# A Hybrid Trust Model against Insider Packet Drop Attacks in Wireless Sensor Networks
## 5 Performance Evaluation
### Simulation Results
#### Detection accuracy  
In addition to early detection capability, a good trust model must have high detection accuracy, which can be evaluated by using _DR_ and _FAR_. Thus, a desirable trust model has a high \(DR\) and a low _FAR_. A comparison of the detection accuracy of the beta trust model and our hybrid trust model is as follows. First, our hybrid trust model can detect an inside packet drop attacker not only more quickly, but also more accurately than the beta trust model. We already demonstrated that our hybrid trust model can detect the attacker much faster than the beta trust model in (_I_) _detection speed and the damage to the network_. Figure 8 shows how \(DR\)s of the beta GRP and our hybrid GRP change as the simulation time proceeds when _TH_ is 0.7. In this figure, the value of \((1-DR)\) at time \(t\) indicates the percentage of victim nodes that cannot detect the attacker. That is, the difference between \(DR\)s of the two trust models shows the difference in the detection accuracy of the two trust models. The \(DR\) of our hybrid trust model is always above that of the beta trust model, which means that victim nodes within our hybrid trust model always detect the attacker faster and more accurately. Figure 7: The number of packets dropped due to attacks N\({}_{\text{A}}\) (TH = 0.7). (**a**) Attack rate = 100%. (**b**) Attack rate = 60%. (**c**) Attack rate = 30%. In particular, the beta trust model cannot completely detect the attacker when the attack rate is set to be equal to or less than 100 \(\times\) (1 \(-\)\(T\)H). Meanwhile, our hybrid trust model can detect the attacker whose attack rate is 100 \(\times\) (1 \(-\)\(T\)H). For example, in Figure 8c, when the attack rate is 30% and _TH_ is 0.7, more than 80% of victim nodes with the beta trust model fail to detect the attacker within the maximum simulation time (three hours). Meanwhile, all victim nodes with our hybrid trust model detected the attacker in the early stage. This is due to the limitation of the design of the beta trust model. That is, in the beta trust model, if an attacker continues to randomly drop 30% of received packets, its trust value \(T\) gradually lowers to 0.7 according to Equation (1). In practice, it is assumed that the attacker is likely to start dropping packets after it has a high trust value [31] to avoid being detected by a trust model. For this reason, the attacker's trust value rarely falls below 0.7, and thus the beta trust model with _TH_ = 0.7 fails to detect it. On the other hand, our hybrid trust model significantly penalizes the attacker's repeating consecutive drops, and thus can detect the attacker with the same trust threshold. However, when the attack rate is less than 100 \(\times\) (1 \(-\)\(T\)H), both the beta trust model and our hybrid trust model failed to detect the attacker. When the attacker knows the trust threshold, they can estimate its trust value before dropping any packet to make sure that they will never be caught. Although our hybrid trust model cannot defend against such an attacker, the damage that the attacker can cause to the network is limited according to the _TH_. For example, when the _TH_ is 0.7, the attacker cannot drop more than 30% of packets without being caught. It will be interesting (and challenging) to study this problem, for example from the point of view of game theory [38; 39]. However, since a detailed discussion to address this problem is out of the scope of this paper, we leave this for future work. Second, our hybrid trust model generates a small _FAR_ that is slightly higher than that of the beta trust model. A high _FAR_ must be avoided, because it may negatively affect network connectivity, decrease the number of available relay nodes in the network, and thus significantly degrade the packet delivery performance of a routing. As shown in Table 4, we see that both our hybrid GRP and beta GRP do not have high _FAR_.