Reversible data hiding in encrypted 3D meshes is a critical technique for safeguarding 3D content while ensuring perfect reversibility and structural integrity. However, existing prediction-based approaches often face challenges such as limited embedding capacity, ineffective vertex classification, and the absence of authentication support. To address these limitations, this paper proposes a novel and robust framework that integrates effective vertex traversal, vertical embedding, and multi-hider secret sharing. The traversal strategy improves prediction accuracy by identifying high-quality embeddable-reference vertex pairs, while the vertical embedding design allows each vertex to carry both hidden data and an authentication code, enabling pre-embedding model authentication. Moreover, multi-MSB prediction is combined with Huffman coding to compress auxiliary information and improve embedding efficiency. To further enhance robustness and capacity, a threshold secret sharing scheme is introduced, allowing multiple data hiders, and securely reusing previously non-embeddable bits for message embedding. Unlike conventional sharing methods, this design significantly increases usable space while maintaining reversibility. Experimental results on various 3D models show that the proposed method achieves near-100% embedding rates and outperforms existing techniques in embedding capacity, authentication, and robustness, offering a new benchmark for secure and authenticable data hiding in encrypted 3D mesh environments.
TSAI et al. (Mon,) studied this question.