Chaos-Based Image Encryption with 5D Keystreams and 3D Voxel Scrambling: A Survey and Reference-Implementation Study

Abstract: Digital images used in medical, financial, surveillance and cloud settings need protection that general-purpose ciphers provide inefficiently, because images are large and strongly redundant. Chaos-based ciphers address this with confusion–diffusion structures driven by keystreams from chaotic and hyperchaotic systems. This paper surveys recent work (2018–2026) on hyperchaotic image encryption, organizes it by chaotic source and cipher structure, and then studies one representative design in depth: 3D voxel scrambling of a 512×512 image combined with a keystream from a five- dimensional Lorenz-type system seeded by SHA-384. A complete Python reference implementation recovers all test images losslessly and gives cipher entropy of 7.9993 bits, adjacent-pixel correlation below 0.02 in magnitude, NPCR of 99.60–99.62 % and UACI of 33.47–33.51 %, all inside the 5 % critical intervals of Wu et al. Two findings are hidden by these headline metrics. First, the Lyapunov spectrum of the 5D system has a single positive exponent (+1.13), so the system is chaotic, not hyperchaotic. Second, the cipher is exactly affine over Z₂₅₆, which makes its differential behaviour independent of the plaintext and exposes it to chosen-plaintext attack. We conclude with concrete design recommendations and open problems.

Keywords: image encryption, hyperchaotic system, 3D pixel scrambling, Fisher–Yates shuffle, confusion–diffusion, NPCR, UACI, Lyapunov exponent