Four-Pixel Sum-Preserving Encryption Using the Chaotic Map for High Thumbnail-Preserving Image Security

In cloud environments, traditional image encryption techniques often protect privacy at the expense of usability. To address this problem, thumbnail-preserving encryption (TPE) has been developed. In TPE, all information is hidden except for a recognizable low-resolution thumbnail of the encrypted image. This paper proposes a four-pixel sum-preserving encryption (SPE) method based on the use of a chaotic map. The method specifically addresses the problem of unencrypted residual pixels that arises with existing TPE schemes, particularly the three-pixel SPE scheme. This problem stems from the fact that pixel group sizes (which are powers of three) are not integer divisors of typical image block sizes (which are powers of two). The proposed method also offers higher security, algorithmic robustness, and computational efficiency. A sum-preserving substitution operation ensures that the sum of the pixel values in each encrypted four-pixel group is unchanged after encryption, guaranteeing perfect reversibility. Experimental results demonstrated that the design effectively hides the high-frequency details of an image while producing a recognizable thumbnail. Furthermore, the use of four-pixel SPE ensures a large key space and high sensitivity, resulting in high resistance to statistical and brute-force attacks.