# Chaotic Henon-Logistic Map Integration: A Powerful Approach for Safeguarding Digital Images
## 3 The Proposed Scheme
The generation process for the 1D CLM map, which facilitates pixel shuffling along rows and columns, is shown in Equation (2) and Equation (3), respectively. \[\text{CLM-Row}(i)=X_{n+1}=rX_{n}(X_{n}-1) \tag{2}\]  
where CLM-Row is a 1D CLM map of size \(R\) and \(i\leq R\) is the row index. \[\text{CLM-Col}(j)=X_{n+1}=rX_{n}(X_{n}-1) \tag{3}\]  
where CLM-Col is a 1D CLM map of size \(C\) and \(j\leq C\) is the column index. Another example of a discrete-time system that exhibits chaotic behavior is the chaotic Henon map, which is given by Equation (4):  
\[ \begin{split} X_{n+1}&=1-aX_{n}^{2}+Y_{n}\\ Y_{n+1}&=bX_{n}\end{split}  \tag{4}\]  
where the map depends on two parameters, \(a\) and \(b\), and the values for the classical chaotic Henon map are typically \(a=1.4\) and \(b=0.3\). \(X_{0}=0.1\) and \(Y_{0}=0.1\) are the initial values for the chaotic map. The number of random values \(n\) equals the number of pixels in the image to be encrypted and reshaped to match the image size. When encrypting a digital image using the chaotic Henon map, a bitwise XOR operation is applied between the encryption key and the image. This operation alters the image by flipping bits where the corresponding key bit is 1 while leaving bits unchanged where the key bit is 0. Importantly, this process is inherently reversible. By applying the same bitwise XOR operation between the same key and the encrypted image, the original image is restored. For decryption, the recipient must have access to the identical key used for encryption. The original image can be retrieved by performing the same bitwise XOR operation between the encrypted image and the key. The security of the key is of utmost importance, as the image may be readily decrypted by anyone having the key. This underscores the recipient's responsibility for maintaining the key's security. To improve the security of encrypted images, it is crucial to repeat both the confusion and diffusion processes multiple times. Research indicates that a single round of a substitution-permutation network-based cryptosystem lacks sufficient security to prevent vulnerabilities, even when utilizing a chaotic system as the foundation for encryption [41]. Furthermore, other studies demonstrate that employing four rounds of confusion and diffusion significantly bolsters the security of their encryption methods [6; 7]. In summary, implementing multiple iterations of these processes can greatly enhance encrypted data protection. Figure 2 illustrates the effectiveness of the proposed encryption technique, which consists of three primary components: the chaotic parameter generator, confusion, and diffusion. The chaotic parameter generator plays a crucial role in the process, computing specific chaotic parameters like \(r\), \(x\), \(a\), and \(b\). These parameters introduce a high level of complexity and randomness, enhancing the security of the encryption. The confusion stage rearranges the plain image's rows and columns using a 1D chaotic vector generated by the CLM map generator. Each permuted color channel is then encrypted in the diffusion phase by performing a bitwise XOR operation with a 2D chaotic matrix, Algorithm 1 explains in details the encryption process of the proposed method. The encryption method involves four rounds of confusion and diffusion, making it robust against known plaintext attacks. The following subsections elaborate on the key parser, encryption, and decryption processes in greater detail. Figure 3 illustrates the proposed decryption method, detailing the roles of the various components in restoring the original data. At the core, the chaotic parameter generator produces specific chaotic parameters, which are crucial for the decryption sequence. These parameters guide the logistic map generator, a key player in generating a 1D key that introduces a complex level of confusion, ensuring the data are accurately unscrambled.