## 4 Results and Discussion
### Time Analysis  
Finally, we focus our attention on the last parameter, probably one of the most relevant elements when we analyze the performance of cryptographic algorithms represented by the computational time that should be minimal for performing privacy-preserving face authentication and encryption in an attempt to achieve the best results and develop a robust and reliable mechanism of authentication. Time plays a crucial role in the entire encryption and decryption process, and a wide variety of external and internal factors related to computer performance such as hardware components, software applications, and cryptographic algorithm structure influence it.  
For the current study, we analyzed biometric images from different users, using different dimensions as shown in the graphs presented below. As displayed in Figures 4 and 5, there is a major distinction between the homomorphic encryption algorithms; the BGV algorithm is clearly superior to the BFV algorithm in terms of time encryption for facial biometrics in all image dimensions.  
Considering the graphs below, it can be emphasized, that the smallest values for time encryption are obtained through the BGV algorithm, which spends up to 1 s for image encryption for the biometric image with 256 pixels that we used for experimentation. However, the highest value for the BGV algorithm is obtained for biometric images with  
Figure 4: Time factor analysis using BFV encryption algorithm.  
Figure 5: Time factor analysis using BGV encryption algorithm.  
a size of 2048 pixels, which validates the assertion that time is directly proportional to the increase in image size.  
In contrast to the BGV algorithm, the resulting values for the BFV algorithm are distributed over a larger interval of time and indicate that this is a time-consuming alternative that uses important computational resources for realizing image encryption. Also, the results prove that this is not a viable solution to be implemented in real-time applications, because it takes more time than expected for encryption even for the smallest biometric image sizes, and needs significant optimization in order to be applied in practice.  
In addition, the values obtained indicate the lack of uniformity of the time factor when encryption is performed with this algorithm, which oscillates in large intervals of time as can be seen in Figure 4, between 212 and 797 s. This is an enormous amount of time, without being able to establish any rule in the encryption process, specifically the rule regarding the direct correlation between time encryption and image dimension which is not valid in this case or to identify a potential factor that generates these noteworthy differences.  
The best option for an effective implementation that can reasonably be applied to the proposed authentication mechanism is obviously the BGV algorithm because it requires less computational time for different image sizes than the other algorithm, which means it provides reliability and is more convenient when applied to the encryption process.  
Overall, the preliminary experimental results reveal that the BGV fully homomorphic encryption algorithm should be applied to improve the security level in the authentication process because it offers a major advantage in terms of performance and efficiency for the proposed system capabilities designed especially for IT systems with high-security requirements. Considering the tests performed, the optimal operating parameters of this algorithm are for an image of 512 pixels, to ensure a sufficient image accuracy and a suitable encryption time. Despite its potential benefits, we identified a limitation that significantly influences the encryption process related to the performances of the computational resources, so that for an optimized time for the process of information encryption and decryption, it is necessary to provide powerful resources, especially regarding the CPU and system memory.