A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain
Abstract
:1. Introduction
- A greedy algorithm is employed to classify the vertex into the embedded set and the reference set to increase the embedding capacity.
- The module length of the prediction error is expanded to embed data in the encryption domain.
- The embedding capacity of the proposed method is superior to that of the existing RDH-ED methods.
2. Related Work
3. Background
4. The Proposed Method
4.1. Preprocessing and Encryption
4.2. Processes of Data Hiding
4.2.1. Vertex Classification
4.2.2. Prediction Error Computation
4.2.3. Data Embedding
4.2.4. Parameter d
4.3. Data Extraction and Model Recovery
- -
- Step b-1. All vertices are classified into the embedded set and the reference set according to the greedy algorithm.
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- Step b-2. The prediction error of vi″ is computed.
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- Step b-3. Equation (21) is used to obtain the range of sw:
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- Step b-4. Via d and sw, the original 3D model is recovered as:
5. Experimental Results and Discussion
5.1. Discussion of Parameters d and n
5.2. Vertex Classification Comparison
5.3. Performance Comparison
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
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Jiang [41] | Li [42] | Li [43] | Proposed | |
---|---|---|---|---|
Vertex Classification | Yes | No | Yes (Dyeing algorithm) | Yes (Greedy algorithm) |
PEE | No | No | Yes (Angle) | Yes (Module length) |
Embedded bits in one vertex | One | Less than one | More than one | More than one |
Side information | Small | Huge | Huge | Small |
Encryption | Stream bit encryption | Paillier | Paillier | Paillier |
Vertex List | Face Information | ||||
---|---|---|---|---|---|
Index of Vertex | X-Axis | Y-Axis | Z-Axis | Index of Face | Elements in Each Face |
1 | v1,x | v1,y | v1,z | 1 | (2, 3, 1) |
2 | v2,x | v2,y | v2,z | 2 | (5, 1, 4) |
3 | v3,x | v3,y | v3,z | 3 | (3, 6, 7) |
4 | v4,x | v4,y | v4,z | 4 | (5, 2, 1) |
5 | v5,x | v5,y | v5,z | 5 | (3, 10, 7) |
... | ... | ... | ... | ... | ... |
3D Model | Nv | Proposed | Jiang [41] | Li [43] | |||
---|---|---|---|---|---|---|---|
Se | Connected Vertex | Se | Connected Vertex | Se | Connected Vertex | ||
Fairy | 4252 | 1389 | 0 | 1356 | 312 | 1086 | 0 |
Boss | 10,663 | 3412 | 0 | 3515 | 948 | 2498 | 0 |
Devil | 27,872 | 8640 | 0 | 8357 | 2146 | 6944 | 0 |
Thing | 110,812 | 34,905 | 0 | 35,820 | 9420 | 23,368 | 0 |
Lord | 250,343 | 80,109 | 0 | 81,521 | 21,321 | 53,548 | 0 |
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Luo, T.; Li, L.; Zhang, S.; Wang, S.; Gu, W. A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain. Symmetry 2021, 13, 1090. https://doi.org/10.3390/sym13061090
Luo T, Li L, Zhang S, Wang S, Gu W. A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain. Symmetry. 2021; 13(6):1090. https://doi.org/10.3390/sym13061090
Chicago/Turabian StyleLuo, Ting, Li Li, Shanqin Zhang, Shenxian Wang, and Wei Gu. 2021. "A Novel Reversible Data Hiding Method for 3D Model in Homomorphic Encryption Domain" Symmetry 13, no. 6: 1090. https://doi.org/10.3390/sym13061090