# Satellite Network Security Routing Technology Based on Deep Learning and Trust Management
## 3 Problem Modeling
### Safe Ant Colony Algorithm  
In the process of using the traditional ant colony algorithm to find the way, the satellite network does not consider security, and its initialization process is not efficient, so it is prone to stagnation. Therefore, the formula for selecting the next hop node can be modified to improve the efficiency of the ant colony algorithm. First of all, when the satellite node starts to initialize the routing table, we do not forward the ant packet with random probability, because according to the predictability of the topology of the satellite network, the distance and direction of the current target satellite and the source satellite can be calculated in advance. The distance and direction between the target node and the source node can be calculated in advance to select the nearest neighbor node to forward the packet, which can reduce the initial pathfinding time of satellite network nodes and improve the overall efficiency of the system. In the routing process of the ant colony algorithm, the formula of finding the next hop node is modified in this paper, so that the ant colony algorithm not only considers the influence of pheromone but also the security of the next hop node in the routing process. The following formula is improved:  
\[P_{ij}^{k}=\frac{\tau_{ij}{}^{a}w_{ij}^{\beta}}{\sum\limits_{j\in M}\tau_{ij} \alpha^{*}w_{ij}^{\beta}} \tag{15}\]  
\[P_{ij}^{k}=\frac{(\tau_{ij}\cdot m_{ij})^{A}\cdot w_{ij}^{\beta}}{\sum\limits_ {j\in M}(\tau_{ij}\cdot m_{ij})^{A}\cdot w_{ij}^{\beta}} \tag{16}\]  
where \(P_{ij}^{k}\) represents the probability of the ant \(k\) moving from node \(i\) to node \(j\), indicating that the current ant is at node \(i\). \(M\) represents the set of nodes that the kth ant has not yet visited. \(\tau_{ij}\) represents the concentration of pheromones on path \(ij\). \(w_{ij}\) represents the heuristic factor of the ant colony algorithm on path \(ij\). \(\alpha\) and \(\beta\) are two predefined parameters used to weigh pheromones and visibility, respectively. \(w_{ij}\) is calculated as follows:  
\[w_{ij}=\frac{1}{d_{ij}} \tag{17}\]  
where \(d_{ij}\) indicates the distance from node \(i\) to \(j\). The original ant pathfinding Formula (15) only considers the pheromone concentration and the visibility between nodes in the pathfinding process, where the visibility between nodes can be recorded in the form of a matrix at the beginning. The revised Formula(16) combines the security assessment factor \(m_{ij}\) stored in the node \(i\) with its pheromone. Specifically, this paper adopts a distributed trust management model, so the node \(i\) only records the security evaluation factors of neighboring nodes and does not obtain the security evaluation factors of other nodes across the neighbors. When the ant is pathfinding, the node where the ant is located has stored the security assessment factor of the neighboring nodes for a period of time, and the ant can comprehensively consider the probability of the next hop according to the pheromone concentration, security assessment factor, and visibility of node \(i\) and node \(j\). If visibility is low or the product of the safety assessment factor and pheromone goes to zero, the ant abandons the path and tries to find a more efficient and safer path. To avoid the ant colony algorithm falling into local optimal without exploring new routes, the random probability \(q\) is set to compare with the fixed threshold \(r\). If this \(q>r\), then we randomly read the security information of the next jump node. We choose a neighbor node; if \(q\leq r\), we still choose the way according to the above formula. \[p_{ij}^{k}=\left\{ \begin{array}{ll}\text{Uniform probability}&\text{if }q>r\\ \frac{(\tau_{ij}\cdot m_{ij})^{A}\cdot w_{ij}^{B}}{\sum\limits_{j\in M}{(\tau _{ij}\cdot m_{ij})^{A}\cdot w_{ij}^{B}}}&\text{if }q\leq r\end{array} \right.