## 4 Results and Discussion
### Histogram Analysis  
The first statistical parameter used in the present research is the histogram of the facial biometric image, calculated for 512-pixel images. According to [57], this concept is defined by the distribution of every pixel intensity per grayscale image, estimating the data density and providing a grayscale personalized representation. When we analyze the histograms displayed in Figure 3, generated for the original biometric image and its encrypted variants using the BFV and the BGV encryption algorithms, in terms of visual effects, we can observe significant differences in pixel intensity dissemination. While the users' original biometric images have a left-skewed distribution or right-skewed distribution which indicates a positive or negative luminous pixel distribution in the image structure, for the encrypted images, characterized by unimodal distribution, it can be seen that stability and uniformity dominate and the values, as well as the shape of the image, are centrally located and have a constant shape with very small differences. In the histograms below, the X-axis indicates the pixel intensity distribution with the specific range intervals between [0, 255], and the Y-axis displays the frequency of occurrence, which means the degree of data uncertainty and diffusion. It is clear from the graphical representations of the histograms on the Y-axis that higher values are acquired through the BFV algorithm compared to the BGV encryption algorithm, which indicates that it provides an improved level of security, making it impossible to discern the original image through its histogram for the attack vectors. The minimum correlation between the cipher and the original image outlines the performance and effectiveness of the analyzed algorithms. To resolve a challenging task and to make this study more complete, we recruited a pair of identical male twins for the experimental results to check the ability of the proposed device to distinguish almost identical physical characteristics and verify the accuracy of the authentication process. This hypothesis of effective recognition and authentication on twins is necessary to verify the acceptance error rate in the system because the possibility of errors is maximum due to the inaccuracies generated by feature extraction, matching, or verification. Figure 3 shows the histograms from a pair of identical male twins. While the histograms of the encrypted images with the BFV algorithm are identical, the histograms generated on encrypted images with the BGV algorithm have almost similar shapes and almost identical values but show a series of differences visible to the naked eye. We can deduce from these results that the BGV algorithm is more suitable for implementation. It generates different histograms even for almost identical people, which is an advantage because it makes it difficult to decipher them in case of a potential attack. The reliability and accuracy of the proposed device and its automatic facial recognition algorithm were demonstrated while trying to authenticate and distinguish the twins in the system. The experimental results proved the possibility of differentiating the twins in short period of time and with high precision by the biometric sensor.