**6. Evaluation and security analysis**

To prove the robustness of the proposed security framework, we evaluate it using various metrics or tools for different standard images. This section contains the statistical analysis, the key analysis, Know Plain Text and Chosen Plain Text Attack, and the speed.

#### **6.1 Statistical analysis**

Statistical analysis indicates the factor of coincidence between plain and cipher images to test the ability of the algorithm to defend against attacks. Statistical analysis can include the image histogram, the entropy, the normalized correlation, the correlation coefficient (*ρ*), the peak signal to noise ratio (*PSNR*), and structural similarity index measure (*SSIM*) tools.

#### *6.1.1 Histogram analysis*

The histogram represents the data distribution in function of the pixel's values. A perfect secure algorithm must create a cipher image with uniform and totally different histograms compared to the original images. We analyze the histograms of original and encrypted samples and the contents are very different as shown in **Figure 7**. As a consequence, it is so hard to understand the encrypted image's appearance.

#### *6.1.2 PSNR, SSIM, and entropy analysis*

After encryption, the entropy factor, the PSNR, and SSIM are calculated as reported in **Table 1**. Practically, a perfect cryptosystem performs random information equal to "8" [10]. As given in **Table 2**, we constate that the entropy value of the cipher sample is close to the ideal value "8." This means that our algorithm put forward can resist statistical attacks. When analyzing the PSNR results. We note that the value is lower than 5 dB (<5 dB). Following the reference [11], the suggested cryptosystem gives a bad quality between both plain and cipher samples. Thus, it is hard to predict the original image from the cipher one. When turning to the SSIM factors computed between the original and the cipher images, we constate that values are close to 0. Therefore, we cannot extract the content of the clear sample from the cipher one. A comparative study of other existing work for entropy and PSNR evaluation tools is

**Figure 7.** *Histogram of the plain samples and their corresponding of the cipher samples.*

reported in **Table 3**. This comparison lets us conclude that our cryptographic model outperforms the other works and can resist statistical attacks.
