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Cited by 3Chaos-based Image/Signal EncryptionComputer Science and EngineeringCryptographic Implementations and Security

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

Open access
Mamdouh, Eyad, Aboshousha, Amr, Alexan, Wassim·2026·Scientific Reports
DOI 10.1038/s41598-026-58982-1PMC PMC13315892
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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.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes a three-stage chaos–chess hybrid cipher for color satellite images, combining fractional-order hyperchaotic key generation, dynamic per-channel S-boxes, and Knight’s Tour-guided bit-level diffusion. It reports near-ideal randomness, strong differential resistance, near-zero adjacent-pixel correlation, a large key space, and near-real-time runtimes.

Key findings

  • Across satellite and natural images, the scheme achieved average entropy 7.999001, NPCR 99.6171%, UACI 30.9532%, and near-zero encrypted-image adjacent-pixel correlations (PCC ≈ 0), with key space >2^3827.
  • The proposed S-boxes met NL = 108, SAC ≈ 0.506–0.508, LAP = 0.0781, and DAP = 0.015625, compared with ideal values of 112, 0.5, 0.0625, and 0.015625, respectively.
  • NIST SP 800-22 tests on a 10^6-bit concatenated ciphertext stream all passed with p-values > 0.01.
  • Runtime was 0.851602 s in the comparative table, and time consumption scaled from about 0.06 s for 64×64 images to about 13.3 s for 1024×1024 images; memory rose from about 300 MB to nearly 3109 MB over the same range.

Methods

  • Design: a three-stage encryption pipeline: (1) 2×2 pixel-matrix mixing per RGB channel using invertible matrices from a 6D fractional-order hyperchaotic Vaidyanathan system; (2) online plaintext-sensitive per-channel S-box substitution from a 4D fractional-order hyperchaotic system; (3) XOR diffusion over 8×8 blocks traversed by Knight’s Tour paths using 4D hyperchaotic key-streams.
  • Data: test images from the SIPI database and satellite images, resized to 256×256 unless otherwise stated; implementation on an AMD Ryzen 5 5600H with 16 GB RAM.
  • Analysis: statistical metrics (MSE, PSNR, entropy, NPCR, UACI, MAE, PCC), S-box criteria (NL, SAC, BIC, LAP, DAP), visual/histogram/DFT analysis, NIST SP 800-22, noise/occlusion/chosen-plaintext tests, ablation, key sensitivity, and time/memory scaling.

Limitations

  • The paper states a security–robustness trade-off under occlusion: higher MSE and lower PSNR indicate enhanced security at the expense of reduced image recoverability under partial data loss.
  • It notes finite-precision arithmetic can degrade digitally implemented chaotic dynamics; the implementation uses numeric precision on the order of 10^-16 and discretizes/whitens sequences before use.
  • The paper lists future work needed for hardware acceleration, standards alignment, ROI-aware integration, advanced threat modeling (chosen-ciphertext, adversarial, side-channel), key management, and algorithmic refinements; evident from the text, the evaluation is mainly at 256×256 and does not include FPGA/ASIC deployment or full high-resolution 4K–8K security validation.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/s41598-026-58982-1

Cites

48 of 48 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

7 of 24 cited sources checked · 4 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Conventional cryptographic algorithms such as AES and RSA may not be efficient or adaptable for large-scale, real-time satellite image encryption due to their computational overhead and structural rigidity.

    “Conventional cryptographic algorithms such as AES and RSA, while robust for general-purpose data protection, may not be efficient or adaptable for large-scale, real-time satellite image encryption due to their computational overhead and structural rigidity.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [4] Alexan, W. et al. A new multiple image encryption algorithm using hyperchaotic systems, svd, and modified rc5. Sci. Rep. 15(1), 9775 (2025). source

      The Introduction says AES can be inefficient for large, highly redundant satellite images, and Related literature says many existing methods are too computationally intensive for real-time satellite-image processing. The cited passages do not make that assessment of RSA or identify “structural rigidity” as a cause. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
  • Interpretationreasoning

    The combination of local algebraic mixing, channel-specific dynamic substitution, and knight-guided bit-level diffusion yields a tightly coupled architecture that is structurally distinct from existing chaos+chess scrambling frameworks.

