## 3 System Model
### Node Hidden Communication Model  
#### Correctness Analysis of Communication Model  
This paper introduces a model of node hidden communication, which consists of three kinds of nodes: source node composed of sender \(S\), destination node composed of receiver \(D\) and relay node (Relay node \(R_{(i,j)}(i=1,2,\cdots,m;j=1,2,\cdots,n)\)). The entry node of the forwarding network is the first row of forwarding relay nodes and the next hop of the source node, which is represented by \(R_{(i,j)}(i=1,2,\cdots,m;j=1,2,\cdots,n)\); the outlet node of forwarding network is the last relay node in its path and the last hop of destination node, which is represented by \(R_{(i,j)}(i=1,2,\cdots,m;j=n)\).  
In the data forwarding network based on network coding, assuming that there is no transmission error probability, all network coding information, local coding matrix and global coding vector existing in \(m\) paths can be transmitted to the destination node, through these information, the target node can correctly recover the information sent by the source node [14; 15].  
After \(n\) network coding, information fragmentation \(M_{i}\) can be transformed into information \(M_{i}{}^{(n)}\), the following is the specific transformation process:  
\[\begin{array}{ll}M_{i}{}^{(n)}&=C_{(i,n)}\oplus M_{i}{}^{(j-1)}=C_{(i,n-1)} \oplus M_{i}{}^{(j-2)}\\ &=C_{(i,n)}\oplus\left(C_{(i,n-1)}\oplus\left(C_{(i,n-2)}\oplus M_{i}{}^{(i-3) }\right)\right)\\ &=C_{(i,n)}\oplus\left(C_{(i,n-1)}\oplus\left(C_{(i,n-2)}\oplus\left(\cdots \left(C_{(i,0)}\oplus M_{i}\right)\right)\right)\right)\\ &=\underset{k=0}{\oplus}C_{(i)}\oplus M_{i}\end{array} \tag{14}\]  
The global coded vector ciphertext \({EV_{i}}^{(0)}\) is calculated by \(n\) times, and then the ciphertext \({EV_{i}}^{(n)}\) of the global encoding vector can be obtained:  
\[\begin{array}{ll}{EV_{i}}^{(n)}&=\underset{k=1}{\overset{n}{\sum}}C_{(k,n-1 )}^{k}{EV_{i}}^{(n-1)}\\ &=\underset{k=1}{\overset{n}{\sum}}C_{(k,n-1)}^{k}{\overset{n}{\sum}}\left( \underset{k=1}{\overset{n}{\sum}}C_{(k,n-2)}^{k}{\overset{k}{\sum}}\left( \underset{k=1}{\overset{n}{\sum}}\cdots\left(\underset{k=1}{\overset{n}{ \sum}}C_{(k,1)}^{k}{EV_{i}}^{(0)}\right)\right)\right)\\ &=\underset{k=1}{\overset{n}{\sum}}C_{(k,n-1)}^{k}{\overset{n}{\sum}}\left( \underset{k=1}{\overset{n}{\sum}}C_{(k,n-2)}^{k}{\overset{n}{\sum}}\cdots \left(\underset{k=1}{\overset{n}{\sum}}C_{(k,1)}^{k}{EC_{(1,0)}^{i}}^{i},{EC_{ (2,0)}^{i}},\cdots,{EC_{(m,0)}^{i}}\right)\right)\right)\\ &=\underset{k=0}{\overset{n-1}{\sum}}{EC_{(1,1)}^{i}}\underset{k=0}{\overset{ n-1}{\sum}}{EC_{(1,2)}^{i}},\cdots,\underset{k=0}{\overset{n-1}{\sum}}{EC_{(1,k)}^{i}} ^{i}\end{array} \tag{15}\]  
By decrypting the secret key, the target node can decrypt the global encoding vector's ciphertext \({EV_{i}}^{(n)}\), and get the global encoding vector \({V_{i}}^{(n)}\):  
\[\begin{array}{ll}{EV_{i}}^{(n)}&=\underset{k=1}{\overset{n}{\sum}}C_{(k,n- 1)}^{k}{EV_{i}}^{(n-1)}\\ &=\underset{k=1}{\overset{n}{\sum}}C_{(k,n-1)}^{k}{\overset{n}{\sum}}\left( \underset{k=1}{\overset{n  
In the forwarding network, the future self-organizing anonymity of cities and counties can generate the anonymity of the senders of cities and counties with multiple virtual source nodes through the use of pseudonym strategy; the anonymity of the receiver can be realized by broadcasting information from the exit node to the target node; the anonymity of communication relationship between them can be realized through anonymous relay and forwarding network, In each hop of the forwarding network, a group of nodes is included. Each group of nodes can only understand the specific information of the group nodes of the previous and next hop, and can communicate between the group nodes, thus realizing the anonymity of the communication relationship [16; 17]. Figure 1 shows the process of constructing forwarding network and the related anonymity strategy.