## 5 Results and Discussion
### Discussion  
The proposed study highlights that the introduction of small noise by FHE enhances the accuracy of the Decision Classifier when compared to plaintext data. Without this noise, the model's sensitivity to outliers or noisy instances in the data could have been too strong. The encryption process may add small, consistent noise across similar data points, effectively reducing the noise and making the data more homogeneous. This kind of homogenization may help the Decision Classifier come up with more consistent and generalized rules. Although FHE introduces some computational overhead and loss in model performance, choosing the right ML model can effectively manage this. XGBoost has been the best performer on all metrics for accuracy, execution time, RMSE, and hamming loss, thus increasing its popularity for the application that focuses on privacy preservation using FHE. On the other hand, models such as Random Forest are efficient in terms of time, and Decision Classifiers performed well on encrypted data in terms of accuracy and precision. By balancing security and performance, the analysis has shed some important light on the choice of models for encrypted environments.  
Scalability and Feasibility of Fully Homomorphic Encryption  
FHE offers a strong privacy guarantee by allowing computations on encrypted data without the need for decryption. However, its primary challenge lies in the computational overhead, which limits its scalability in real-world applications, such as smart home activity recognition. In this study, we applied FHE uniformly across the entire dataset to ensure consistent privacy protection. Selectively applying FHE to only sensitive data, as seen  
Figure 7: RMSE of XGBoost, Random Forest, and Decision Classifier with and without FHE.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **XGBoost** & \begin{tabular}{c} **XGBoost with** \\ **FHE** \\ \end{tabular} & **Random Forest** & \begin{tabular}{c} **Random Forest** \\ **with FHE** \\ \end{tabular} & \begin{tabular}{c} **Decision** \\ **Classifier with** \\ **FHE** \\ \end{tabular} & \
\begin{tabular}{c} **Decision** \\ **Classifier with** \\ **FHE** \\ \end{tabular} \\ \hline
\begin{tabular}{c} Execution \\ Time (s) \\ \end{tabular} & 0.000117 & 1.90000 & 0.000013 & 0.0500 & 0.000049 & 54.170 \\ \hline Loss & 0.015889 & 0.05600 & 0.016500 & 0.0780 & 0.032690 & 0.0200 \\ \hline RMSE & 0.126051 & 0.23664 & 0.128409 & 0.2792 & 0.180801 & 0.1414 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Execution time, loss, and RMSE in XGBoost, Random Forest, and Decision Classifier with and without FHE.  
in hybrid encryption approaches, might reduce computational load but is difficult to implement in smart home environments. Since even seemingly non-sensitive data can reveal critical patterns of behavior, leaving parts of the data unencrypted under a less secure scheme would introduce privacy risks.  
To mitigate the performance issues associated with FHE, several scalability solutions have been explored in recent work, and these can be leveraged to improve the feasibility of FHE in practice:  
* Cloud-based Parallelization: By distributing the FHE computations across cloud platforms with multi-core or GPU-based systems, the processing time can be significantly reduced. This allows for the practical application of FHE at scale.
* Efficient FHE Libraries: New optimizations in FHE libraries (e.g., CKKS, TFHE) focus on improving bootstrapping times, which is traditionally a bottleneck in FHE computations. These optimizations make FHE more feasible for larger datasets.
* Approximate Homomorphic Encryption: While our study focused on exact FHE methods, approximate homomorphic encryption could also be explored in future work, where slight imprecisions in data are acceptable, thus reducing computational complexity.