Adaptive Image Encryption Algorithm Based on a 2D Hyperchaotic Map

Existing two-dimensional chaotic maps typically have narrow or fragmented chaotic windows, which restricts their use in image encryption. We propose a two-dimensional hyperchaotic exponential-adjusted logistic map with linear cross-diffusion (2D-HELD); both Lyapunov exponents remain positive across the examined parameter range, and pseudorandom sequences drawn from the map pass all fifteen NIST SP 800-22 tests. Using this map we build a 2D chaotic–dynamic–adaptive diffusion (2D-CDAD) image cipher that combines chaotic index permutation with adaptive dynamic diffusion. The permutation order and the keystream come from 2D-HELD, whereas the diffusion templates are regenerated from the SHA-512 digest of the plaintext, so no two images share a template. Template sizes of 2×2, 3×3 and 5×5 are allocated by ranking the complexities of the 8×8 sub-blocks at proportions of about 70%/25%/5% that adapt with the global gain. Feeding the same digest into the chaotic parameters gives each image its own keystream. Over the 15 colour test images the mean ciphertext entropy is 7.9982, the Number of Pixel Change Rate (NPCR) and Unified Average Changing Intensity (UACI) lie close to their theoretical values, and the effective key space reaches 2384. The cryptosystem is robust against cropping and noise attacks.