# Public Key-Based Authentication and En-Route Filtering Scheme in Wireless Sensor Networks
## 6 Performance Evaluation
### Resilience to Selective Forwarding Attacks  
The authors compare the performance of PDF, DSEDA, and PKAEF in terms of resilience to selective forwarding attacks. Additionally, to compare the proposed report forwarding protocol and multi-path routing protocol, the authors also simulated PKAEF adopting a 2-path routing protocol, denoted as PKAEF_2 MP. During each experiment, _fn_ forwarding nodes around an event area were compromised randomly. When a forwarding node was compromised, it would drop each report that passed by it, with the probability of _ps_. The authors evaluate the resilience to selective forwarding attacks based on data availability, which is measured as the proportion of available reports (the proportion of normal reports that can reach the BS). The proportion of available reports is affected by _fn_ and _ps_. The larger the _fn_ is, the lower the proportion of available reports is. The larger the _ps_ is, the lower the proportion of available reports is. Figure 6a,b shows the proportions of available reports affected by the number of compromised forwarding nodes in Scenario 1 and Scenario 2, respectively. During the experiments, _fn_ varied from 1 to 20 in Scenario 1, and from 1 to 40 in Scenario 2. The probability _ps_ was set to 0.3 and 0.6 in Scenario 1 and Scenario 2, respectively. Shown in Figure 6, the proportions of available reports of PDF, DSEDA, PKAEF_2 MP, and PKAEF decrease as _fn_ increases. The proportions of available reports of PDF and DSEDA are almost the same, both lower than those of PKAEF_2 MP and PKAEF, as they do not provide any strategy to resist selective forwarding attacks. The proportion of available reports of PKAEF_2 MP is higher than those of PDF and DSEDA, but lower than that of PKAEF. Figure 5: Proportion of correct reports as a function of the number of compromised cluster nodes. (**a**) in Scenario 1; (**b**) in Scenario 2. Figure 6: Proportion of available reports as a function of the number of compromised forwarding nodes. (**a**) in Scenario 1; (**b**) in Scenario 2. Figure 7a,b shows the results of the proportion of available reports when _ps_ varied from 0.05 to 1.0 in Scenario 1 and Scenario 2, respectively. During the experiments, the number of compromised forwarding nodes was set to 30% and 60% of the total number of forwarding nodes in Scenario 1 and Scenario 2, respectively--_fn_ = 6 in Scenario 1 and _fn_ = 24 in Scenario 2. It can be observed that the proportions of available reports of PDF, DSEDA, PKAEF_2 MP, and PKAEF decrease as _ps_ increases. The proportions of available reports of PDF and DSEDA are almost the same, both lower than those of PKAEF_2 MP and PKAEF, and PKAEF has the highest proportion of available reports. Therefore, PKAEF is more resilient to selective forwarding attacks than PDF and DSEDA, and this study's report forwarding protocol is superior to the 2-path routing protocol. Considering the report forwarding protocol of PKAEF, once the sender finds that the selected forwarding node does not forward the report, it will select another trusted upstream node with the highest trust value to forward the report, rather than randomly selecting an upstream node to forward the report. To compare the performance of the two methods: randomly selecting forwarding nodes and selecting forwarding nodes based on trust values, the authors performed simulation experiments for PKAEF by using these two methods respectively. PKAEF is denoted as PKAEF_TV when the forwarding nodes are selected based on trust values and denote PKAEF as PKAEF_NTV when the forwarding nodes are randomly selected. Three groups of experiments were carried out based on the value of _ps_, where the values of _ps_ were set to 0.2, 0.6, and 1.0 respectively. Each group of experiments was run 1000 times and, in each run, 50 reports in an event area were sent to the BS by different cluster heads. The authors evaluate the performance of PKAEF_TV and PKAEF_NTV according to the average energy expenditure of forwarding a report at each hop.