## 3 Key Technologies in Trust Management for WSNs
### Trust Evaluation Methods
#### 3.4.1 Direct Trust Evaluation  
_Threshold-limiting methods_  
In the models we reviewed, all evaluations of the packet-sending rate and some evaluations of the energy consumption rate used the threshold-limiting method. However, the methods for setting thresholds and calculations varied. One of the simplest methods, and the one used by most models, is to set an upper limit threshold value. Once the evaluated metric exceeds this upper limit, the node is considered untrustworthy. For example; in the trust-based technique for monitoring medical implants [7], the calculated trust value is binary, either 0 (untrustworthy) or 1 (trustworthy). The calculation method is shown in Equation (1)  
\[T=\begin{cases}0,\;\;D_{rate}\geq th\\ 1,\;\;D_{rate}<th\end{cases} \tag{1}\]  
where \(T\) represents the trust value, \(D_{rate}\) represents the data packet sending rate, and \(th\) represents the upper limit of the data packet sending rate. The threshold is set based on the patient's environment (home, workplace, public places) and the specific metrics of different implants (heart rate, body temperature, blood pressure, etc.).  
In EITMRM [4], the evaluation of the new flow-sending rate still uses an upper limit threshold. However, the trust value is not binary; instead, it decreases as the packet-sending rate increases. The calculation method is shown in Equation (2):  
\[PT_{ij}(t)=\frac{1}{\left|\frac{intl_{j}}{F_{\tau}}\right|} \tag{2}\]  
where \(F_{\tau}\) is the maximum number of new flows a node can receive from one of its neighbors during a period \(t\). It adapts to the actual network environment. \(intl_{j}\) is the number of new flows node \(j\) sends during period \(t\).  
In the TSW model [10], the upper limit threshold is divided into three levels, causing the trust value to decrease at different rates within different threshold intervals. The calculation method is shown in Equation (3):  
\[T_{x,y}^{Metric}=\begin{cases}1,\;\;N_{y}\leq\eta 1\\ 1-\frac{\eta 1-N_{y}}{2(\eta-\eta)},\;\eta 1<N_{y}\leq\eta\\ \frac{N_{y}-\eta 0}{2(\eta-\eta 0)},\;\;\eta<N_{y}\leq\eta 0\\ 0,\;\;\text{\emph{otherwise}}.\end{cases} \tag{3}\]  
where \(N_{y}\) represents the number of new flows send by node \(y\) and \(\eta\) represents the maximum number of expected data and packet-in messages from the sending node. The threshold points \(\eta 1\) and \(\eta 0\) are calculated as follows: \(\eta 1=\eta/2\) and \(\eta 0=\eta+\eta/4\).  
We set the upper limit threshold value of the above three calculation methods to 50 and plotted the function curves of the three algorithms for comparison, as shown in Figure 6.  
From the above figure, we can see that the methods corresponding to Equations (1) and (2) maintain a state of trust until the evaluated metric reaches the threshold. After exceeding the threshold, the method corresponding to Equation (1) sets the trust value directly to 0, while the method corresponding to Equation (2) decreases the trust value gradually in a stepwise manner. In contrast, the method corresponding to Equation (3) starts to decrease the trust value linearly as the evaluated metric approaches the threshold, and after exceeding the threshold, it decreases linearly at a faster rate until it reaches 0. Based on the comparison, the third method responds more promptly and sensitively to changes in trust metrics.