    “This combination of local algebraic mixing, channel-specific dynamic substitution, and knight-guided bit-level diffusion yields a tightly coupled architecture that is structurally distinct from existing chaos+chess scrambling frameworks16,26.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [16] Alqahtani, N. A novel privacy framework for satellite images based on theory of chaos and chess pieces castle and king (IEEE Access, 2025). source
    • cites [26] He, C. et al. An algorithm based on 6d fractional order hyperchaotic system and knight tour algorithm to encrypt image. Phys. Scr. 99(5), 055205 (2024). source
  • Findingown data

    Robustness under occlusion and noise attacks (salt-and-pepper, Gaussian) is evidenced.

    “robustness under occlusion and noise attacks (salt-and-pepper, Gaussian) is evidenced”
    Quote in the paperSubstantial claim
  • Findingown data

    Measured runtimes indicate suitability for real-time or near-real-time operation.

    “measured runtimes indicate suitability for real-time or near-real-time operation”
    Quote in the paperSubstantial claim
  • Findingown data

    Experiments demonstrate a large key space (>2^3827).

    “a large key space (>2^{3827})”
    Quote in the paperSubstantial claim
  • May combine two claims. 30
  • Classified as probably not a substantial claim. 10
  • The quote only partly states this claim. 1

  • May combine two claims.

    Premisecitation

    Chaotic systems are highly sensitive to initial conditions and exhibit pseudo-random behavior, making them well-suited for creating confusion and diffusion in image data.

    “Chaotic systems are highly sensitive to initial conditions and exhibit pseudo-random behavior, making them well-suited for creating confusion and diffusion in image data.”
    Quote in the paperSubstantial claim1 of 5 sources checked
    • cites [5] Gao, S. et al. A 3d memristive cubic map with dual discrete memristors: Design, implementation, and application in image encryption. IEEE Trans. Circuits Syst. Video Technol. 35(8), 7706–7718 (2025). source
    • cites [6] Ding, S., Shi, F., Erkan, U., Toktas, A., Li, Q., Wang, C., Gao, S. & Mou, J. Design of a three-dimensional logistic map and its application to seafood image encryption: S. ding et al. The Journal of Supercomputing, 82(4), 225, (2026). source
    • cites [7] El-Damak, D. et al. Fibonacci q-matrix, hyperchaos, and galois field ($$2^8$$) for augmented medical image encryption. IEEE Access 12, 102718–102744 (2024). source
    • cites [8] Shabasy, N. H. E., Mansy, A. & Alexan, W. An improved bülban map and its application in multiple image encryption (J. King Saud Univ. Comput. Inf, Sci, 2026). source
    • cites [9] Ding, S. et al. Sra: A sine-based reconstruction approach to improve 2d chaotic map performance. Eur. Phys. J. Plus 141(2), 182 (2026). source

  • May combine two claims.

    Premisecitation

    Image data exhibits strong spatial redundancy and high correlation among neighboring pixels.

    “image data exhibits strong spatial redundancy and high correlation among neighboring pixels”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [4] Alexan, W. et al. A new multiple image encryption algorithm using hyperchaotic systems, svd, and modified rc5. Sci. Rep. 15(1), 9775 (2025). source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Recent literature has shown the utilization of the Knight's Tour in image encryption applications.

    “Recent literature has shown the utilization of the Knight’s Tour in image encryption applications29.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [29] Singh, M., Kakkar, A. & Singh, M. Image encryption scheme based on knight’s tour problem. Proc. Comput. Sci. 70, 245–250 (2015). source

  • May combine two claims.

    Premisecitation

    The 6D hyperchaotic Vaidyanathan fractional-order system exhibits four positive Lyapunov exponents, indicating hyperchaotic dynamics, with a Kaplan-Yorke dimension equal to 4.105.

