## 5 Conclusions  
Addressing the issues of limited embedding capacity and inadequate security encountered in current RDH-EI algorithms based on secret sharing, we propose an RDH-EI algorithm based on AMED prediction and MSS secret sharing. We have developed a uniquely designed AMED prediction technique with high accuracy and integrated it with the MSS scheme to create this advanced RDH-EI algorithm. The algorithm allows multiple data hiders to independently embed secret data, and receivers can determine the presence of attacks in the transmission environment through identifying information. The experimental results show that compared to existing methods, our algorithm significantly improves the embedding rate, achieving 7.2713 bpp, while achieving a PSNR of \(\infty\). Furthermore, the algorithm exhibits a pixel correlation close to 0 for marked encrypted images, with NPCR and UACI stabilizing around 99.609% and 33.464%, respectively, effectively resisting differential attacks. In the face of various unknown attack methods in diverse and dynamic environments, further enhancements are required to bolster the algorithm's security. Our future endeavors will center on enhancing the embedding rate and extending the algorithm's utility across a range of security scenarios.  
Conceptualization, Z.J. and M.Z.; methodology, Z.J. and W.D.; software, Z.J., C.J. and F.D.; validation, C.J. and F.D.; formal analysis, Z.J. and W.D.; resources, M.Z.; data curation, C.J. and F.D.; writing--original draft preparation, Z.J. and W.D.; writing--review and editing, Z.J., M.Z. and C.J.; visualization, W.D. and F.D.; supervision, M.Z.; project administration, M.Z. and C.J.; funding acquisition, M.Z. All authors have read and agreed to the published version of the manuscript.  
This research was supported by The National Natural Science Foundation of China, Funding Number: 62272478, 62102450, 62102451.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Images**} & \multicolumn{6}{c}{**NPCR (\%)**} & \multicolumn{6}{c}{**UACI (\%)**} \\ \cline{2-11}  & \(\mathbf{IM_{1}}\) & \(\mathbf{IM_{2}}\) & \(\mathbf{IM_{3}}\) & \(\mathbf{IM_{4}}\) & \(\mathbf{IM_{5}}\) & \(\mathbf{IM_{1}}\) & \(\mathbf{IM_{2}}\) & \(\mathbf{IM_{3}}\) & \(\mathbf{IM_{4}}\) & \(\mathbf{IM_{5}}\) \\ \hline Airplane & 99.6853 & 99.6512 & 99.6452 & 99.6021 & 99.5324 & 33.4852 & 33.1220 & 33.6542 & 33.4526 & 33.7512 \\ Baboon & 99.5624 & 99.6452 & 99.6975 & 99.5135 & 99.4965 & 33.8102 & 33.5615 & 33.6412 & 33.2351 & 33.1522 \\ Lena & 99.5621 & 99.4860 & 99.6541 & 99.7031 & 99.6514 & 33.5615 & 33.8143 & 33.2545 & 33.3254 & 33.8472 \\ Jetplane & 99.7112 & 99.6421 & 99.5815 & 99.3215 & 99.6256 & 33.6781 & 33.2548 & 33.8972 & 33.2482 & 33.7957 \\ Tiffany & 99.5568 & 99.5406 & 99.6452 & 99.5945 & 99.6512 & 33.2418 & 33.5751 & 33.7251 & 33.1241 & 33.7512 \\ Man & 99.5612 & 99.6425 & 99.7029 & 99.5612 & 99.4942 & 33.1458 & 33.5216 & 33.5782 & 33.9875 & 33.5442 \\ \hline \hline \end{tabular}
\end{table}
Table 13: The embedding rates and peak signal-to-noise ratio of the algorithm proposed in this paper across various datasets.  
Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.