\) using the requesting vehicle's private key \((x_{i}+y_{i})\). Without this private key, the authenticated vehicle cannot extract the identity of the requesting vehicle. If an adversary attempts a man-in-the-middle attack, they must possess \((x_{i}+y_{i})\) to complete identity authentication and key exchange. However, \((x_{i}+y_{i})\) remains unknown to any adversary.
5. Resistance to impersonation attacks: To successfully impersonate a vehicle, an attacker needs to know the private key \((x_{i}+y_{i})\) of the requesting OBU to generate a legitimate signature \(\sigma\). Since the attacker cannot obtain the private key \((x_{i}+y_{i})\) of the requesting vehicle, they cannot generate a valid signature, thus preventing impersonation.
6. Resistance to Replay Attacks: in the proposed protocol, timestamps \(T_{a}\) and \(T_{b}\) ensure that session keys cannot be reused by adversaries to disrupt the mutual authentication process.
7. Perfect forward secrecy: Forward secrecy ensures that even if participants' long-term private keys and previous session keys are compromised, the current session key remains secure. In the proposed protocol, if the private keys \((x_{i}+y_{i})\) and \(\big{(}x_{j}+y_{j}\big{)}\) of two participants are leaked, adversaries still cannot access the session key without knowing the temporary keys. Assuming the current session keys are \(SK_{j-i}=h_{3}\big{(}ID_{i}^{\prime}||ID_{j}||d(kA^{\prime}+X_{i})\big{)}\) and \(SK_{i-j}=h_{3}\big{(}ID_{i}\big{|}||ID_{j}\big{|}||D(ka+X_{i})\big{)}\), adversaries might access \(ID_{i}\) and \(ID_{j}\). For \(d(kA^{\prime}+X_{i})\), it should be computed as \(d(ka+x_{i})P\), where \(k=h_{1}(ID_{i}||ID_{j}\mid A\mid\mid D\mid T_{b})\). However adversaries do not have access to the temporary keys d or a involved in generating the session key. Therefore, our protocol meets the requirements for forward secrecy.
8. Resistance to Random Number Leakage: during the authentication process, even if the random numbers \(a\), \(b\), and \(d\) are leaked, adversaries cannot generate the correct session key because the secret keys of the vehicles are used as part of the session key.