DPPAD-IE: Dynamic Polyhedra Permutating and Arnold Diffusing Medical Image Encryption Using 2D Cross Gaussian Hyperchaotic Map

With the rapid improvement of medical consumer electronics (CE), the transmission of multiple images has become increasingly common in the medical field. During the transmission and storage of image data, sensitive information, including medical images, may be accessed by unauthorized parties, resulting in possible privacy violations. Consequently, several multi-image encryption (MIE) algorithms have been proposed to solve this real-world problem. Nevertheless, current MIE schemes exhibit several drawbacks, including insufficient security in permutation and diffusion algorithms, as well as the insensitivity of chaotic maps. This paper presents a new encryption algorithm called DPPAD-IE. The algorithm primarily consists of three components. First, we developed an innovative hyperchaotic map called the 2D Cross Gaussian Hyperchaotic Map (2D-CGHM), which has an expanded chaotic interval and is proficient in producing chaotic sequences with improved pseudorandomness. Second, we introduce a new Dynamic Polyhedra Permutation algorithm (DPP) that successfully alters pixel locations of the image, hence diminishing the connection between neighboring pixels. Third, we propose an Arnold Diffusion algorithm (AD), using chaotic sequences to further encrypt the permuted image. The DPPAD-IE is capable of encrypting images of any quantity and size concurrently. The experimental results confirm that this approach is both robust and effective, capable of defending against various security attacks. The code are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/QuincyQAQ/DPPAD-IE</uri>.