## 3 Proposed Trust-CH Framework
### Trust-Based Calculation  
This trust-table is passed to all WSN nodes associated with the CH as well as to other CHs, which in turn pass it on to the rest of the WSN nodes. Updates to those tables are sent in encrypted form to the rest of the nodes, as will be explained later. In this process, we ensure that active and trusted WSN nodes are not subject to trust calculations more than once, which in turn contributes to energy savings. However, if any new WSN node joins the existing set of WSN nodes, then a computation for that WSN node is carried out using a set of criteria. These criteria are discussed in detail as follows:  
1. Packet of Transmission Behavior  
When two WSN nodes are within one hop distance, the direct trust of \(x^{i}\) is calculated by \(x^{j}\) at time \(t\). Each cyclic trust evaluation round includes WSN node \(x^{i}\) observing WSN node \(x^{i}\) directly. Since aggressive users are primarily concerned with packet loss and fake acknowledgment, the packet of transmission behavior (TB) parameter allows for accurate estimation of the WSN node through \(x\)_-rate_ estimation [40]. \[TB\Big{(}x^{i}(t)\Big{)}=(PF(x^{i,j})\times w_{1})+(AF(x^{i,j})\times w_{2}) \tag{1}\]  
where \(PF\big{(}x^{i,j}\big{)}\) denotes the successful packet forwarding ratio \(x^{i}\) by \(x^{j}\), \(AF(x^{i})\) denotes the availability factor of \(x^{i}\) by \(x^{j}\), \(x^{j}\), \(w_{1}\) and \(w_{2}\) donate the weight parameters some of them is 1. Weight parameters represent the Trust-coefficient between the nodes. The \(PF\) is calculated as shown in Equation (2) [40]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Description** \\ \hline \(x^{i}\) & Node number \(i\) \\ \(x^{j}\) & Node number \(j\) \\ \(t\) & Time \\ \(w\) & The weight of the node \\ \(\lambda\) & Constant values \\ \(b\) & Block size \\ \(P_{TX}\) & The power consumed when the node sends the message \\ \(q\) & Message length \\ \(d\) & The distance \\ \(P_{TX-amp}\) & The node transmitter circuit consumption based on signal amplification \\ \(\beta_{8m}\) & Free space model \\ \(\beta_{trm}\) & Two-ray grounded propagation models \\ \(P_{RX}\) & The power consumed when the node receives the message \\ \(P_{RX-dcc}\) & The power dissipated by the receiving node in the reception of \(q\) \\ \(Th(n)\) & The power threshold of a node \\ \(N_{adj}\) & The number of neighboring nodes \\ \(P_{elec}\) & Power expanded by transmitter and receiver \\ \(\sigma\) & The average of interactive factors \\ \(n\) & Total number of nodes \\ \(Tn\) & Candidate node \\ \(\partial(Tn)\) & Average distance \\ \(\omega\) & The average weights \\ \(a\) & The number of adjacent nodes \\ \(P_{r}\) & Residual energy \\ \(\partial\) & The average distances between the candidate node (Trusted node) and the \\  & existing CH nodes \\ \(c\) & Minimum number of host nodes \\ \(d_{Th}\) & Distance between CH nodes and the host nodes \\ \(m\) & Total number of CHs operating at time (\(t\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations and their description. \[PF\Big{(}x^{i,j}(t)\Big{)}=\frac{f(x^{i,j}(t))-f(x^{i,j}(t-1))}{f(x^{i,j}(t))+f(x^{ i,j}(t-1))} \tag{2}\]  
where, \(f(x^{i,j}(t))\) is the number of successful packets sent by \(x^{i}\) at time \(t\). This parameter effectively protects the network from cyber threats and identifies the malicious behavior of WSN nodes in the network by calculating \(x^{i}\) ACK packets. For further explanation, suppose that node \(x^{i}\) forwards data packets from another node and broadcasts 4 ACK packets. During this time, the node \(x^{i}\) collects such ACK packets of node \(x^{i}\) to estimate the number of sensing packets. Calculated data transmission packet rate in time \(t\) is illustrated in Equation (2). In addition, the AF is also used to identify malicious nodes by calculating the Hello messages sent. The \"Hello\" packet is transmitted by \(x^{i}\) to check whether \(x^{i}\) is available to receive this packet.