Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application
Abstract
:1. Introduction
2. Preliminaries
3. Discrete-Time Fractional-Order Food Chain Model
3.1. Stability of Fixed Points
3.1.1. Stability Analysis of
3.1.2. Stability Analysis of
3.1.3. Stability Analysis of
3.1.4. Stability Analysis of
4. Numerical Simulations
5. Hybrid Image Encryption Scheme
6. Security Analysis of the Proposed Scheme
6.1. Numerical Simulations
6.2. Keyspace Analysis
6.3. Analysis of Key Sensitivity
6.4. Analysis of Information Entropy
6.5. Differential Attacks Analysis
6.6. Resistance against Other Attacks
7. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Image | |||
---|---|---|---|
Original King Tut | |||
Encrypted King Tut | 289 | 293 | 278 |
Original baboon | |||
Encrypted baboon | 252 | 248 | 228 |
Original pepper | |||
Encrypted pepper | 267 | 309 | 215 |
Original pyramids | |||
Encrypted pyramids | 298 | 209 | 269 |
Image | Key Value | Mismatch (%) | Average Difference (%) |
---|---|---|---|
King Tut | |||
King Tut | |||
King Tut | |||
Baboon | |||
Baboon | |||
Baboon | |||
Pepper | |||
Pepper | |||
Pepper | |||
Pyramids | |||
Pyramids | |||
Pyramids |
Image | Information Entropy (R) | (G) | (B) |
---|---|---|---|
King Tut | 7.9975 | 7.9973 | 7.9977 |
Baboon | 7.9968 | 7.9966 | 7.9978 |
Pepper | 7.9967 | 7.9976 | 7.9967 |
Egyptian pyramids | 7.9972 | 7.9974 | 7.9975 |
Image | NPCR (R, G, B) % | UACI (R, G, B) % |
---|---|---|
King Tut | 99.6268, 99.6402, 99.6361 | 33.531, 33.531, 33.533 |
Baboon | 99.6332, 99.6329, 99.6241 | 33.537, 33.536, 33.536 |
Pepper | 99.6112, 99.6351, 99.6293 | 33.528, 33.506, 33.511 |
Egyptian pyramids | 99.6339, 99.6383, 99.6154 | 33.471, 33.483, 33.485 |
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Askar, S.; Al-khedhairi, A.; Elsonbaty, A.; Elsadany, A. Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application. Symmetry 2021, 13, 161. https://doi.org/10.3390/sym13020161
Askar S, Al-khedhairi A, Elsonbaty A, Elsadany A. Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application. Symmetry. 2021; 13(2):161. https://doi.org/10.3390/sym13020161
Chicago/Turabian StyleAskar, Sameh, Abdulrahman Al-khedhairi, Amr Elsonbaty, and Abdelalim Elsadany. 2021. "Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application" Symmetry 13, no. 2: 161. https://doi.org/10.3390/sym13020161