Reversible Data Hiding for Encrypted 3D Model Based on Prediction Error Expansion

Abstract

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.

Application of Realistic 3D Model in Building Prefabricated Nanomaterial Structure

“…From the point of view of the structure, the structure should be divided into the rationality of the structure, such as the composite floor supported by four sides, the direction of plate splitting (plate seam) should be perpendicular to the long side; the joint of the component is selected in the part of low stress; and the sleeve joint of column-beam structure system of high-rise building should avoid plastic hinge position. Specifically, the end of the top beam of the column foot of the first layer and the tension side column of the column beam structure should not be designed for sleeve connection [ 19 , 20 ]. Avoid the plastic hinge position of the beam end, and the connecting node of the beam should not be located within the range of H from the beam end; unify and reduce component specifications as much as possible; it should be coordinated with the separation of adjacent related components, such as the separation of composite plates and support beams [ 21 ].…”

A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain

“…BER is used to evaluate the correctness of the data extraction. For the parameter D, we compute the maximum module lengths for the 3D models, and it is concluded that D < 250 [43]. For the parameter D, we compute the maximum module lengths for the 3D models, and it is concluded that D < 250 [43].…”

“…Moreover, the cipher mapping table should be transmitted to the receiver for data decryption. In order to increase the embedding capacity, Li et al encrypted the 3D model using the Paillier cryptosystem and used the dyeing algorithm to classify vertices into the embedded set and the reference set for data embedding [43]. To embed more than one bit into the embedded vertex, each bit is mapped to the direction of the vertex, which should be recorded in a mapping table.…”

“…Finally, to better distinguish the proposed method from some related methods, some differences are listed in Table 1. Similar to Jiang's [41] and Li's [43] methods, the vertex is classified, but the proposed method uses a greedy algorithm to improve the embedding capacity. Similarly to Li's [43] method, the proposed method uses PEE but expands the module length of the prediction error to embed data.…”

“…Similar to Jiang's [41] and Li's [43] methods, the vertex is classified, but the proposed method uses a greedy algorithm to improve the embedding capacity. Similarly to Li's [43] method, the proposed method uses PEE but expands the module length of the prediction error to embed data. Compared with Jiang's [41] and Li's [42] methods, the proposed method embeds more than one bit for one vertex.…”