Separable and high-capacity reversible data hiding for encrypted 3D mesh models based on dual multi-MSB predictions

Abstract

Three-dimensional (3D) models, essential for building virtual worlds, are encountering growing challenges in privacy and copyright protection as their usage increases. Reversible data hiding (RDH) in encrypted 3D mesh models not only protects the privacy of the original models through encryption but also embeds additional data for covert communication or access control. This paper proposes a high-capacity, separable RDH method for encrypted 3D models. The approach utilizes integer mapping and incorporates an enhanced dual multiple most significant bit (multi-MSB) prediction strategy to maximize embedding capacity. First, each vertex coordinate is scaled to a decimal value within a predefined range. These values are then encoded into binary digits using integer mapping, with the number of digits determined by a compression threshold. Subsequently, all vertices are processed to identify redundant data that served as embedding room using a multi-MSB self-prediction algorithm, significantly increasing the embedding capacity. Next, after disregarding the redundancy in the MSBs of each vertex, the vertices are classified into an embeddable set and a reference set. The embeddable vertices are then further processed to create additional embedding room through secondary multi-MSB prediction. The auxiliary data, compressed using arithmetic coding, is embedded into the multi-MSB of each encrypted vertex, resulting in encrypted vertices that contain both the auxiliary data and available embedding room. Using the auxiliary data, encrypted additional data is embedded into the reserved embedding room within the multi-MSB of each vertex through bit substitution. Finally, the embedded data can be extracted without errors, and the original 3D mesh can be recovered losslessly. The experimental results demonstrate that the proposed method is highly effective, achieving superior embedding capacity compared to several state-of-the-art methods.