Advancing Secret Sharing in 3D Models Through Vertex Index Sharing

Secret sharing is a robust data protection technique that secures sensitive information by partitioning it into multiple shares, such that the original data can only be reconstructed when a sufficient number of shares are combined. While this method has seen remarkable progress in the realm of images, its exploration and application in 3D models remain in their early stages. Given the growing prominence of 3D models in multimedia applications, ensuring their security and privacy has emerged as a critical area of research. At present, secret sharing approaches for 3D models predominantly rely on the vertex coordinates of the model as the basis for embedding and reconstructing secret messages. However, due to the limited quantity of vertex coordinates, these methods face significant constraints in embedding capacity, thereby limiting the potential of 3D models in secure data sharing. In contrast, the vertex indices of polygons, characterized by higher information density and greater structural flexibility, present a promising alternative medium for embedding secret shares. Building on this premise, the present study investigates the feasibility of leveraging shared vertex indices as a foundation for message embedding. It highlights the advantages of this approach in enhancing both the embedding capacity and the overall security of 3D models. By integrating the Chinese Remainder Theorem into vertex index-based sharing, the proposed method strengthens existing algorithms, offering improved model protection and enhanced embedding security. Experimental evaluations reveal that, compared to traditional vertex coordinate-based methods, incorporating vertex indices into secret sharing techniques significantly increases embedding efficiency while bolstering the security of 3D models. This study not only introduces an innovative approach to safeguarding 3D model data but also paves the way for the broader application of secret sharing techniques in the future.