# Distributed Reputation for Accurate Vehicle Misbehavior Reporting (DRAMBR)
## 5 DRAMBR Technical Implementation
### DRAMBR: Offline Evaluation  
We assume that the system consists of \(N\) vehicles \(\{V_{1},V_{2},\ldots,V_{N}\}\), where each vehicle communicates with others within the network. Let \(V_{j}\) be the \(\mathit{Tar_{\mathrm{Veh}}}\) observed by the \(\mathit{Rep_{\mathrm{Veh}}}\)\(V_{i}\). \(V_{i}\) evaluates multiple messages, each containing an _Action-ID_, which uniquely identifies  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Definition** \\ \hline \(\mathit{Rep_{\mathrm{Veh}}}\) & Reporting vehicle. \\ \hline \(\mathit{Tar_{\mathrm{Veh}}}\) & Target vehicle. \\ \hline MR & Misbehavior report. \\ \hline \(\mathit{MR_{f}}\) & False misbehavior report. \\ \hline \(\tau_{Rep}\) & RV threshold. \\ \hline \(\mathit{RV_{V_{i}}}\) & RV for vehicle (i). \\ \hline \(\mathit{RV_{V_{i}}}(t)\) & RV at a specific time. \\ \hline \(\mathit{pc}\) & Pseudonym certificate. \\ \hline \(\mathit{Msg}\) & Received message in OE. \\ \hline \(I_{\mathrm{Inc}}\) & Incident ID. \\ \hline \(S_{I_{\mathrm{Inc},k}}\) & DBSCAN majority-reported status. \\ \hline \(C_{i}\) & Confidence scores of \(\mathit{Rep_{\mathrm{Veh}}}\) within the cluster in DBSCAN. \\ \hline \(G_{I_{\mathrm{Inc}}}\) & DBSCAN cluster. \\ \hline \(\tau_{if}\) & iForest anomaly score threshold. \\ \hline \(H(x)\) & iForest harmonic number measures the number of splits to isolate MR. \\ \hline \(c(n)\) & iForest path length normalization. \\ \hline \(RV_{Vi}^{\mathrm{new}}\) & The updated RV. \\ \hline \hline \end{tabular}
\end{table}
Table 7: DRAMBR Notations.  
actions (e.g., initiate, update, cancel) as per ETSI EN 302 637-3 V1.2.1 standards [17]. The system associates each incident with an _Incident-ID_ (\(I_{\text{inc}}\)) that aligns with the _Action-ID_ to ensure consistent tracking and grouping of related messages.  
Let \(RV_{V_{i}}\) represent the RV of vehicle \(i\), where \(i\in\{1,2,\dots,N\}\). The \(RV_{V_{i}}\) is a continuous variable defined in the range \([0,1]\). Thus, \(RV_{V_{i}}(t)=1\) implies that vehicle \(V_{i}\) is fully trusted at a specific time \(t\), and \(RV_{V_{i}}(t)=0\) indicates complete distrust. We set the RV threshold as \(\tau_{Rep}\). Each vehicle \(V_{i}\) makes an acceptance decision based on the RV:  
\[\text{Msg Acceptance Decision}=\begin{cases}\text{Accept }M_{sg}\text{ from}V_{j},&\text{if }RV_{V_{j}}(t)\geq\tau_{Rep}\\ \text{Ignore }M_{sg}\text{ from }V_{j},&\text{if }RV_{V_{j}}(t)<\tau_{Rep}\end{cases} \tag{1}\]  
After \(M_{sg}\) acceptance, if \(V_{i}\) identifies \(V_{j}\) as a misbehaving vehicle, the process of generating and encrypting a misbehavior report MR is as follows:  
1. Vehicle \(V_{i}\) generates a misbehavior report \(MR\) regarding \(V_{j}\).
2. The \(MR\) is symmetrically encrypted using a session key \(K_{s}\), producing the following ciphertext: \[C=\text{Enc}_{K_{s}}(MR)\] (2)
3. The session key \(K_{s}\) is encrypted with the RS's public key \(K_{\text{pub}}^{S}\), resulting in \[K_{s}^{*}=\text{Enc}_{K_{\text{pub}}^{RS}}(K_{s})\] (3)
4. The ciphertext \(C\) is signed by \(V_{i}\) using its private key \(K_{\text{priv}}^{i}\), yielding the following digital signature: \[\sigma_{A}=\text{Sign}_{K_{\text{priv}}^{i}}(C)\] (4)