## 5 Simulation  
The proposed MRFCO-ZTS model and existing Zero-Trust Authentication Approach with Hyperelliptic Curve Cryptography (ZTAP-HECC) [1] are implemented in MATLAB (R2024b). During the simulation, the number of satellite users varies in a range of 50 to 250, which is considered as an input. The simulations and model evaluations were executed on a standalone desktop system with the following specifications (Tables 3-6):  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Classification Result \(\overset{\wedge}{\boldsymbol{y}}\)** & **Detector Action** \\ \hline \(i=\) Legitimate & Give full access to all services \\ \hline \(S_{i}=\) Attacker & Immediate block, alert, forensic log \\ \hline \hline \end{tabular}
\end{table}
Table 2: Classification result and detector action.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Element** & **Value/Description** \\ \hline User Sessions Simulated & 250 to 1200 dynamic users per run \\ \hline Session Duration & 600 s (10 min real-time simulation) \\ \hline Cost Function Range & 0.1 to 4.8 \\ \hline Authentication Cycle & Every 1.5–3 s (configurable interval) \\ \hline Attack Behavior & Injected synthetic mimicry, burst, and random attacks \\ \hline Trust Score Model & Probabilistic model based on user activity logs \\ \hline Classification Output & Binary (Legitimate, Attacker), with risk tagging \\ \hline \hline \end{tabular}
\end{table}
Table 6: Simulation Input Models.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Specification** \\ \hline Processor (CPU) & Intel Core i5-11400F @ 2.60 GHz (6 cores, 12 threads) (Intel Corporation, Santa Clara, CA, USA) \\ \hline RAM & 16 GB DDR4 @ 3200 MHz (MHzKingston Technology, Fountain Valley, CA, USA) \\ \hline Storage & 512 GB NVMe SSD (Kingston Technology, Fountain Valley, CA, USA) \\ \hline GPU (optional use) & NVIDIA GTX 1650 (4 GB GDDR6, CUDA-capable) (NVIDIA Corporation, Santa Clara, CA, USA) \\ \hline Power Supply & 500 W PSU, consistent 220 V input (Corsair Components, Fremont, CA, USA) \\ \hline Operating System & Windows 10 Pro (64-bit), version 22H2 (Microsoft Corporation, Redmond, WA, USA) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hardware configuration.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Configuration** \\ \hline Simulation Platform & MATLAB R2024b (64-bit) \\ \hline MATLAB Toolboxes & Optimization Toolbox; Statistics and Machine Learning Toolbox \\ \hline Programming Language & MATLAB scripting (M-code) \\ \hline Execution Mode & Script and function-based batch simulations \\ \hline Parallel Computing & Disabled (single-node simulation) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Software environment.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Function** & **Description** \\ \hline fmincon() & Constrained optimization (baseline comparison) \\ \hline Custom mrfo\_cost\_function() & Implements MRFO-based attacker classification \\ \hline rand(), normrnd() & Random-number generation for synthetic user behavior \\ \hline surf(), plot3(), bar() & Visualization of cost landscapes and classification results \\ \hline Custom trust-score module & Rule-based and probabilistic trust-score evaluation \\ \hline tic; loc; & Used for measuring simulation time \\ \hline \hline \end{tabular}
\end{table}
Table 5: Used libraries and functions.  
In the MRFCO-ZTS Model, continuous authentication is based on the cost function of ZTS. The following Table 7 shows the evaluation of five user sessions.  
The simulation performance output of the developed MRFCO-ZTS approach is compared against the conventional existing Zero-Trust Authentication Protocol with Hyperel-liptic Curve Cryptography (ZTAP-HECC) [1] using the below metrics:  
* Security level;
* Latency;
* Efficiency.