A new image encryption algorithm with feedback key mechanism using two-dimensional dual discrete quadratic chaotic map

With the continuous advancement of information technology, the security of digital images is becoming increasingly important. To ensure the secure transmission of images, this paper proposes an image encryption algorithm based on a two-dimensional dual discrete quadratic chaotic map (2D-DDQCM). The digital sequences generated by the 2D-DDQCM exhibit high randomness and unpredictability, making them suitable as pseudo-random number generators in cryptography. In the first round of encryption, the algorithm generates an initial key using natural noise and transforms the pixel positions and values of the image using a pseudo-random key stream generated by the 2D-DDQCM, achieving confusion and diffusion. To ensure the security of the encryption process, the algorithm employs a feedback key mechanism, which ensures the dynamism and unpredictability of the encryption keys, making it more difficult for attackers to crack. In the second round of encryption, the ciphertext is used as input into a hash function to generate a new key. Through a series of pixel-level operations, the security of the ciphertext is further enhanced. The algorithm is tested on a set of standard test images, and the information entropy of the ciphertext was found to be 7.9993, with correlations in the three directions being 0.0006, 0.0003, -\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document} 0.0012, respectively. Additionally, compared with existing image encryption algorithms, the results indicate that the image encryption algorithm based on the 2D-DDQCM and the feedback key mechanism provides an effective solution for the secure transmission of images.