Reversible Data Hiding in Encrypted Polygonal Faces Using Vertex Index Similarity

Reversible data hiding techniques serve as a cornerstone in the protection of embedded information across diverse media. Traditionally, methods applied to 3D models have primarily focused on modifying vertex coordinates. However, this approach neglects the untapped potential of polygonal faces, which, being more abundant than vertices, offer a scalable and efficient avenue for data embedding. By leveraging polygon indices for reversible data hiding—particularly when integrated with encryption—it becomes possible to randomize the model's structure, facilitating secure modifications while preserving geometric integrity. This study introduces an innovative reversible data hiding algorithm that embeds messages within the polygon indices of encrypted 3D models. The algorithm harnesses the inherent similarities among vertex indices to conceal additional information. To maintain the consistency of polygon normal vectors, we implement a right circular shifting mechanism that systematically reorganizes the indices, ensuring that the smallest value consistently occupies the initial position. Additionally, we incorporate techniques such as leading zero count and multi-MSB prediction to enhance embedding capacity while keeping index values within permissible ranges. Experimental results demonstrate that our approach significantly outperforms conventional vertex-based methods, yielding substantial improvements in embedding efficiency. Crucially, the reversible nature of the proposed technique ensures the exact restoration of the original 3D model upon data extraction, guaranteeing zero information loss and no compromise in quality. Moreover, the algorithm is designed to integrate with vertex-based reversible data hiding techniques for encrypted 3D models, potentially enhancing data embedding capacity under compatible conditions.