## 4 Algorithm Design of Improved Tree Attack Strategy
### Study in Attack Information Metric Index
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Identification** & **Name** & **Meaning** \\ \hline \multirow{2}{*}{\(\mathbf{A_{1}}\)} & \multirow{2}{*}{Physical node attack} & The physical destruction of the terminal node is performed by various means such as tearing, scratching, and high temperature. \\ \hline \multirow{2}{*}{\(\mathbf{A_{2}}\)} & \multirow{2}{*}{Transmission signal analysis} & Crack the encryption information by algorithm, and then analyze the information characteristics to determine the data type and effect. \\ \hline \multirow{2}{*}{\(\mathbf{A_{3}}\)} & \multirow{2}{*}{Signal interception and node reconstruction} & The node is reconstructed by tapping the communication data of the network node to acquire sensitive information in the channel. \\ \hline \multirow{2}{*}{\(\mathbf{A_{4}}\)} & \multirow{2}{*}{Communication interference} & Block all levels of nodes from receiving normal communication signals, resulting in a link interruption by using flooding attacks, wormhole attacks, etc. \\ \hline \multirow{2}{*}{\(\mathbf{A_{5}}\)} & \multirow{2}{*}{Network Protocol Attack} & Through pseudo-terminal technology, send random data that receiving nodes cannot identify, parse, and recover.It also sends malformed data causing a crash. \\ \hline \multirow{2}{*}{\(\mathbf{A_{6}}\)} & \multirow{2}{*}{Spurious data injection} & Send false information that completely complies with the communication mechanism and network protocol so that it can process and distribute false information. \\ \hline \multirow{2}{*}{\(\mathbf{A_{7}}\)} & \multirow{2}{*}{Wireless RF injection} & Send information of virus-carrying, Trojans, or other malicious programs that fully comply with the communication mechanism and network protocol, and inject it into the data processing system to infect hosts, industrial computers, etc. \\ \hline \multirow{2}{*}{\(\mathbf{A_{8}}\)} & \multirow{2}{*}{Data copying, tampering, and deletion} & Use the injected malicious code and software vulnerabilities to complete the copying, tampering, and deletion on the target database. \\ \hline \multirow{2}{*}{\(\mathbf{A_{9}}\)} & \multirow{2}{*}{Network paralysis} & Cause the entire network data to lose normal application pass rates by maliciously attacking/multiple pseudo-terminals. \\ \hline \multirow{2}{*}{\(\mathbf{A_{10}}\)} & \multirow{2}{*}{Illegal control} & Obtain root privileges of the system and achieve complete control of the system, including system operation, service provision, network management, etc. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Names and meanings of attacking node ways. \(r_{i}\) denotes the sequence number for the importance of the node \(v_{i}\); thus, under one sampling, the probability of the injection of the node is:  
\[\
abla_{i}=\frac{\pi_{i}}{\sum\limits_{t=1}^{N}\pi_{t}}=\frac{r_{i}^{-\delta}}{ \sum\limits_{t=1}^{N}r_{t}^{-\delta}} \tag{4}\]  
It can be inferred that the larger \(\delta\) is, the more likely that the important nodes are to be extracted, that is, the higher the accuracy of the node attack information. There exist two extreme situations, as follows:  
(1) When \(\delta=0\),  
\[\
abla_{i}=\frac{r_{i}^{-\delta}}{\sum\limits_{t=1}^{N}r_{t}^{-\delta}}=\frac {1}{N} \tag{5}\]  
In this condition, the probability that the node is to be extracted is the same, and the attack information is called random information. (2) When \(\delta=\infty\),  
\[\sum\limits_{i=1}^{N}r_{t}^{-\infty}=\sum\limits_{t=1}^{N}t^{-\infty}=1+\sum \limits_{t=2}^{N}t^{-\infty}=1 \tag{6}\]  
Assume that \(r_{i*}=1\)  
\[\
abla_{i}=\left\{ \begin{array}{ll}\frac{1}{\sum\limits_{t=1}^{N}r_{t}^{- \delta}}=1&i=i*\\ \frac{1}{\sum\limits_{t=1}^{N}r_{t}^{-\delta}}=0&i\
eq i*\\ \end{array} \right. \tag{7}\]  
In this condition, the most important node is always preferentially extracted, and this attack information is called priority information.