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Separable Reversible Data Hiding for Encrypted Three-Dimensional Models Based on Spatial Subdivision and Space Encoding

Reversible data hiding for encrypted media not only preserves the privacy of the media content but also can convey additional information during message transmission. Some studies advocate separability, that is, the message can be correctly extracted irrespective of whether the encrypted media has been decrypted. However, current research has focused on encrypted images. Urgent research is required on encrypted three-dimensional (3D) models. This paper proposes a separable reversible data hiding method based on spatial subdivision and space encoding for encrypted 3D models. A bounding volume is first constructed using the vertices with boundary values in the processing model. Each vertex coordinate value is then converted into a ratio (between 0 and 1) of the distance between the vertex and minimum boundary point to the side length of the bounding volume. The owner of the 3D model then uses a secret key to encrypt all ratios except those of the boundary vertices to obtain an encrypted 3D model of the same size as the original model. The spatial subdivision technique and a subdivision threshold are subsequently used to divide the bounding volume into a series of blocks and simultaneously control the vertex distortion. The secret message is embedded in the encrypted vertex by using the space encoding method with an embedding threshold. Experimental results indicate that the proposed algorithm enables high privacy, performs separable reversible data hiding, and has low computational complexity, high embedding capacity, and controllable distortion.