## 3 Proposed Method for Real-Time Mouse Data Protection Using Generative Adversarial Networks (GANs)
### Generation of Fake Mouse Data Using GANs  
In generating fake mouse data, to obscure the detection of continuous mouse movements, the included features cover not only the X and Y coordinates of the actual mouse but also the elapsed time. Previous studies have shown that adding features such as elapsed time and distance significantly improves the detection performance of fake data from the attacker's perspective [10; 11]. This might be because the combination of elapsed time and distance features encapsulates inherent characteristics, such as movement speed, and these are important for distinguishing real mouse movements from randomly generated ones.  
Therefore, in this study, the feature set includes not only the X and Y coordinates of the mouse sequence data but also the elapsed time. To generate realistic mouse data based on this tabular, continuous-feature dataset, we employ the CTGAN model [20; 21]. The CTGAN model extends the CGAN model by proposing a method specialized in generating tabular data that includes both categorical and continuous variables. In particular, it effectively addresses the sparsity of both types of variables using techniques such as conditional sampling and mini-batch discrimination [20; 22; 23]. These methods allow the model to handle the sparsity of small values in continuous variables, such as mouse coordinates and elapsed time, and generate them accurately. When generating fake data using the CTGAN model, the distance feature is excluded because, even if included, attackers can use the X and Y coordinates of the mouse to calculate the actual distance and use this information for detection. Thus, including the distance feature becomes redundant. Figure 2 compares the distribution of fake mouse data generated by the CTGAN model using X-coordinate, Y-coordinate, and elapsed time features against the distribution of actual data from Dataset A-1. The comparison is based on the distribution of real and fake data.  
The upper distribution in Figure 2 shows the X and Y coordinate distributions of randomly generated fake mouse data and real mouse data with elapsed time as the axis. The lower distribution shows the fake mouse data generated using CTGAN. In the distribution, blue represents real mouse data, while red represents fake mouse data. The X-axis  
\begin{table}
\begin{tabular}{c c c} \hline
**Dataset** & **Data Collection Details** & **Number of Collected Movement Data** \\ \hline Dataset A-1 & Collected from the first experiment on page A & 16,623 \\ Dataset A-2 & Collected from the second experiment on page A & 16,628 \\ Dataset B-1 & Collected from the first experiment on page B & 11,364 \\ Dataset B-2 & Collected from the second experiment on page B & 11,365 \\ Dataset C-1 & Collected from the first experiment on page C & 7947 \\ Dataset C-2 & Collected from the second experiment on page C & 7952 \\ Dataset D-1 & Collected from the first experiment on page D & 10,074 \\ Dataset D-2 & Collected from the second experiment on page D & 10,147 \\ \hline \end{tabular}
\end{table}
Table 1: Dataset configuration and the number of collected data for real mouse movements.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Seq\#** & **Elapsed Time** & **X-Coordinate** & **Y-Coordinate** \\ \hline
1 & 0.117283 & 0.431419 & 0.580363 \\
2 & 0.195521 & 0.430637 & 0.581614 \\
3 & 0.194678 & 0.429465 & 0.585366 \\
4 & 0.184249 & 0.509965 & 0.205128 \\
5 & 0.1165 & 0.506839 & 0  
represents the mouse's X and Y coordinates, and the Y-axis represents the elapsed time. As shown in the distribution, the fake mouse data generated by CTGAN closely resemble the real mouse data distribution, unlike the randomly generated fake data.