SCIENCE CHINA Information Sciences, Volume 60, Issue 12: 122107(2017) https://doi.org/10.1007/s11432-017-9266-1

## 3D textured model encryption via 3D Lu chaotic mapping

• AcceptedSep 26, 2017
• PublishedNov 9, 2017
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### Abstract

In the emerging Virtual/Augmented Reality (VR/AR) era, three dimensional (3D) content will be popularized just as images and videos today. The security and privacy of these 3D contents should be taken into consideration. 3D contents contain surface models and solid models. Surface models include point clouds, meshes and textured models. Previous work mainly focused on the encryption of solid models, point clouds and meshes. This work focuses on the most complicated 3D textured model. We propose a 3D Lu chaotic mapping based encryption method for 3D textured models. We encrypt the vertices, polygons, and textures of 3D models separately using the 3D Lu chaotic mapping. Then the encrypted vertices, polygons and textures are composited together to form the final encrypted 3D textured model. The experimental results reveal that our method can encrypt and decrypt 3D textured models correctly. Furthermore, typical statistic and brute-force attacks can be resisted by the proposed method.

### Acknowledgment

This work was partially supported by National Natural Science Foundation of China (Grant Nos. 61402021, 61401228, 61640216, 61772047), Science and Technology Project of the State Archives Administrator (Grant No. 2015-B-10), Open Funding Project of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (Grant No. BUAA-VR-16KF-09), Fundamental Research Funds for the Central Universities (Grant Nos. 2016LG03, 2016LG04), China Postdoctoral Science Foundation (Grant No. 2015M581841), and Postdoctoral Science Foundation of Jiangsu Province (Grant No.1501019A).

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• Figure 1

(Color online) A full 3D surface model containing vertices, polygons and textures.

• Figure 2

(Color online) Proposed method for 3D textured model encryption.

• Figure 3

(Color online) Simulation results. We test our method on 3D models with various contents.

• Figure 4

(Color online) Decryption with slightly changed keys. The dog and cat examples are shown. We only show the changed keys. The full original keys are shown in Table 1.

• Figure 5

(Color online) Decryption with slightly changed keys. The phone, toy and clock examples are shown. We only show changed keys. The full original keys are shown in Table 1. Note that, in this figure, for each example, we slightly change the original keys twice to show the key-sensitivity of our method. For each example, the decrypted results of both times are completely different from the correctly decrypted results.

• Figure 6

(Color online) VFH of 3D textured models before and after encryption.

• Figure 7

(Color online) Distribution of occupied positions per $z$-coordinate of the 3D textured models before and after encryption.

• Figure 8

(Color online) Encryption and decryption time costs of the proposed method for 3D model encryption against the number of vertices.

• Table 1   The secret keys of the 3D Lu maps in (), where $a=36$, $b=3$, and $c=20$
 Encryption phase Keys Vertices encryption $x_0^{v}=-6.045$, $y_0^{v}=2.668$, $z_0^{v}=16.363$ Polygons encryption $x_0^{p}=-5.045$, $y_0^{p}=2.668$, $z_0^{p}=16.363$ Texture encryption $x_0^{t1}=-6.045$, $y_0^{t1}=2.668$, $z_0^{t1}=20.363$, $x_0^{t2}=-5.045$, $y_0^{t2}=3.668$, $z_0^{t2}=16.363$

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