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.

Until now, some reversible data hiding in encrypted images (RDH-EI) schemes based on secret sharing (SIS-RDHEI) still have the problems of not realizing diffusivity and high embedding capacity. Therefore, this paper innovatively proposes a high capacity RDH-EI scheme that combines adaptive most significant bit (MSB) prediction with secret sharing technology. Firstly, adaptive MSB prediction is performed on the original image and cryptographic feedback secret sharing strategy encrypts the spliced pixels to spare embedding space. In the data hiding phase, each encrypted image is sent to a data hider to embed the secret information independently. When $r$ copies of the image carrying the secret text are collected, the original image can be recovered lossless and the secret information can be extracted. Performance evaluation shows that the proposed method in this paper has the diffusivity, reversibility, and separability. The last but the most important, it has higher embedding capacity. For $512 \times 515$ grayscale images, the average embedding rate reaches 4.7358 bits per pixel (bpp). Compared to the average embedding rate that can be achieved by the Wang et al.'s SIS-RDHEI scheme, the proposed scheme with (2, 2), (2, 3), (2, 4), (3, 4), and (3, 5)-threshold can increase by 0.7358 bpp, 2.0658 bpp, 2.7358 bpp, 0.7358 bpp, and 1.5358 bpp, 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 limited channel robustness of invertible neural networks against Gaussian noise, JPEG compression, and scaling/resampling in image information hiding, while maintaining their embedding capacity, we propose an invertible steganography algorithm that integrates a dual-branch attention mechanism in the frequency domain. First, a dual-branch attention module is designed to adaptively generate embedding weights from both global subband energy and local texture pixel dimensions after wavelet multi-frequency decomposition, thereby constructing a four-channel extended secret payload. Second, a four-channel extension strategy is developed to enhance embedding capacity without introducing random noise distortion. Additionally, dual enhancement mechanisms are employed to preprocess the original carrier before embedding, optimize frequency-domain feature distribution, and restore images contaminated by noise, compression, or scaling attacks during reconstruction. Experimental results demonstrate that under a 1:1.34 embedding ratio, the proposed algorithm achieves a clean-channel C-PSNR of 36.27 dB; under Gaussian noise (σ=10) and JPEG(QF=50) attacks, PSNR values for all channels reach 27.96 dB and 29.43 dB respectively. Compared to comparable models without attention mechanisms, this approach improves carrier quality and secret recovery metrics by over 2 dB on average, combining high transmission capacity with excellent channel robustness and visual imperceptibility.