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<p>The rapid advancement in image quality, led to a surge in image storage demands. Transmitting images to cloud servers offers a practical solution to address limited storage capacity. Yet, cloud servers are neither fully secure nor trustworthy, posing risks of information leakage. Recently, Thumbnail-Preserving Encryption (TPE) has been proposed as a method to balance image privacy and usability, but it only supports pixel groups composed of two pixels. Subsequently, Flexible Thumbnail-Preserving Encryption (F-TPE) was introduced, which not only accommodates pixel groups of arbitrary lengths but also reduces time consumption. While both TPE schemes achieve a trade-off between privacy and usability, they face bottlenecks such as dimensional constraints and high computational complexity. To address these limitations, this paper proposes a novel Constant Time Complexity Rank-then-Encipher (CTC-RtE) method. CTC-RtE retrieves all possible pixel value combinations that match the sum of the input pixel group across varying dimensions, thereby dramatically reducing time overhead. Building on CTC-RtE, a Multidimensional Thumbnail-Preserving Encryption (MD-TPE) framework is designed, capable of adapting to pixel groups of different lengths. Furthermore, a diffusion step is introduced after the ranking operation to ensure a more uniform distribution of pixel values in the encrypted image. Experimental results demonstrate that MD-TPE achieves O(1) time encryption across multiple dimensions, outperforming existing methods in time efficiency. Specifically, for a 256<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11760_2025_4658_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>256 image with pixel groups of size two, MD-TPE achieves a 94.02% improvement in efficiency compared to F-TPE. The effectiveness of the diffusion step is validated through adjacent pixel correlation analysis and histogram analysis.</p>

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MD-TPE: multidimensional thumbnail-preserving encryption based on rank-then-encipher with constant time complexity

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Shengcai Zhang,
  • Haitao Chen,
  • Dezhi An

摘要

The rapid advancement in image quality, led to a surge in image storage demands. Transmitting images to cloud servers offers a practical solution to address limited storage capacity. Yet, cloud servers are neither fully secure nor trustworthy, posing risks of information leakage. Recently, Thumbnail-Preserving Encryption (TPE) has been proposed as a method to balance image privacy and usability, but it only supports pixel groups composed of two pixels. Subsequently, Flexible Thumbnail-Preserving Encryption (F-TPE) was introduced, which not only accommodates pixel groups of arbitrary lengths but also reduces time consumption. While both TPE schemes achieve a trade-off between privacy and usability, they face bottlenecks such as dimensional constraints and high computational complexity. To address these limitations, this paper proposes a novel Constant Time Complexity Rank-then-Encipher (CTC-RtE) method. CTC-RtE retrieves all possible pixel value combinations that match the sum of the input pixel group across varying dimensions, thereby dramatically reducing time overhead. Building on CTC-RtE, a Multidimensional Thumbnail-Preserving Encryption (MD-TPE) framework is designed, capable of adapting to pixel groups of different lengths. Furthermore, a diffusion step is introduced after the ranking operation to ensure a more uniform distribution of pixel values in the encrypted image. Experimental results demonstrate that MD-TPE achieves O(1) time encryption across multiple dimensions, outperforming existing methods in time efficiency. Specifically, for a 256 \(\times \) × 256 image with pixel groups of size two, MD-TPE achieves a 94.02% improvement in efficiency compared to F-TPE. The effectiveness of the diffusion step is validated through adjacent pixel correlation analysis and histogram analysis.