## 5 Conclusions and Future Work  
This paper proposed the concept of the RSP for constructing a message authentication scheme for use in VANETs. In the proposed scheme, all RSUs and vehicles must register with the TA to receive the original registration set (ORG). At any time, all RSUs have a common secret pool that is generated by a PRNG with a common seed value that is sent by the TA in every time slot. The RSUs act as issuers that can assign a sub-set of secrets to any vehicles that have been authenticated with their ORG or NRG, which were obtained in the previous time slot. For every T1, or whenever vehicles enter the VANET for the first time, vehicles request the new registration set (NRG) with the information in ORG. In other time slots, the vehicles can obtain the new registration set with the information in NRG to generate a new NRG. In the proposed scheme, vehicles randomly choose one of their IDs in NRG and the set of secret index to announce their presence periodically. Using the ID and secret index set,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**FunctionsScheme** & **DCS [7]** & **PASS [8]** & **CH-IBC [9]** & **BDH [11]** & **Proposed Scheme** \\ \hline
**Anonymity** & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline
**Conditional un-traceability** & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline
**Authentication in sparse** & \(\times\) & \(\times\) & \(\surd\) & \(\times\) & \(\surd\) \\
**RSU environment** & & & & & \\ \hline
**Does not need certification** & \(\times\) & \(\times\) & \(\surd\) & \(\times\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of functionality.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PhaseMethod** & **DCS [7]** & **PASS [8]** & **CH-IBC [9]** & **BDH [11]** & **Proposed Scheme** \\ \hline
**Signing** & \(2\)\(T_{m}\) & \(1\)\(T_{m}\) & \(2\)\(T_{e}\) & \(2\)\(T_{m}\) & _HMAC_ \\ \hline
**Verification** & \(5\)\(T_{P}+3\)\(T_{m}\) & \(3\)\(T_{p}+4\)\(T_{m}\) & \(2\)\(T_{e}\) & \(T_{P}+T_{m}\) & _HMAC_ \\ \hline
**Total Number of** & \(5\)\(T_{P}+5\)\(T_{m}\) & \(3\)\(T_{P}+5\)\(T_{m}\) & \(4\)\(T_{e}\) & \(T_{P}+3\)\(T_{m}\) & _2 HMAC_ \\ \hline
**Required Time** & \(25.5\) ms & \(16.5\) ms & \(2.16\) ms & \(6.3\) ms & \(0.004\) ms \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of schemes in terms of number of computations and time required.  
neighboring vehicles can compute the mutual pairing value or find vehicles that can help them with message authentication.  
In message authentication, a polynomial function is formed by the pairing values and the _HMAC_ key. The _HMAC_ of the message with the key will be attached to the broadcast message. Vehicles that receive a broadcast message use their pairing value to retrieve the _HMAC_ key and to authenticate the message. Some vehicles are asked to rebroadcast the message for vehicles that do not have a common secret with the sender. The proposed scheme is very simple but satisfies all the requirements of a VANET, such as defense against masquerade, forgery and replay attacks, anonymity, un-traceability, message authentication, confidential communication, and a light revocation list. The only computation that is involved in signing and verification for message authentication is that associated with _HMAC_, so the proposed scheme outperforms previously proposed schemes.  
In message authentication, the index-set of a secret sub-set must be broadcast, potentially leaking information of the secret pool, so future work should seek to hide the index set while ensuring that the load associated with message authentication is light.