# Chaotic Henon-Logistic Map Integration: A Powerful Approach for Safeguarding Digital Images
## 1 Introduction  
Cryptography, the study of secure communication, plays a crucial role in protecting sensitive data from unauthorized access or alterations. A specialized branch of this field, image cryptography, concentrates on ensuring the security of digital images. By utilizing cryptographic methods, it safeguards the confidentiality, integrity, and authenticity of image data. Applications of image cryptography are diverse and extend across sectors such as healthcare, military, and finance [1, 2, 3]. In healthcare, patient medical images are often sensitive, and image cryptography ensures that only authorized personnel can access and interpret them. In the military, the secure transmission of satellite imagery and surveillance data relies on image cryptography to prevent interception by adversaries. Financial transactions involving visual data, such as digital signatures on checks or the secure transmission of financial documents, also benefit from image cryptography to maintain the confidentiality and trustworthiness of the information. As technology advances, image cryptography's importance becomes increasingly pronounced in our digitally interconnected world [4, 5]. Chaotic approaches have proven valuable in image cryptography due to their inherentcomplexity and sensitivity to initial conditions. Chaotic systems exhibit unpredictability and nonlinearity, making them suitable for creating secure encryption algorithms [6, 7]. In image cryptography, chaotic maps such as logistic maps and Henon maps have been employed to scramble pixel values or positions, providing a basis for encryption. These chaotic approaches enhance the security of the image by introducing a high level of entropy, making it difficult for adversaries to decipher the encrypted content without the correct decryption key. Researchers have explored different chaotic transformations and their combinations to develop robust image encryption techniques, ensuring the confidentiality and integrity of visual information in diverse applications [8, 9, 10, 11, 12].  
Hyper-chaotic approaches represent an advanced extension of chaotic systems, incorporating multiple chaotic maps or dimensions to further enhance the security of image cryptography. Hyper-chaotic systems offer increased complexity and control parameters, making them even more attack-resistant. In image encryption, hyper-chaotic systems are employed to introduce additional layers of complexity, often in the form of multi-dimensional chaotic transformations. The synergistic combination of chaotic and hyper-chaotic approaches in image cryptography aims to create encryption schemes that can withstand sophisticated attacks and provide a higher level of security for visual data in applications ranging from secure communication to medical imaging and beyond [13, 14, 15, 16]. This research paper aims to introduce and evaluate a new integrated chaos-based algorithm for image encryption that integrates the chaotic Henon map with the chaotic logistic map (CLM) to significantly improve the security of digital image communication. By generating cryptographic keys through chaos theory, the algorithm is designed to produce highly unpredictable and complex keys that are crucial for robust encryption. This paper aims to demonstrate the algorithm's effectiveness in confidently resisting various well-known attacks, such as chosen-plaintext, noise, clipping, occlusion, and known-plaintext attacks, while assessing its performance based on encryption time, throughput, and image quality metrics. Through this research, the authors strive to establish the chaotic Henon-logistic map integration as a powerful method for protecting digital images in secure communication environments.  
The structure of this paper is organized as follows. Section 2 offers an overview of recent relevant research, and Section 3 provides a detailed discussion of the proposed scheme. The results and their analysis are expounded upon in Section 4, while Section 5 encapsulates a concise summary of the conclusions drawn from this study.