A 3D Memristive Hyperchaotic Map with Bounce-Escape Zigzag Scrambling for Color Image Encryption

As the need for secure image encryption grows, chaotic cryptography using hyperchaotic systems has attracted significant attention. This article proposes a novel three-dimensional (3D) memristive hyperchaotic map. We analyze the map using phase portraits, Lyapunov exponents, sensitivity analysis, the 0-1 test, Lyapunov dimension, bifurcation diagrams, and Kolmogorov–Sinai entropy. The map has two positive Lyapunov exponents, and the Kaplan–Yorke dimension equals three, confirming strong hyperchaotic dynamics across a wide parameter range. Based on this map, we introduce a new color image encryption scheme. It incorporates a key derived from both an external 256-bit secret key and the SHA-256 hash of the plaintext; a novel Bounce-Escape Zigzag (BEZ) scrambling algorithm with boundary-bouncing diagonal trajectories, variable-length diagonal traversals, and adaptive collision escape; dynamic DNA encoding; and chaotic XOR diffusion. Comprehensive security analysis on standard test images demonstrates near-ideal entropy values, NPCR and UACI close to the theoretical ideals, and correlation coefficients close to zero. The proposed scheme also shows strong robustness against differential, known-plaintext, and chosen-plaintext attacks, as well as cropping and noise corruption, with an effective key space of 2256. By integrating hyperchaotic dynamics, BEZ scrambling, and multi-layer DNA-XOR diffusion, the proposed method achieves superior performance. It is well-suited for secure image communication and storage applications.