# Random Routing Algorithm for Enhancing the Cybersecurity of LEO Satellite Networks
## 4 Simulation Results and Discussion  
In this section, we show the simulation results and compare the performance of the proposed random routing algorithm with some of the most widely used routing algorithms (k-DG, k-DS, k-LO, and k-SP) as shown in [8]. The study has been performed in the LSN framework of ICARUS [8] that uses a simulation performed on the Starlink constellation consisting of 1584 satellites. The values of \(a_{1},a_{2}\), and \(a_{3}\) have been obtained after 50 iterations using the Bayesian optimization algorithm and the best values are found to be 0.377, 0.403, and 0.412, respectively. This algorithm is the one that proved to be the most efficient in increasing the cost while maintaining a good MaxUp. The probability mass functions (PMFs) of the four algorithm are shown in Table 1.  
In Figure 2, the histogram plot of the attackers' costs for the considered LSNs are shown. The frequency in the plot refers to the bin frequency. The cost is normalized with respect to the one ISL bandwidth that is 20 Gbps. The cost includes the feasibility of the attack on the downlinks and inter-satellite link of the LSN. As for the case of the uplink attacks, the compromised bots have to be in the coverage area of a given satellite and hence the MaxUp is very high, meaning the attacks will be easily detectable. We can observe that the proposed algorithm is able to increase the cost of the attacks so that the attacker has to deploy more scattered compromised bots probabilistically to lead to a successful attack. The average and median of the cost of attack is shown in Table 2. It is to be noted that the k-RAND provides the optimum median and average cost while maintaining a good functionality over the network. Compared to the k-SP, it provides an improvement of 1.71% in the average cost and 2.05% in the median cost. In the case of a dense LEO satellite communication network, such a percentage would matter as the DDoS attacks must be distributed over a larger area to be less detectable. Concentrating the attack in a certain area will be easily detectable as there will be significant traffic increase in that particular area. Probabilistically, the attacker also will have uncertainty in the choice of the particular routing algorithm used and this will, therefore, force them to utilize more network traffic. \begin{table}
\begin{tabular}{l l} \hline \hline
**Algorithm** & **PMF** \\ \hline k-SP & 0.377 \\ \hline k-DG & 0.026 \\ \hline k-DS & 0.009 \\ \hline k-LO & 0.588 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PMF of Algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Average** & **Median** \\ \hline k-SP & 0.9107 & 0.9480 \\ \hline k-DG & 0.9088 & 0.9665 \\ \hline k-DS & 0.9168 & 0.9635 \\ \hline k-LO & 0.9264 & 0.9665 \\ \hline k-RAND & 0.9262 & 0.9675 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cost statistics. Figure 3 shows the cumulative distribution function (CDF) of the cost of the attacks with the considered algorithms. The CDF denotes the empirical distribution function and is defined as:  
\[F_{n}(x)=\frac{1}{n}\sum_{i=1}^{n}\mathds{1}_{X_{i}\leq x} \tag{2}\]  
where \(X_{i}\) are the sample observations, \(n\) is the number of observations, and \(\mathds{1}\) denotes the indicator function. It is notable that the k-RAND algorithm provides the highest probability of exceeding a certain cost for the DDoS attack between the cost values from 0.82 to 0.96. Furthermore, it is notable that k-RAND provides optimum results compared to all the other algorithms. The probability that the attacker's cost exceeds the average values (shown in Table 2) is highest for the k-RAND algorithm. Thus, it can provide robustness against the DDoS attacks. Besides, it provides an additional layer of uncertainty to the attacker by the choice  
Figure 3: CDF of the attackers’ costs of launching DDoS Attack on an LEO satellite network. Figure 2: Histogram plot of the attackers’ costs of launching DDoS Attack on an LEO satellite network.