    “For the specified parameter set, the system exhibits four positive Lyapunov exponents, indicating the presence of hyperchaotic dynamics, as discussed in 26, where the Kaplan-Yorke dimesion equals to 4.105.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [26] He, C. et al. An algorithm based on 6d fractional order hyperchaotic system and knight tour algorithm to encrypt image. Phys. Scr. 99(5), 055205 (2024). source

      Section 2.2 states that the 6D Vaidyanathan system has four positive Lyapunov exponents for the specified parameters and initial values, then describes converting it to a fractional-order system. The copy does not state that the fractional-order system has four positive exponents or give a Kaplan–Yorke dimension of 4.105 (searched: “Kaplan Yorke,” “Lyapunov dimension,” and “4.105”). (LLM, conf=0.88)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Interpretationreasoning

    The scheme is suitable for SIMD/GPU acceleration and FPGA implementations in bandwidth-constrained remote-sensing pipelines.

    “making the scheme suitable for SIMD/GPU acceleration and FPGA implementations in bandwidth-constrained remote-sensing pipelines22,31,32.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [22] Alexan, W. & Megalli, Y. A new fast high dimensional and memristive hyperchaotic multiple image encryption method and its fpga implementation. Discov. Electron. 2(1), 1–33 (2025). source

      Section 4.3 reports that the scheme was implemented on an Artix-7 FPGA, and the Conclusions identify satellite imaging as a suitable application. Our copy does not establish SIMD/GPU acceleration or suitability specifically for bandwidth-constrained remote-sensing pipelines; the reported parallel processing and FPGA throughput do not demonstrate those additional claims. No page numbers were provided in our copy. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites [31] Alexan, W. et al. Triple layer rgb image encryption algorithm utilizing three hyperchaotic systems and its fpga implementation. IEEE Access 12, 118339–118361 (2024). source
    • cites [32] Alexan, W. et al. Fpga realization of a novel hyperchaos augmented image encryption algorithm. IET Comput. Dig. Techn. 2026(1), 6416727 (2026). source

  • May combine two claims.

    Findingown data

    Noise-like ciphertexts and lossless recovery are verified via visual, histogram, and DFT analyses.

    “Noise-like ciphertexts and lossless recovery are verified via visual, histogram, and DFT analyses”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In ablation tests, simplified configurations with individual stages or combinations removed exhibited slightly lower computational complexity but noticeable degradation in security-related performance metrics.

    “As illustrated in Fig. 14, simplified configurations exhibited slightly lower computational complexity; however, they resulted in noticeable degradation in security-related performance metrics.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Visual, histogram, and DFT analyses confirmed noise-like ciphertexts and faithful, lossless recovery.

    “Visual, histogram, and DFT analyses confirmed noise-like ciphertexts and faithful, lossless recovery.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Under occlusion attacks, the proposed encryption method yields higher MSE values and lower PSNR than existing schemes, indicating enhanced security at the expense of reduced robustness.

    “The proposed encryption method yields higher MSE values and lower PSNR under occlusion attacks, indicating enhanced security performance at the expense of reduced robustness.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Histogram analysis shows that the distinct patterns of plain images are transformed into a uniform distribution in cipher images, hiding original content and mitigating statistical information leakage.

    “histogram analysis, also in Fig. 6, demonstrates that the distinct patterns of the plain images are transformed into a uniform distribution in the cipher images, thereby effectively hiding original content and mitigating statistical information leakage.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The proposed scheme has a key space of 2^3827 and an encryption time of 0.851602 s on the stated machine.

    “Proposed | 8.4689 | 7.999001 | 99.6171 | 30.9532 | 2^{3827} | 0.851602 | AMD® RyzenTM 5600H, 3.3 GHz, 16 GB | 2.8102866”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    When the correct key is used, the original image is accurately reconstructed without distortion; even minimal key modifications (one or two bits) result in completely unsuccessful decryption with severely distorted outputs.

    “When the correct key is used, the original image is accurately reconstructed without any distortion. However, even minimal modifications to the key, such as altering a single bit or two bits, result in completely unsuccessful decryption, producing severely distorted outputs with no resemblance to the original image.”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data

    The proposed S-boxes achieve NL 108, SAC approximately 0.506-0.508, BIC 108, LAP 0.0781, and DAP 0.015625.

