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Reversible data hiding in encrypted images (RDH-EI) schemes based on secret sharing have emerged as a significant area of research in privacy protection. However, existing algorithms have limitations, such as low embedding capacity and insufficient privacy protection. To address these challenges, this paper proposes an RDH-EI scheme based on adaptive median edge detection (AMED) and matrix-based secret sharing (MSS). The algorithm creatively leverages the AMED technique for precise image prediction and then integrates the (r, n)-threshold MSS scheme to partition the image into n encrypted images. Simultaneously, it embeds identifying information during segmentation to detect potential attacks during transmission. The algorithm allows multiple data hiders to embed secret data independently. Experimental results demonstrate that the proposed algorithm significantly enhances the embedding rate while preserving reversibility compared to current algorithms. The average maximum embedding rates achieved are up to 5.8142 bits per pixel (bpp) for the (3, 4)-threshold scheme and up to 7.2713 bpp for the (6, 6)-threshold scheme. With disaster-resilient features, the algorithm ensures (n − r) storage fault tolerance, enabling secure multi-party data storage. Furthermore, the design of the identifying information effectively evaluates the security of the transmission environment, making it suitable for multi-user cloud service scenarios. [ABSTRACT FROM AUTHOR]

In the current distributed environment, reversible data hiding in encrypted domain (RDH-ED) cannot grant corresponding privileges according to users' identity classes. To address this issue, this paper proposes a hierarchical authorization structure embedding scheme based on secret image sharing (SIS) and users' hierarchical identities. In the first embedding, the polynomial coefficient redundancy generated in the encryption process of the SIS is utilized by the image owner. For the second, the participants are categorized into two parts. One is core users with adaptive difference reservation embedding, and the other is ordinary users with pixel bit replacement embedding. At the time of reconstruction, more than one core user must provide pixel differences, which grants more privileges to core users. The experimental results demonstrate that the average embedding rate (ER) of the test images is 4.3333 bits per pixel (bpp) in the (3, 4) threshold scheme. Additionally, the reconstructed image achieves a PSNR of +∞ and an SSIM of 1. Compared to existing high-performance RDH-ED schemes based on secret sharing, the proposed scheme with a larger ER maintains strong security and reversibility. Moreover, it is also suitable for multiple embeddings involving multilevel participant identities. In conclusion, the results underscore the efficacy of our technique in achieving both security and performance objectives within a complex distributed setting. [ABSTRACT FROM AUTHOR]