# SatGuard: Satellite Networks Penetration Testing and Vulnerability Risk Assessment Methods
## 3 Satellite Networks Vulnerability Risk Assessment Method
### Satellite Networks Vulnerability Risk Assessment Formula
#### 3.1.1 Core Risk Factors  
Core risk factors constitute the foundational elements of vulnerability evaluation, reflecting intrinsic threat characteristics and immediate consequences.  
Impact (I): This parameter quantifies potential damage across strategic, operational, and economic dimensions, with scores ranging from 1 to 5 (\(I\in[1,5]\)).  
Likelihood (L): Likelihood evaluates the probability of successful exploitation based on historical data, exploit complexity, and attacker capabilities; assigned a score between 1 and 5 (\(L\in[1,5]\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Name** & **Definition** & **Value/Range** \\ \hline I & Impact & Potential damage across strategic, operational, and economic dimensions & I \(\in[1,5]\) \\ \hline L & Likelihood & Probability of successful exploitation based on historical data and complexity & L \(\in[1,5]\) \\ \hline M & Measurability & Detection capability of existing monitoring systems & M \(\in[1,5]\) \\ \hline D & Defense Difficulty & Remediation costs & D \(\in[1,5]\) \\ \hline T & Technical Complexity & Attack execution difficulty & T \(\in[1,5]\) \\ \hline \(\alpha\) & Impact Amplification & Exponent for prioritizing high-impact vulnerabilities & \(\alpha\in[1,0,1.5]\) \\ \hline \(\beta\) & Likelihood Dampening & Exponent for mitigating over-penalization of low-probability threats & \(\beta\in[1,0,1.3]\) \\ \hline \(\gamma\) & Measurability Adjustment & Exponent for addressing stealth attacks with low detection likelihood & \(\gamma\in[0.5,1.0]\) \\ \hline \(\delta\)(t) & Time Decay Factor & Exponential decay function adjusting risk over time, distinguishing patched/unpatched states & \(\delta(t)=1.2e^{-k(t-t_{0})}\) \\ \hline C & Confidence & Adjust risk scores based on data source reliability & \(C\in[0.7,1.3]\) \\ \hline \(\omega_{s}\) & Segment Weight & Prioritizes risks based on criticality of affected network segments & \(\omega_{s}=1.5\) (space), 1.2 (ground), 1.0 (user) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter definitions for Formula (1).  
Measurability (M): Measurability reflects the detection capability of existing monitoring systems; measured on a scale from 1 to 5 (\(M\in[1,5]\)).  
Nonlinear exponents (\(\alpha\), \(\beta\), \(\gamma\)): The exponents are designed as tunable parameters to reflect operational priorities:  
1. Impact amplification (\(\alpha\)): A range of \(\alpha\in[1.0,1.5]\) allows operators to prioritize high-impact vulnerabilities (e.g., \(\alpha\) = 1.5 for mission-critical systems) or align with linear scoring (\(\alpha\) = 1.0).
2. Likelihood dampening (\(\beta\)): The range \(\beta\in[1.0,1.3]\) balances rare but catastrophic events (e.g., orbital collisions) with common threats.
3. Adjustment (\(\gamma\)): A lower \(\gamma\in[0.5,1.0]\) amplifies risks from stealth attacks (e.g., \(\gamma\) = 0.5 for undetectable firmware exploits).  
In this study, the values of \(\alpha\), \(\beta\), and \(\gamma\) were determined through analysis of historical satellite cybersecurity incidents. The exponent \(\alpha\) = 1.2 was derived from analyses of the 2022 Viasat attack, where ground segment compromises triggered cascading service disruptions across space and user segments. This value balances systemic risk prioritization without overfitting to outlier events. Similarly, \(\beta\) was determined to be 1.1, balancing likelihood and risk assessment. And \(\gamma\) was set to 0.8 after studying stealth attacks with low measurability, ensuring these threats are not underestimated.  
Defense difficulty (D) and technical complexity (T): These parameters assess remediation costs (\(D\in[1,5]\)) and attack execution difficulty (\(T\in[1,5]\)), respectively. The arithmetic mean \(\frac{D+T}{2}\) balances defense pressure across both dimensions, avoiding bias from single parameters.