    “Proposed S-box 1 | 108 | 0.506592 | 108 | 0.0781 | 0.015625”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The encrypted output exhibits a noise-like appearance with no discernible information from the original image retained, while decrypted images are perfectly reconstructed without distortion or artifacts, verifying lossless recovery.

    “The encrypted output exhibits a noise-like appearance, ensuring no discernible information from the original image is retained, while the decrypted images are perfectly reconstructed without any distortion or artifacts, verifying lossless recovery.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Original images maintain strong correlations between adjacent pixels, while encrypted images exhibit correlations near zero.

    “the pixel correlation coefficient (PCC) analysis, detailed in Table 7 demonstrates that original images maintain strong correlations between adjacent pixels. In contrast, the encrypted images exhibit correlations near zero, confirming the effective randomization of pixel relationships.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The entropy of the encrypted images is approximately 8, near the ideal value, indicating a high degree of randomness.

    “The entropy of the encrypted images (H_E) is approximately 8, which is near the ideal value, indicating a high degree of randomness and affirming the cryptographic robustness of the scheme.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationreasoning

    The 2×2 matrix mixing provides efficient confusion suitable for parallelization.

    “providing efficient confusion suitable for parallelization”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Many of these methods lack standardization, real-time validation, or scalability to high-resolution datasets.

    “many of these methods lack standardization, real-time validation, or scalability to high-resolution datasets”
    Quote in the paperSubstantial claim0 of 10 sources checked
    • cites [12] Elias, E. P. & Santhanavijayan, A. Secure satellite image transmission with dynamic encipherment and authkex protocol. Adv. Space Res. 20, 23 (2025).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [13] Shen, H. et al. A novel secure scheme for remote sensing image transmission: An integrated approach with compression and encoding. Earth Sci. Inform. 17(5), 4875–4900 (2024). source
    • cites [14] Makhloufi, A. E., Adib, S. E. & Raissouni, N. Hardware pipelined architecture with reconfigurable key based on the aes algorithm and hamming code for the earth observation satellite application: Sentinel-2 satellite data case, e-Prime-Advances in Electrical Engineering. Electron Energy 8, 100548 (2024).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [15] Karmouni, H. et al. Secure and optimized satellite image sharing based on chaotic e$$\pi$$ map and racah moments. Exp. Syst. Appl. 236, 121247 (2024). source
    • cites [16] Alqahtani, N. A novel privacy framework for satellite images based on theory of chaos and chess pieces castle and king (IEEE Access, 2025). source
    • cites [17] Kanwal, S. et al. A robust approach to satellite image encryption using chaotic map and circulant matrices. Eng. Rep. 6(12), e13010 (2024).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [18] Zhao, L., Zhao, L., Cui, F. & Sun, T. Satellite image encryption based on rna and 7d complex chaotic system. Visual Comput. 40(8), 5659–5679 (2024). source
    • cites [19] Javid, M., Khan, M. & Amin, M. Improvement of blowfish encryption algorithm based on galois ring for electro-optical satellite images, Multimedia Tools and Applications 1–20 (2024). source
    • cites [20] Peng, Y. et al. An optical remote sensing image encryption algorithm for sensitive targets in sea-related scenes. Nonlinear Dyn. 112, 16537–16558 (2024). source
    • cites [21] Jasmine, J. J., Raja, S. E., Muniraj, R. & Ulaganathan, M. Optimized modified single shot multibox detector with hybrid encryption algorithm for satellite image security and classification. Earth Sci. Inform. 18(3), 309 (2025). source

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Many image-tailored ciphers provide strong security metrics but fall short on scalable, near-real-time performance and robustness assessment under realistic channel impairments.

    “or (ii) provide strong security metrics but fall short on scalable, near-real-time performance and robustness assessment under realistic channel impairments”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given

    The resulting modular design provides a scalable pathway for protecting remote sensing data and supports future integration with ROI-aware processing and hardware acceleration.

    “The resulting modular design provides a scalable pathway for protecting remote sensing data and supports future integration with ROI-aware processing and hardware acceleration”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Many image-tailored ciphers emphasize permutation-heavy designs without sufficiently strong, plaintext-adaptive nonlinearity.

