A Novel Chaos-Based Image Encryption Using Magic Square Scrambling and Octree Diffusing

Abstract

Digital chaotic maps have been widely used in the fields of cryptography owing to their dynamic characteristics, however, some unfavorable security properties arise when they operate on devices with limited precision. Thus, enhancing the properties of chaotic maps are beneficial to the improvement of chaos-based encryption algorithms. In this paper, a scheme to integrate a one-dimensional Logistic map by perturbation parameters with a delayed coupling method and feedback control is proposed and further deepens the randomness by selectively shifting the position of the chaotic sequence. Then, through a number of simulation experiments, the results demonstrate that the two-dimensional chaotic map treated by this mode exhibits better chaotic characteristics, including a larger chaos range and higher complexity. In addition, a new image encryption algorithm is designed based on these modified chaotic sequences, in which magic square theorem is incorporated to exchange pixel positions, and the octree principle is invoked to achieve pixel bit shifting. Several simulation experiments present findings that the image encryption algorithm contains a high level of security, and can compete with other encryption algorithms.

Keywords

• digital chaotic map
• image encryption
• delay coupling
• feedback
• magic square
• octree