Hyperchaotic fractional-order image encryption with Knight’s tour scrambling for satellite imagery

Abstract

Abstract Secure dissemination of high-resolution satellite imagery remains challenging because many image-tailored ciphers either (i) emphasize permutation-heavy designs without sufficiently strong, plaintext-adaptive nonlinearity, or (ii) provide strong security metrics but fall short on scalable, near-real-time performance and robustness assessment under realistic channel impairments. To address these gaps, this work proposes a three-stage chaos-chess hybrid encryption pipeline for color satellite images that couples fractional-order hyperchaotic key generation with lightweight algebraic mixing, dynamic substitution, and structured bit-level diffusion. First, multiple images are optionally augmented and each RGB channel is partitioned into $$2\times 2$$ pixel matrices that are mixed via invertible matrices derived from a 6D fractional-order hyperchaotic Vaidyanathan system, providing efficient confusion suitable for parallelization. Second, plaintext-sensitive S-boxes are constructed online from a 4D fractional-order hyperchaotic system and applied per channel to enhance nonlinearity and satisfy stringent criteria (NL $$=108$$ , SAC $$\approx 0.5$$ , low LAP and DAP). Third, the resulting bit-streams are diffused by traversing $$8\times 8$$ blocks using Knight’s Tour paths and XORing with 4D hyperchaotic key-streams to amplify avalanche propagation. Experiments on satellite and natural images demonstrate high ciphertext randomness (entropy $$\approx 7.999$$ ), strong differential resistance (NPCR $$\approx 99.62\%$$ , UACI $$\approx 30.95\%$$ ), near-zero adjacent-pixel correlation (PCC $$\approx 0$$ ), and a large key space ( $$>2^{3827}$$ ), while measured runtimes indicate suitability for real-time or near-real-time operation. Noise-like ciphertexts and lossless recovery are verified via visual, histogram, and DFT analyses, and robustness under occlusion and noise attacks (salt-and-pepper, Gaussian) is evidenced. The resulting modular design provides a scalable pathway for protecting remote sensing data and supports future integration with ROI-aware processing and hardware acceleration.