New 2D hyperchaotic Cubic-Tent map and improved 3D Hilbert diffusion for image encryption

Abstract

In image encryption, the effectiveness of chaotic maps significantly affects the effect of image encryption technology. However, existing chaotic maps have an issue of uneven value distribution when generating chaotic sequences, which could pose a threat to information security. To address this issue, a new two-dimensional Cubic-Tent map (2D-CTM) has been developed based on the Cubic and Tent maps. A series of comparative experiments on the 2D-CTM effectively validate its excellent chaotic properties. A novel image encryption algorithm utilizing 2D-CTM (CTM-IEA) is developed to encrypt images. This algorithm includes bit-level random scrambling, bit-level flipping, and improved 3D Hilbert diffusion process. First, the binary elements corresponding to different pixels in the plaintext image are randomly scrambled. Subsequently, the scrambled binary elements are flipped using a chaotic matrix, thoroughly obfuscating the binary information of the plaintext image and successfully hiding the plaintext information. Finally, the improved 3D Hilbert diffusion is applied to the image, eliminating pixel correlation in the original image and enhancing its security. Additionally, bit-level scrambling and diffusion are carried out in three rounds, which bolster the image’s defense against differential attacks. Compared to traditional encryption methods, this approach offers improved security by ensuring more uniform chaotic sequences and integrating a multi-round, bit-level encryption process. The security analysis shows that the key space reaches \({2}^{471}\), with correlation coefficients of 0.0006, 0.00004, and \(-\) 0.0010, and an information entropy of 7.9998. The NPCR is 99.6084%, and the UACI is 33.4620%, which prove the effectiveness and reliability of the algorithm.