# Public Key-Based Authentication and En-Route Filtering Scheme in Wireless Sensor Networks
## 6 Performance Evaluation
### Performance of False Report Filtering  
The authors compare the performance of PDF, DSEDA, and PKAEF on the aspect of false report filtering. During each experiment, \(cn\) cluster nodes in the two event areas were compromised randomly and each of them injected a forged report into the network. Regarding DSEDA, if the CH was compromised, it was assumed that the other compromised cluster nodes also could obtain the private \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **In Scenario 1** & **In Scenario 2** \\ \hline Communication range \(R_{c}\) & 80 m & 80 m \\ Sensing range \(R_{s}\) & 40 m & 40 m \\ \(T\) in DSEDA & 5 & 6 \\ \(t\) & 4 & 5 \\ Power consumption of transmitting 1 byte & 16.25 uJ & 16.25 uJ \\ Power consumption of receiving 1 byte & 12.5 uJ & 12.5 uJ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. Figure 2: Energy expenditure for report generation. (**a**) in Scenario 1; (**b**) in Scenario 2.  
key of the CH, and then they could forge reports with correct signatures. Concerning PDF, a forwarding node verifies the signature of a report with the probability of \(p_{f}\). The authors simulated \(p_{f}=100\%\) and \(p_{f}=50\%\) for PDF, and PDF is denoted as PDF_100 and PDF_50, respectively. The lengths of a signed report message in PDF and PKAEF were 39 bytes in both Scenario 1 and Scenario 2, while the lengths of a signed report message in DSEDA were 72 bytes in Scenario 1 and 80 bytes in Scenario 2. The authors evaluate the performance of false report filtering based on two metrics: the en-route filtering probability (the percentage of dropped false reports by the forwarding nodes), and the filtering energy expenditure (the average energy expenditure for filtering out a false report since it is injected into the network until it is dropped). Figure 3a,b shows the results of the en-route filtering probability when \(cn\) varied from 1 to 20 in Scenario 1 and Scenario 2, respectively. The authors observe that when \(cn<t\), the en-route filtering probabilities of PDF_100 and PKAEF are 100%, which are higher than those of PDF_50 and DSEDA. This is because when \(cn<t\), the adversary cannot infer the private key in PDF_100, PDF_50, and PKAEF. The forged reports in PDF_100 and PKAEF will be filtered out at their 1-hop forwarding nodes, while the forged reports in PDF_50 can escape the verification of each forwarding node with a probability of 50%, some of which will reach the BS. Regarding DSEDA, a compromised node might be a CH, then the adversary can obtain its private key and the forged reports in that cluster will pass the verification of forwarding nodes and reach the BS. Therefore, the en-route filtering probability of DSEDA is lowest when \(cn<t\). When \(cn\geq t\), the en-route filtering probabilities of PDF_100 and PDF_50 are 0%, because the adversary can infer the system private key in PDF_100 and PDF_50, and thus can forge reports with correct signatures, all of which will reach the BS. The en-route filtering probabilities of DSEDA and PKAEF gradually decrease to 0% with the increase of \(cn\). When \(cn<6\) in Scenario 1 (\(cn<9\) in Scenario 2), PKAEF has a higher en-route filtering probability than DSEDA, otherwise DSEDA has higher en-route filtering probability. However, it should be noted that a random node capture was adopted in the experiments, which is very beneficial for DSEDA. Since the CHs in DSEDA are fixed, the adversary would prefer to capture the CHs rather than the non-CH nodes to obtain the private keys, in fact. Figure 4a,b shows the results of the filtering energy expenditure when \(cn\) varied from 1 to 20 in Scenario 1 and Scenario 2, respectively. It is observed that when \(cn<t\), PDF_100 and PKAEF have the same filtering energy expenditures and both outperform PDF_50 and DSEDA because the en-route filtering probabilities of PDF_100 and PKAEF are highest and the forged reports in PDF_100 and PKAEF are filtered out within one hop.