## 3 Proposed Method for Real-Time Mouse Data Protection Using Generative Adversarial Networks (GANs)
### Simulation of Fake Data Classification from the Attacker's Perspective  
In this section, simulations were conducted assuming that attackers use various machine learning models to classify real and fake data. The attackers might also generate fake data using random methods or the GAN-based technique proposed in this paper and then train a model to classify the fake mouse data. To simulate this, machine learning models such as K-Nearest Neighbor, Logistic Regression, Random Forest, Gradient Boosting, Support Vector Machine, and Multi-Layer Perceptron were used. The dataset used for the simulation was collected by attempting authentication twice on the same image-based authentication page. Data from the first and second attempts were paired together to simulate the classification from an attacker's perspective. Additionally, real and fake data were merged based on the collection time and re-ordered using cumulative elapsed time to simulate how an attacker might combine data. Table 3 shows a sample of the mixed mouse sequence data  
Figure 2: Comparison of random and GAN-based fake mouse data generation results. generated for Image Authentication Page A. The data include fake mouse data generated by CTGAN using the actual mouse sequence data from the first trial (Dataset A-1) and the actual data from the second trial (Dataset A-2). In Table 3, the elapsed time is calculated based on the cumulative elapsed time of the two-sequence data, which are integrated into a single sequence and then recalculated. X Distance and Y Distance refer to the distances moved from the previous sequence's X and Y coordinates. Lastly, the Class column indicates whether the data are real or fake, with 1 representing real data and 0 representing fake data. In this dataset, the data from Dataset A-2 are labeled as 1, while the fake data generated from Dataset A-1 are labeled as 0. To determine optimal performance from the defender's perspective, the number of epochs during the CTGAN model training was varied to generate fake data. Various machine learning-based classification models were then employed to evaluate and identify the optimal epoch that resulted in the lowest classification performance. Figure 3 presents the results of this preliminary experiment aimed at determining the optimal number of epochs. Figure 3: Performance evaluation results of generated fake mouse data based on different epochs. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Seq\#** & **Elapsed Time** & **X** & **Y** & **X Distance** & **Y Distance** & **Class** \\ \hline
1 & 0.143747 & 0.431419 & 0.580363 & 0 & 0 & 1 \\
2 & 0.085557 & 0.794842 & 0.791745 & 0.36385 & 0.212846 & 0 \\
3 & 0.104029 & 0.782337 & 0.160725 & 0.01252 & 0.63539 & 0 \\
4 & 0.050052 & 0.430637 & 0.581614 & 0.352113 & 0.423804 & 1 \\
5 & 0.154898 & 0.451348 & 0.595372 & 0.020736 & 0.013854 & 0 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
33,249 & 0.18158 & 0.415006 & 0.377111 & 0.071596 & 0.627204 & 1 \\
33,250 & 0.184869 & 0.415006 & 0.377736 & 0 & 0.00063 & 1 \\
33,251 & 0.188698 & 0.415006 & 0.378361 & 0 & 0.00063 & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Sample data of the mixed dataset of dataset A-2 and synthetic data created based on dataset A-1. The X-axis in Figure 3 represents different machine learning algorithms, while the Y-axis displays the average performance metrics (accuracy, precision, recall, etc.) of the classification models. The number of epochs for training the CTGAN model is indicated in the legends. F1 and F2 in the legends represent two feature combinations: (Elapsed Time, X Coordinate, Y Coordinate) and (Elapsed Time, X Coordinate, Y Coordinate, X Distance, and Y Distance), respectively. The lowest classification performance occurred at 50 epochs for all feature sets, and subsequent experiments were conducted with 50 epochs. Both the generator and discriminator learning rates were set to 2 \(\times\) 10\({}^{-4}\) for stability.