    “many image-tailored ciphers either (i) emphasize permutation-heavy designs without sufficiently strong, plaintext-adaptive nonlinearity”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Plaintext-sensitive S-boxes are constructed online from a 4D fractional-order hyperchaotic system and applied per channel.

    “plaintext-sensitive S-boxes are constructed online from a 4D fractional-order hyperchaotic system and applied per channel”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    A scalable and modular cryptosystem has been demonstrated that integrates chaos-based confusion/diffusion, algebraic mixing on 2×2 pixel matrices, and chess-inspired traversal to enhance security without sacrificing practical deployability.

    “Overall, a scalable and modular cryptosystem has been demonstrated that integrates chaos-based confusion/diffusion, algebraic mixing on 2×2 pixel matrices, and chess-inspired traversal to enhance security without sacrificing practical deployability.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductown data

    Figure 2 displays various plots that verify the hyperchaotic behavior of the fractional order system in (2).

    “Figure 2 displays various plots that verify the hyperchaotic behavior of the fractional order system in (2).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The proposed algorithm has strong resistance to occlusion and noise-based attacks, affirming its applicability in high-security domains such as satellite and remote-sensing imaging.

    “Collectively, these results validate the proposed algorithm’s strong resistance to occlusion and noise-based attacks, affirming its applicability in high-security domains such as satellite and remote-sensing imaging, where maintaining both data integrity and confidentiality is critical.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Across satellite and natural images, the scheme achieved near-ideal entropy, strong differential resistance (high NPCR and appropriate UACI), near-zero adjacent-pixel correlations, and a large key space, indicating robustness against statistical, brute-force, and differential attacks.

    “Across a diverse set of satellite and natural images, the scheme achieved near-ideal entropy, strong differential resistance (high NPCR and appropriate UACI), near-zero adjacent-pixel correlations, and a large key space, indicating robustness against statistical, brute-force, and differential attacks.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Each module of the proposed scheme plays a significant role in enhancing randomness, reducing pixel correlation, and improving resistance against cryptographic attacks.

    “The experimental findings indicate that each module plays a significant role in enhancing randomness, reducing pixel correlation, and improving resistance against cryptographic attacks.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    The image is partitioned into multiple subblocks, with each subblock traversed according to a distinct Knight's tour.

    “The image is partitioned into multiple subblocks, with each subblock traversed according to a distinct Knight’s tour.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Fractional-order chaotic systems generalize integer-order dynamics by introducing a nonlocal (history-dependent) operator, i.e., the state evolution depends not only on the current value but also on past states through the fractional derivative.

    “Fractional-order (FO) chaotic systems generalize integer-order dynamics by introducing a nonlocal (history-dependent) operator, i.e., the state evolution depends not only on the current value but also on past states through the fractional derivative.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The proposed S-box meets or exceeds the security performance of state-of-the-art designs, confirming its suitability for applications requiring high security, such as satellite image encryption.

    “The experimental results indicate that the proposed S-box meets or exceeds the security performance of state-of-the-art designs, confirming its suitability for applications requiring high security, such as satellite image encryption.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductown data

    Figure 1 displays various plots that verify the hyperchaotic behavior of the fractional order system in (1).

    “Figure 1 displays various plots that verify the hyperchaotic behavior of the fractional order system in (1).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The proposed image encryption scheme effectively disrupts statistical and structural dependencies, ensuring a high level of security.

    “Collectively, these performance metrics demonstrate the capability of the proposed image encryption scheme to effectively disrupt statistical and structural dependencies, thereby ensuring a high level of security.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning

    The proposed scheme discretizes/whitens generated real-valued sequences into bytes/bits before use and enforces a complete 0-255 permutation during S-box construction to limit bias from repeated or correlated samples.

    “To reduce potential degradation, the generated real-valued sequences are discretized/whitened into bytes/bits before use, and a complete 0-255 permutation is enforced during S-box construction (Algorithm 1) to limit bias arising from repeated or correlated samples.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Finite-precision arithmetic degrades digitally implemented chaotic dynamics, for example by inducing short cycles or reduced complexity.

  • May combine two claims.

