## 5 Conclusions  
In this paper, we propose a method to protect mouse movement sequence data from real-time interception attacks during image-based authentication. The proposed approach generates fake data by leveraging the user's previous mouse movement sequences and mixes this data in real time with the user's current actual mouse movement data. The effectiveness of this method is validated through various simulation experiments designed to mimic real-world scenarios from the attacker's perspective. Specifically, the proposed mouse data protection method utilizes GANs (Generative Adversarial Networks) to generate fake mouse sequence data that closely resemble real data, making it indistinguishable from actual mouse movement data during interception attacks that rely on the GetCursorPos() function. The generated fake data also incorporate elapsed time as an additional feature. Consequently, this process alters not only the mouse position but also the movement sequence itself, thereby preventing attackers from accurately identifying the user's true mouse movement sequence. To demonstrate the effectiveness of the proposed method, we simulated various image-based authentication processes. Using the collected mouse sequence data, fake data were generated and mixed with real data, and classification simulations were conducted using various machine learning models from the attacker's perspective. Comparative evaluations with existing methods that randomly generate fake data for protection showed that these existing methods resulted in attack success rates of up to 99%. In contrast, the proposed method reduced classification accuracy by 30% to 50%. From an absolute classification accuracy perspective, the proposed method achieved an average accuracy of 61.9% and a maximum of 65.5% across all models, which is close to the baseline random selection accuracy of 50% in binary classification. This indicates that attackers were unable to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature Set** & **Metrics** & \begin{tabular}{c} **Randomly** \\ **Generated Method** \\ \end{tabular} & \begin{tabular}{c} **Proposed Method** \\ **Using GANs** \\ \end{tabular} & \begin{tabular}{c} **Difference (+/\(-\))** \\ \end{tabular} \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Elapsed Time, \\ X, Y Coordinates \\ \end{tabular} } & Accuracy & 0.923 & 0.544 & \(-\)0.379 \\  & Precision & 0.860 & 0.545 & \(-\)0.315 \\  & Recall & 0.978 & 0.522 & \(-\)0.456 \\  & F1-score & 0.915 & 0.534 & \(-\)0.381 \\  & AUC & 0.942 & 0.562 & \(-\)0.380 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Elapsed Time, \\ X, Y Coordinates \\ X, Y Distances \\ \end{tabular} } & Accuracy & 0.995 & 0.619 & \(-\)0.376 \\  & Precision & 0.999 & 0.690 & \(-\)0.309 \\  & Recall & 0.989 & 0.485 & \(-\)0.504 \\  & F1-score & 0.994 & 0.569 & \(-\)0.425 \\  & AUC & 0.997 & 0.675 & \(-\)0.322 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of classification performance between the randomly generated method and the proposed method using GANs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature Set** & **\(t\)-Statistic** & **Confidence Interval (95\%)** & **\(p\)-Value** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Elapsed Time, \\ X, Y Coordinates \\ \end{tabular} } & 22.200 & 0.337–0.420 & 2.731 \(\times\) 10\({}^{-7}\) \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Elapsed Time, \\ X, Y Coordinates \\ X, Y Distances \\ \end{tabular} } & \multirow{2}{*}{37.059} & \multirow{2}{*}{0.351–0.401} & \multirow{2}{*}{1.288 \(\times\) 10\({}^{-8}\)} \\  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the one-tailed paired \(t\)-test for the classification accuracies between the randomly generated method and the proposed method using GANs. accurately classify individual mouse movement sequence data, rendering attacks focused on intercepting such data during image-based authentication ineffective.