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.

中文翻译：

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基于预测误差扩展的加密3D模型可逆数据隐藏

由于3D模型可以直观地显示现实世界的信息，因此在许多应用领域中都存在潜在的场景，例如建筑模型和医疗器官模型。然而，未经授权的用户可以容易地获得通过互联网共享的3D模型。为了解决云中3D模型的安全性问题，提出了一种基于预测误差扩展的可逆3D模型隐藏数据隐藏方法。在这种方法中，对原始3D模型进行预处理，并使用Paillier密码系统对3D模型的顶点进行加密。在云中，为了提高数据提取的准确性，设计了染色方法，将所有顶点分为嵌入式集和参考集。之后，通过用方向矢量扩展预测误差的方向来嵌入秘密数据。使用参考集计算嵌入集中顶点的预测误差，并根据映射表获得方向矢量，该映射表旨在将多个位映射到方向矢量。可以通过比较预测误差的方向和方向矢量之间的角度来提取秘密数据，并可以使用参考集恢复原始模型。实验结果表明，与现有的加密3D模型数据隐藏方法相比，该方法具有更高的数据隐藏能力，提高了数据提取的准确性。而且，直接解密的模型失真较小。旨在将几个位映射到方向向量。可以通过比较预测误差的方向和方向矢量之间的角度来提取秘密数据，并可以使用参考集恢复原始模型。实验结果表明，与现有的加密3D模型数据隐藏方法相比，该方法具有更高的数据隐藏能力，提高了数据提取的准确性。而且，直接解密的模型失真较小。旨在将几个位映射到方向向量。可以通过比较预测误差的方向和方向矢量之间的角度来提取秘密数据，并可以使用参考集恢复原始模型。实验结果表明，与现有的加密3D模型数据隐藏方法相比，该方法具有更高的数据隐藏能力，提高了数据提取的准确性。而且，直接解密的模型失真较小。并提高了数据提取的准确性。而且，直接解密的模型失真较小。并提高了数据提取的准确性。而且，直接解密的模型失真较小。