Robust reversible watermarking in an encrypted domain is a technique that preserves privacy and protects copyright for multimedia transmission in the cloud. In general, most models of buildings and medical organs are constructed by three-dimensional (3D) models. A 3D model shared through the internet can be easily modified by an unauthorized user, and in order to protect the security of 3D models, a robust reversible 3D models watermarking method based on homomorphic encryption is necessary. In the proposed method, a 3D model is divided into non-overlapping patches, and the vertex in each patch is encrypted by using the Paillier cryptosystem. On the cloud side, in order to utilize addition and multiplication homomorphism of the Paillier cryptosystem, three direction values of each patch are computed for constructing the corresponding histogram, which is shifted to embed watermark. For obtaining watermarking robustness, the robust interval is designed in the process of histogram shifting. The watermark can be extracted from the symmetrical direction histogram, and the original encrypted model can be restored by histogram shifting. Moreover, the process of watermark embedding and extraction are symmetric. Experimental results show that compared with the existing watermarking methods in encrypted 3D models, the quality of the decrypted model is improved. Moreover, the proposed method is robust to common attacks, such as translation, scaling, and Gaussian noise.

Since 3D models can intuitively display real-world information, there are potential scenarios in many application fields, such as architectural models and medical organ models. However, a 3D model shared through the internet can be easily obtained by an unauthorized user. In order to solve the security problem of 3D model in the cloud, a reversible data hiding method for encrypted 3D model based on prediction error expansion is proposed. In this method, the original 3D model is preprocessed, and the vertex of 3D model is encrypted by using the Paillier cryptosystem. In the cloud, in order to improve accuracy of data extraction, the dyeing method is designed to classify all vertices into the embedded set and the referenced set. After that, secret data is embedded by expanding direction of prediction error with direction vector. The prediction error of the vertex in the embedded set is computed by using the referenced set, and the direction vector is obtained according to the mapping table, which is designed to map several bits to a direction vector. Secret data can be extracted by comparing the angle between the direction of prediction error and direction vector, and the original model can be restored using the referenced set. Experiment results show that compared with the existing data hiding method for encrypted 3D model, the proposed method has higher data hiding capacity, and the accuracy of data extraction have improved. Moreover, the directly decrypted model has less distortion.