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Four-pixel sum-preserving encryption using the chaotic map for high thumbnail-preserving image security.
Chia-Hung Kao1,2, Guan-Zhen Chen3, Yi-You Hou4
1Department of Engineering Science, National Cheng Kung University, Tainan, 701, Taiwan. n98134015@gs.ncku.edu.tw.
Scientific Reports
|July 8, 2026
Summary
This study introduces a novel four-pixel sum-preserving encryption (4px-SPE) method to enhance thumbnail-preserving encryption (TPE) security. This approach effectively protects image privacy in cloud services while ensuring thumbnail usability.
Area of Science:
- Computer Science
- Cryptography
- Image Processing
Background:
- Cloud photo-sharing services risk user privacy through exposed thumbnails.
- Thumbnail-preserving encryption (TPE) aims to encrypt images while retaining thumbnail functionality.
- Existing sum-preserving encryption (SPE) methods have limitations with block alignment and plaintext residuals.
Purpose of the Study:
- To develop an improved SPE method for TPE that addresses limitations of existing techniques.
- To enhance image privacy in cloud environments without compromising thumbnail usability.
- To propose a secure and efficient TPE framework using a novel SPE mapping.
Main Methods:
- Introduced a four-pixel SPE (4px-SPE) mapping, a piecewise bijection on 8-bit pixel quadruples, preserving the four-pixel sum and ensuring perfect invertibility.
- Integrated the 4px-SPE into a permutation-substitution TPE framework.
- Utilized a 256-bit master key with deterministic, hash-based key derivation for generating per-image/block keys and permutations, avoiding plaintext-derived material.
Main Results:
- Validated the 4px-SPE mapping's invertibility through mathematical proof and exhaustive verification of all possible quadruples.
- Experimental results on grayscale and color images demonstrated high entropy and lossless recovery.
- The proposed TPE framework successfully maintained thumbnail usability while enhancing image privacy.
Conclusions:
- The novel 4px-SPE mapping provides a secure and efficient solution for thumbnail-preserving encryption.
- This method effectively mitigates privacy risks associated with cloud-based photo sharing.
- The integration into a permutation-substitution TPE framework offers a robust approach to image privacy and thumbnail utility.
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