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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\n                    <jats:inline-formula>\n                      <jats:tex-math>$$2\\times 2$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    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\n                    <jats:inline-formula>\n                      <jats:tex-math>$$=108$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , SAC\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 0.5$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , low LAP and DAP). Third, the resulting bit-streams are diffused by traversing\n                    <jats:inline-formula>\n                      <jats:tex-math>$$8\\times 8$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    blocks using Knight\u2019s Tour paths and XORing with 4D hyperchaotic key-streams to amplify avalanche propagation. Experiments on satellite and natural images demonstrate high ciphertext randomness (entropy\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 7.999$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), strong differential resistance (NPCR\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 99.62\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , UACI\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 30.95\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), near-zero adjacent-pixel correlation (PCC\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 0$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), and a large key space (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$&gt;2^{3827}$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), 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.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-58982-1","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T21:07:34Z","timestamp":1782767254000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Hyperchaotic fractional-order image encryption with Knight\u2019s tour scrambling for satellite imagery"],"prefix":"10.1038","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4228-5174","authenticated-orcid":false,"given":"Eyad","family":"Mamdouh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amr","family":"Aboshousha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6159-4971","authenticated-orcid":false,"given":"Wassim","family":"Alexan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,29]]},"reference":[{"key":"58982_CR1","first-page":"2088","volume":"14","author":"C Vasudevaiah","year":"2024","unstructured":"Vasudevaiah, C. & Shivaswamy, R. 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