3D Non-degenerate Hyperchaos: Design, Analysis, and Application in Image Encryption

The widespread adoption of consumer electronics (CE), particularly in smart home ecosystems, has led to the proliferation of intelligent devices such as smart cameras, video doorbells, and smart door locks. While these devices enhance convenience and automation, they generate massive amounts of visual data containing sensitive personal information, thereby increasing the risk of privacy leakage and challenging traditional encryption methods in consumer IoT networks. To address this issue, a cryptanalysis-driven image encryption scheme via a chaos-based 3D S-box and genetic code is proposed, specifically designed to safeguard visual privacy in consumer applications. First, a novel dynamical architecture, formally termed 3D Non-degenerate Hyperchaos (3D-NDHC), is constructed to serve as a robust entropy source. Explicitly defined as a globally bounded volume-expanding hyperchaotic system, 3D-NDHC distinguishes itself from traditional dissipative maps by exhibiting global robust hyperchaos and scalable complexity, where the Lyapunov exponents grow logarithmically with control parameters, ensuring high unpredictability. Next, a dynamically generated three-dimensional S-box driven by these chaotic sequences is introduced to perform efficient image permutation. Subsequently, a genetic code method enhanced by cryptanalysis is applied to confuse the permuted image matrix, specifically addressing the security vulnerabilities often inherent in lightweight encryption algorithms. Finally, under the control of pseudo-chaotic sequences, a lightweight wave diffusion process is employed to spread the pixel values and produce the final ciphertext image. In contrast to conventional algorithms that rely on standard encryption techniques, the proposed approach integrates a chaos-driven 3D S-box with a cryptanalysis-enhanced genetic code scheme. This combination introduces a high level of confusion and diffusion, significantly increasing the difficulty for attackers attempting to illegally decrypt sensitive images from smart devices. Experimental results and security analyses demonstrate that the scheme effectively resists various cryptographic attacks and outperforms several recently proposed image encryption algorithms, offering a robust solution for protecting digital image privacy in smart home environments.