<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(=108\)</EquationSource> </InlineEquation>, SAC <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\approx 0.5\)</EquationSource> </InlineEquation>, low LAP and DAP). Third, the resulting bit-streams are diffused by traversing <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(8\times 8\)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\approx 7.999\)</EquationSource> </InlineEquation>), strong differential resistance (NPCR <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\approx 99.62\%\)</EquationSource> </InlineEquation>, UACI <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\approx 30.95\%\)</EquationSource> </InlineEquation>), near-zero adjacent-pixel correlation (PCC <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\approx 0\)</EquationSource> </InlineEquation>), and a large key space (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(&gt;2^{3827}\)</EquationSource> </InlineEquation>), 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.</p>

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

  • Eyad Mamdouh,
  • Amr Aboshousha,
  • Wassim Alexan

摘要

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.