To solve the limitations of reversible data hiding in encrypted domains (RDH-ED) that cannot be applied to a distributed variable security environment, a novel RDH-ED scheme based on variable threshold image secret sharing (VTSIS) is proposed. Initially, a security vulnerability analysis of existing changing thresholds in a bivariate polynomial-based secret image sharing (TCSIS) method is conducted and validated through experiments. Subsequently, enhancements are made to the VTSIS scheme to rectify the identified security loopholes. During the image encryption process, additional data can be embedded into the redundancy of VTSIS, which results in a large embedding rate and high security. Finally, theoretical analysis and experimental proofs are carried out for the proposed scheme, and the results show that our scheme broadens the application scenarios of RDH-ED. Notably, the scheme eliminates the need for preprocessing and has the advantages of high security, a large embedding rate, and complete reversibility.

To address the vulnerability of the widely used block permutation and co-XOR (BPCX) encryption algorithm in reversible data-hiding in the encrypted domain (RDH-ED), which is susceptible to known-plaintext attacks (KPAs), and to enhance embedding capacity, we propose a novel technique of reversible data-hiding in encrypted images (RDH-EI). This method incorporates adaptive quadtree partitioning and most significant bit (MSB) prediction. To counteract KPAs, we introduce pixel modulation specifically targeting pixels within blocks of the same level during the encryption phase. During data embedding, we utilize tagging bits to indicate the state of the pixel blocks, capitalizing on pixel redundancy within those blocks to augment embedding capacity. Our experimental results demonstrate that our method not only achieves reversibility and separability but also significantly boosts embedding capacity and method security. Notably, the average embedding rate across the 10,000 images tested stands at 2.4731, surpassing previous methods by 0.2106 and 0.037, respectively.

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.

In the current distributed environment, reversible data hiding in encrypted images has the disadvantages of low security and nonprogressivity. To address this problem, a homomorphic embedding algorithm is proposed based on polynomial secret sharing (PSS) and Chinese remainder theorem. First, the image owner encrypts the carrier image in streaming encryption and sends it to the data hider. Then, the data hider utilizes PSS to split the carrier image into n shares. At the same time, extra secrets after SS are embedded into the carrier shares using homomorphism. After splitting by Chinese remainder theorem, every share of the embedded data is divided into some sub-shares and then distributed to the participants. The participants that satisfy the threshold condition provide part or all of the sub-shares according to the authority of the data extractor. If each participant provides all sub-shares, the secrets and carrier image can be reconstructed completely. If each participant provides part of the sub-shares, the secrets and carrier image can be reconstructed partly. The experimental results show that the proposed scheme has progressivity, high security, and a large embedding rate (ER). Meanwhile, the ER is not affected by the carrier image.

To address the issues of image quality degradation and file size expansion encountered during reversible data hiding (RDH) of JPEG images, a JPEG reversible data hiding algorithm based on block smoothness estimation and optimal zero coefficient selection is proposed. Firstly, a block smoothness estimation strategy is designed based on the number of zero coefficients and non-zero quantisation table values within DCT blocks, prioritising DCT blocks with higher smoothness for information embedding. Subsequently, under a given embedding payload, an optimal zero coefficient selection strategy is introduced. Blocks are partitioned into embedding regions and non-embedding regions based on a preset position threshold T. Within embedding regions, the frequency of zero coefficients at different positions across all blocks is statistically analysed, with embedding prioritised at positions exhibiting the highest zero coefficient frequency to enhance embedding efficiency. Concurrently, by setting positive and negative displacement gaps to constrain the modification range of non-zero coefficients, invalid shifts are minimised. This further enhances visual quality while controlling file expansion. Experimental results demonstrate that, compared to existing algorithms, the proposed method achieves a peak signal-to-noise ratio improvement of 0.75 to 3.62 dB under fixed embedding capacity. File expansion is reduced by 1038 to 2243 bits, whilst enabling fully reversible image restoration.