    Interpretationreasoning

    The proposed cipher uses constant-time operations per pixel and block-local processing that enables parallel execution, making it practical for high-resolution satellite imagery.

    “The proposed cipher is designed to remain practical for high-resolution satellite imagery by relying on constant-time operations per pixel and by using block-local processing that enables parallel execution.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    From a cryptographic standpoint, the memory effect of fractional-order chaotic systems typically enriches the phase-space behavior and increases the dynamical complexity of the generated sequences, which is desirable when chaotic trajectories are used as key-stream sources.

    “From a cryptographic standpoint, this memory effect typically enriches the phase-space behavior and increases the dynamical complexity of the generated sequences, which is desirable when chaotic trajectories are used as key-stream sources.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The ablation results validate the effectiveness of the integrated framework and highlight the importance of incorporating all proposed components to achieve optimal encryption performance.

    “Therefore, the results validate the effectiveness of the integrated framework and highlight the importance of incorporating all proposed components to achieve optimal encryption performance.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The generated bitstream exhibits a high degree of randomness, reflecting the effectiveness of the proposed algorithm in resisting statistical attacks and reinforcing its suitability for secure cryptographic applications.

    “These outcomes confirm that the generated bitstream exhibits a high degree of randomness, reflecting the effectiveness of the proposed algorithm in resisting statistical attacks and reinforcing its suitability for secure cryptographic applications.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The algorithm's performance is consistent across diverse image types, and perfect histogram match after decryption validates its robustness and ability to ensure security irrespective of input characteristics.

    “The consistent performance across diverse image types and the perfect histogram match after decryption validate the algorithm’s robustness and its ability to ensure security irrespective of input characteristics (Table 8).”
    Quote in the paperSubstantial claim
38 of 38

  • The paper relies on this without support.

    Finite-precision arithmetic degrades digitally implemented chaotic dynamics, for example by inducing short cycles or reduced complexity.

    “Finite-precision arithmetic is known to degrade digitally implemented chaotic dynamics (e.g., by inducing short cycles or reduced complexity).”

  • The authors state this as an assumption.

    The proposed scheme is evaluated assuming the algorithm is public and only the secret key remains unknown, under ciphertext-only, known-plaintext, and chosen-plaintext adversary models.

    “In accordance with Kerckhoffs’ principle35, the proposed scheme is evaluated assuming the algorithm is public and only the secret key remains unknown, under adversary models that include ciphertext-only, known-plaintext, and chosen-plaintext access.”
2 of 2

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Normalized time for scheme 20 is 20 times too high

    Major

    The other normalized times equal execution time multiplied by the listed processor clock speed. For scheme 20, 0.4610 × 2.50 = 1.1525, not 23.05; the reported value reverses its normalized-time comparison with the proposed scheme.

    Reported 23.05 · recomputed 1.1525

  • Occlusion results do not uniformly show higher MSE

    Minor

    The text says the proposed method yields higher MSE under occlusion, but at 1/4 occlusion its Mandrill MSE is 11532.2, below scheme 42's 15045.4; its F16 MSE is also below scheme 41's.

2 of 2

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Wenqi, Y. et al. Mar20: A benchmark for military aircraft recognition in remote sensing images. Natl Remote Sens. Bull. 27(12), 2688–2696 (2024).

Cited by

Still being checked.

Authors
Mamdouh, E., Aboshousha, A., & Alexan, W.
Affiliations
German University in Cairo (EG)
Corresponding author
  • Mamdouh, Eyad
  • Alexan, Wassim
ORCID
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2026-06-29
Volume
16
Issue
1
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/s41598-026-58982-1
PMC
PMC13315892
OpenAlex
W7166579969
Cited by
3
References
48
Citations by year
2026: 3
FWCI
9.06
Type
journal article
Language
en
Open access
Licence
Locations
  • Scientific Reports (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • PubMed Central (submittedVersion, cc-by)
Funders
German University in Cairo
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
  • Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
Keywords
image encryption, hyperchaotic systems, fractional-order systems, S-box design, pixel scrambling, confusion and diffusion, differential attack resistance, color image encryption

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-21.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-21.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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