# Chaotic Henon-Logistic Map Integration: A Powerful Approach for Safeguarding Digital Images
## 3 The Proposed Scheme
Table 3 provides a comprehensive evaluation of the proposed encryption method, encompassing metrics such as the Structural Similarity Index Measure (SSIM), Unified Average Changing Intensity (UACI), and Number of Pixels Change Rate (NPCR). This meticulous evaluation, as presented in Table 3, highlights the method's performance, offering a nuanced understanding of its efficacy and resilience to potential vulnerabilities. The comprehensive nature of this evaluation reinforces the research's credibility and the results' reliability. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Image** & **MSE** & **PSNR** & **MSE** & **PSNR** \\
**Index** & **Encrypted** & **Encrypted** & **Decrypted** & **Decrypted** \\ \hline
1 & \(7.70\times 10^{3}\) & 21.3279 & 0 & \(\infty\) \\
3 & \(8.56\times 10^{3}\) & 20.2718 & 0 & \(\infty\) \\
4 & \(8.63\times 10^{3}\) & 20.2004 & 0 & \(\infty\) \\
6 & \(9.04\times 10^{3}\) & 19.7344 & 0 & \(\infty\) \\
7 & \(7.78\times 10^{3}\) & 21.3004 & 0 & \(\infty\) \\
8 & \(9.39\times 10^{3}\) & 19.3507 & 0 & \(\infty\) \\
11 & \(8.73\times 10^{3}\) & 20.0851 & 0 & \(\infty\) \\
13 & \(9.17\times 10^{3}\) & 19.5886 & 0 & \(\infty\) \\
16 & \(7.96\times 10^{3}\) & 21.0065 & 0 & \(\infty\) \\
18 & \(1.08\times 10^{4}\) & 17.9478 & 0 & \(\infty\) \\
20 & \(1.52\times 10^{4}\) & 14.5110 & 0 & \(\infty\) \\
24 & \(8.88\times 10^{3}\) & 19.9059 & 0 & \(\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated MSE and PSNR values for both encryption and decryption. ### Histogram Analysis

Histogram analysis is a vital part of evaluating image encryption methods. By comparing the histograms of the original and encrypted images, we can assess how well an encryption algorithm disguises the original image's statistical properties. This technique focuses on factors such as intensity levels and pixel distributions. It plays a crucial role in determining the strength and efficacy of encryption algorithms, ensuring that the encrypted images resist attacks while exhibiting high entropy and a uniform distribution. The security and effectiveness of encrypted images have been significantly improved by recent advances in image encryption, which have given rise to novel approaches like deep learning and chaotic maps. These advancements ensure that encrypted images show no discernible patterns, making them highly resistant to statistical attacks. This improved security is crucial for protecting sensitive information in various applications [19; 43]. Figure 6 illustrates the histograms of both the original and encrypted images. The histogram of the encrypted image shows a more even distribution of pixel values, resulting in nearly uniform probabilities across all intensity levels. ### Speed Analysis

Table 4 provides information on the performance of the proposed encryption technique by detailing the image index, encryption time, and throughput for each image. The data reflect the method's efficiency, with an average encryption time of 3.238 s across all tested images. This demonstrates the method's ability to encrypt images rapidly, making it well suited for scenarios where time efficiency is paramount. Furthermore, the table reports an average throughput of 0.3868 Mbps, emphasizing the method's strong data