A Three-Dimensional Infinite Collapse Map with Image Encryption
Abstract
:1. Introduction
2. The 3D Infinite Collapse Map
2.1. Mathematical Definition
2.2. Performance Evaluation
2.2.1. Attractor
2.2.2. Lyapunov Exponent
2.2.3. Sample Entropy
3. An Image Encryption Scheme Based on 3D-ICM
3.1. Key Distribution
3.2. Confusion Part
Algorithm 1. The confusion process of the proposed image encryption scheme. |
Input: The plaintext image and three initial values |
Output: The confusion image |
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3.3. Diffusion Part
3.4. Simulation Results
4. Security Analysis
4.1. Key Security Analysis
4.2. Histogram Analysis
4.3. Correlation Analysis
4.4. Differential Attack
4.5. Two-Dimensional Detrending Fluctuation Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Schemes | ||||
---|---|---|---|---|
Diaconu [33] | 0.0567 | 0.2014 | 0.9731 | 3.8377 |
HZ [34] | 0.1335 | 0.5783 | 2.4913 | 9.9185 |
ZBC1 [35] | 0.0796 | 0.3034 | 1.4824 | 5.8175 |
XLLH [36] | 0.0212 | 0.1019 | 0.4924 | 20.144 |
Proposed method | 0.0171 | 0.0304 | 0.1314 | 0.7021 |
Images | Lena | Gray | Ruler | Boat | Pepper |
---|---|---|---|---|---|
252.0624 | 234.4568 | 227.3544 | 226.3549 | 241.9653 |
Schemes | Horizontal | Vertical | Diagonal |
---|---|---|---|
“Lena” image | 0.9400 | 0.9769 | 0.9567 |
DS [9] | −0.0068 | −0.0062 | 0.0070 |
HZ [34] | 0.0034 | −0.0010 | −0.0002 |
XLLH [36] | 0.0003 | 0.0014 | 0.0022 |
ZBC1 [35] | −0.0054 | 0.0042 | 0.0032 |
LSZ [37] | −0.0015 | −0.0021 | 0.0019 |
Proposed method | −0.0009 | −0.0012 | 0.0010 |
Images | NPCR (%) | UACI (%) | ||||
---|---|---|---|---|---|---|
R | G | B | R | G | B | |
4.1.01.tiff | 99.6189 | 99.6108 | 99.6098 | 33.4652 | 33.4636 | 33.4507 |
4.1.03.tiff | 99.6139 | 99.6201 | 99.6149 | 33.4982 | 33.4678 | 33.4789 |
4.1.04.tiff | 99.6246 | 99.6154 | 99.6098 | 33.4532 | 33.4726 | 33.4592 |
4.2.03.tiff | 99.6052 | 99.6209 | 99.6134 | 33.4585 | 33.4677 | 33.4728 |
4.2.07.tiff | 99.6357 | 99.6258 | 99.6072 | 33.5240 | 33.4584 | 33.4601 |
Lena | 99.6145 | 99.6254 | 99.6275 | 33.4612 | 33.4612 | 33.4704 |
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Yan, W.; Jiang, Z.; Huang, X.; Ding, Q. A Three-Dimensional Infinite Collapse Map with Image Encryption. Entropy 2021, 23, 1221. https://doi.org/10.3390/e23091221
Yan W, Jiang Z, Huang X, Ding Q. A Three-Dimensional Infinite Collapse Map with Image Encryption. Entropy. 2021; 23(9):1221. https://doi.org/10.3390/e23091221
Chicago/Turabian StyleYan, Wenhao, Zijing Jiang, Xin Huang, and Qun Ding. 2021. "A Three-Dimensional Infinite Collapse Map with Image Encryption" Entropy 23, no. 9: 1221. https://doi.org/10.3390/e23091221