## 3 Proposed Scheme: RSP-Based Message Authentication for VANET
### 3.9 Broadcasting of Seed Value from TA to All RSUs  
In every time slot, TA must broadcast a seed value to all RSUs to generate a new secret pool. Based on the same secret pool, all of new registration set requested in the same time slot will have the same properties of random secret pre-distribution. However, when an RSU is found to be performing a malicious attack, its right to respond to a new registration request in the following time slots must be suspended. To revoke the right of a malicious RSU to respond, the secret index of the malicious RSU is appended to the set of revoking secret indexes (\(DS_{vk}\)), and \(DS_{br}\) is made the set of secret indexes for broadcasting the new seed value. \(DS_{br}\) will be used by the TA to broadcast the seed value, as follows.  
TA receives \(DS_{vk}\) and sets \(DS_{br}\) as an empty set.  
S1. For all valid RSUs, R\({}_{i}\),  
TA selects any one new secret index in \(DS_{RI}\), but not in \(DS_{vk}\) and \(DS_{br}\); this new secret index is added to \(DS_{br}\).  
S2. TA sets \(FI(x)\)=\(k1+\prod(x-d_{i})\) and \(F2(x)=k2+\prod(x-(SP_{TA}(d_{i})P)^{x})\), for all di in \(DS_{br}\).  
Now, TA can use \(DS_{br}\), \(F_{1}(x)\) and \(F2(x)\) to broadcast a new seed value, as follows.  
S3. TA\(\rightarrow\) all: \(ID_{TA},T_{t}\), \(n\), \(FI(x)\), \(HMACK1(ID_{TA}\parallel T_{t}\parallel n)\), \(F2(x)\), \(Ek2\)(new seed value)  
\begin{table}
\begin{tabular}{c c} \hline
**Real ID** & **Original Reg. Set** \\ \hline \(\vdots\) & \(\vdots\) \\ Real ID of vehicle i & \(\{ID_{TA},T_{0},IDS_{vi},DS_{vi}\,,PRS_{vi}\}\) \\ \(\vdots\) & \(\vdots\) \\ \hline \end{tabular}
\end{table}
Table 5.2: Recording table in RSU\({}_{a}\).  
\begin{table}
\begin{tabular}{c c} \hline
**Anonymous ID** & **New Reg. Set** \\ \hline \(\vdots\) & \(\vdots\) \\ \(\{ID_{Ra},T_{t-2},ID^{\prime}{}_{vi}\,,DS^{\prime}{}_{vi}\}\) & \(\{ID_{Rb},T_{t-1},IDS^{\prime}{}_{vi}\,,DS^{\prime}{}_{vi}\,,PRS^{\prime}{}_{vi}\}\) \\ \(\vdots\) & \(\vdots\) \\ \hline \end{tabular}
\end{table}
Table 5.3: Recording table in RSU\({}_{b}\).  
\begin{table}
\begin{tabular}{c c} \hline
**Anonymous ID** & **New Reg. Set** \\ \hline \(\{ID_{Ra},T_{t-2},ID^{\prime}{}_{vi}\,,DS^{\prime}{}_{vi}\}\) & \(\{ID_{Rb},T_{t-1},IDS^{\prime\prime}{}_{vi}\,,DS^{\prime\prime}{}_{vi}\,,PRS^{ \prime\prime}{}_{vi}\}\) \\ \(\vdots\) & \(\vdots\) \\ \hline \end{tabular}
\end{table}
Table 5.4: Recording table in RSU\({}_{c}\).  
\begin{table}
\begin{tabular}{c c} \hline
**Real ID** & **Original Reg. Set** \\ \hline \(\vdots\) & \(\vdots\) \\ Real ID of vehicle i & \(\{ID_{TA},T_{0},IDS_{vi}\,,DS_{vi}\,,PRS_{vi}\}\) \\ \(\vdots\) & \(\vdots\) \\ \hline \end{tabular}
\end{table}
Table 5.1: Recording table in TA.  
\begin{table}
\begin{tabular}{c c} \hline
**Anonymous ID** & **New Reg. Set** \\ \hline \(\{ID_{Ra},T_{t-2},ID^{\prime}{}_{vi}\,,DS^{\prime}{}_{vi}\}\) & \(\{ID_{Rb},T_{t-1},IDS^{\prime\prime}{}_{vi}\,,DS^{\prime\prime}{}_{vi}\,,PRS^{ \prime\prime}{}_{vi}\}\) \\ \(\vdots\) & \(\vdots\) \\ \hline \end{tabular}
\end{table}
Table 5.4: Recording table in RSU\({}_{c}\).  
S4. RSU(_Ra_) receives the broadcast message.  
Calculates \(K_{ly}=F_{l}(d_{Ra\gamma})\), \(d_{Ray}\in DS_{Ra}\), \(y=I\)\(\sim\)\(N_{R}\)  
Checks whether any \(K_{ly^{\prime}}\) exists such that \(HMAC_{Kly^{\prime}}\) (\(ID_{TA}\parallel T_{t}\parallel n\)) equals \(HMAC_{k1}(ID_{TA}\parallel T_{t}\parallel n)\).  
If \(K_{ly^{\prime}}\) is exist, takes \(d_{Ray}\)\({}^{\prime}\), that \(K_{ly^{\prime}}\) is equal to \(F_{l}(_{Ray^{\prime}}\)), calculate \(Kz^{\prime}=F_{2}\bigg{(}\bigg{(}\frac{PR_{Ray^{\prime}}}{H(ID_{TA}\parallel T _{0}\parallel ID_{Ray^{\prime}})}\bigg{)}^{x}\bigg{)}\) and decrypt \(E_{k}z^{\prime}(.)\) to retrieve the new seed value to generate a new secret pool in time slot \(T_{t}\).  
Because the secret indexes of malicious RSU are not included in \(DS_{br}\), even it quests the secret index in \(DS_{br}\), but it has not the respective private key, so it can not get the decrypted key \(kz^{\prime}\) to retrieve the new seed value.