## 1 Introduction
However, secret sharing may reduce pixel correlation in the sub-secret image, resulting in wasted redundant space and potential security vulnerabilities. In cases of tampering during transmission, these algorithms may struggle to effectively detect such behavior due to the lack of a reference for confirmation, as both tampered and legitimate marked encrypted images appear visually indistinguishable as noisy images. This limitation compromises the ability to verify the authenticity of transmitted data in practical applications, posing security risks. To address this issue, this paper proposes an RDH-EI algorithm based on adaptive median edge detection (AMED) and MSS secret sharing for distributed environments. Firstly, we introduce the innovative AMED pixel prediction technology, which achieves high prediction accuracy. Leveraging AMED technology and Huffman coding, we predict and recode the original image to generate the transitional image. Subsequently, using \((r,\,n)\)-threshold MSS secret sharing in the \(GF(2^{8})\) domain, the transitional image is fragmented into \(n\) encrypted images, with identifying information embedded. The encrypted images are then distributed to individual data hiders, who independently embed secret data to acquire \(n\) marked encrypted images. Upon collecting \(r\) marked encrypted images, the original image can be reconstructed using the corresponding key, and the embedded data can be extracted. Discrepancies in the embedded identifying information before and after embedding can reveal tampering attacks. The algorithm is illustrated in the context of the IPR scenario in Figure 1b. Experimental results indicate a marked improvement in the embedding capacity of the proposed algorithm compared to the current algorithms [5; 14; 21; 22; 23; 24]. Furthermore, the algorithm also possesses resilience, allowing up to \((n-r)\) fault points to occur. Table 1 outlines the limitations of previous algorithms and the solutions provided by the algorithm presented in this paper. The main contributions of this paper's algorithm are as follows:  
1. Introduction of the innovative AMED prediction technique, achieving superior prediction accuracy and surpassing the limitations of fixed predictors in existing MED techniques [15; 26]. This enhancement significantly boosts the embedding capability of the algorithm. 2. This article introduces an RDH-EI algorithm based on AMED prediction and MSS secret sharing, innovatively executing image segmentation within the \(GF(2^{8})\) domain. Compared to existing algorithms [23], the proposed method does not require additional data to store overflow pixels and avoids complex preprocessing, effectively reducing the usage of embedding space. 3. The creative design of identifying information effectively enhances the monitoring of the security of the transmission environment and ensures the authenticity of the data. 4. In comparison with existing algorithms, the algorithm proposed in this paper not only guarantees reversibility but also effectively increases embedding rates, thereby enhancing its practicality. \begin{table}
\begin{tabular}{c c c} \hline \hline
**RDH-EI Algorithms** & **Limitations** & **Approach to Problem-Solving** \\ \hline [PERSON] et al. [4] & Low security & Using scrambling and exclusive or (XOR) encryption \\ [PERSON] et al. [10] and [PERSON] et al. [26] & Low prediction accuracy & Using AMED technology \\ [PERSON] et al. [13] & High-entropy constraints on & Pre-encryption recoding \\  & ciphertext state & Utilizing the characteristics of the cipher \\ [PERSON] et al. [18] & Embedding rate constrained by & itself to embed data. \\ [PERSON] et al. [24] and [PERSON] et al. [25] & Inability to ensure data integrity & Designing identifying information \\  & & for detection \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of previous algorithm limitations and solutions offered by our proposed algorithm. Figure 1: Application scenarios of double-blind IPR. (**a**) Traditional review application scenario.