A Novel Threshold Changeable Secret Image Sharing Scheme
Abstract
:1. Introduction
2. Related Work
3. Preliminaries
3.1. Two-Variable One-Way Function
3.2. Yuan et al.’s Secret Sharing Scheme with a Changeable Threshold
3.2.1. Sharing Procedure
3.2.2. Recovering Procedure
4. Proposed Scheme
4.1. Secret Sharing Procedure
4.1.1. Share Generation Phase
Algorithm 1 Polynomial generator. |
Input:, j, , |
Output: |
; |
; |
while do |
end while |
4.1.2. Stego Images Generation Phase
4.2. Recovery Procedure
5. Experiment and Analysis
5.1. Simulation Results
5.2. Performance Analysis
5.3. Security Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Notation | Meaning |
---|---|
S | Gray-scale secret image S |
C | Gray-scale cover image C |
and are the width and height of secret image S | |
and is the width and height of cover image C | |
n | The number of participants |
Participant i | |
The stego images holed by participant | |
N | The number of changeable thresholds |
The value of the changeable threshold | |
m | A prime number, and |
The polynomial corresponding to threshold | |
A two-variable one-way function | |
The identification of participant | |
The key corresponding to threshold | |
Coefficient operator. If , then | |
The ceiling function | |
The flooring function | |
D | Converted data of secret image |
R | Cover data of the cover image |
M | Non-embedded location map m-ary data |
Location map share data of participan |
Cover Images | Stego 1 | Stego 2 | Stego 3 | Stego 4 | Stego 5 | Stego 6 | Average |
---|---|---|---|---|---|---|---|
Lena | 47.14 | 47.13 | 47.16 | 47.17 | 47.13 | 47.14 | 47.15 |
Peppers | 47.20 | 47.19 | 47.22 | 47.20 | 47.23 | 47.22 | 47.21 |
Boat | 47.22 | 47.13 | 47.22 | 47.24 | 47.15 | 47.20 | 47.19 |
Fruits | 47.03 | 47.12 | 47.00 | 47.14 | 47.03 | 47.10 | 47.07 |
Couple | 47.15 | 47.22 | 47.22 | 47.13 | 47.15 | 47.22 | 47.18 |
Crowd | 47.17 | 47.16 | 47.15 | 47.17 | 47.13 | 47.15 | 47.15 |
Airplane | 47.11 | 47.12 | 47.13 | 47.13 | 47.12 | 47.11 | 47.12 |
Tiffany | 47.03 | 47.14 | 47.11 | 47.14 | 47.06 | 47.03 | 47.08 |
Barbara | 47.16 | 47.19 | 47.19 | 47.18 | 47.17 | 47.20 | 47.18 |
m | Pixel Change Range | PSNR |
---|---|---|
7 | [−3, 3] | 47.15 |
11 | [−5, 5] | 43.32 |
13 | [−6, 6] | 41.81 |
17 | [−8, 8] | 39.33 |
19 | [−9, 9] | 38.34 |
23 | [−11, 11] | 36.55 |
Number | Thresholds | PSNR (dB) |
---|---|---|
1 | {2, 3, 4} | 44.25 |
2 | {2, 4, 7} | 44.24 |
3 | {3, 4, 5} | 47.15 |
4 | {3, 5, 7} | 47.15 |
5 | {6, 7, 8} | 51.18 |
Functionality | Yang et al. [22] 2007 | Lin et al. [7] 2010 | Ulutas et al. [26] 2013 | Yuan et al. [31] 2016 | Guo et al. [14] 2018 | Liu et al. [33] 2019 | Ours |
---|---|---|---|---|---|---|---|
Threshold | |||||||
Threshold changeability | No | No | No | Yes | No | Yes | Yes |
Collusion Attack Resistance | Yes | Yes | Yes | Yes | Yes | No | Yes |
Number of recovering polynomials | 1 | 1 | 1 | − | 1 | 1 | |
Meaningful stego image | Yes | Yes | Yes | Yes | Yes | No | Yes |
Quality of stego images | 46.0 dB | 48.36 dB | 52.79 dB | 46.02 dB | 48.0 dB | − | 46.65 dB |
Lossless secret image | Yes | Yes | Yes | Yes | Yes | No | Yes |
Lossless cover image | No | Yes | Yes | No | No | No | Yes |
Maximum capacity (pixels) | − | * |
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Wu, G.; Wang, M.; Wang, Q.; Yao, Y.; Yuan, L.; Miao, G. A Novel Threshold Changeable Secret Image Sharing Scheme. Symmetry 2021, 13, 286. https://doi.org/10.3390/sym13020286
Wu G, Wang M, Wang Q, Yao Y, Yuan L, Miao G. A Novel Threshold Changeable Secret Image Sharing Scheme. Symmetry. 2021; 13(2):286. https://doi.org/10.3390/sym13020286
Chicago/Turabian StyleWu, Guohua, Mingyao Wang, Qiuhua Wang, Ye Yao, Lifeng Yuan, and Gongxun Miao. 2021. "A Novel Threshold Changeable Secret Image Sharing Scheme" Symmetry 13, no. 2: 286. https://doi.org/10.3390/sym13020286
APA StyleWu, G., Wang, M., Wang, Q., Yao, Y., Yuan, L., & Miao, G. (2021). A Novel Threshold Changeable Secret Image Sharing Scheme. Symmetry, 13(2), 286. https://doi.org/10.3390/sym13020286