Abstract
The fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust watermark method in the protection of the copyright of hardware, images, and other electronic files.
This is a preview of subscription content, log in via an institution to check access.
References
Abdeljawad T, 2011. On Riemann and Caputo fractional differences. Comput Math Appl, 62(3):1602–1611. https://doi.org/10.1016/j.camwa.2011.03.036
Anastassiou GA, 2011. About discrete fractional calculus with inequalities. In: Anastassiou GA (Ed.), Intelligent Mathematics: Computational Analysis. Springer, Berlin, Germany, p.575–585. https://doi.org/10.1007/978-3-642-17098-0_35
Atici FM, Eloe P, 2009. Initial value problem in discrete fractional calculus. Proc Amer Math Soc, 137(3):981–989. https://doi.org/10.1090/S0002-9939-08-09626-3
Bai YR, Baleanu D, Wu GC, 2018. A novel shuffling technique based on fractional chaotic maps. Optik, 168:553–562. https://doi.org/10.1016/j.ijleo.2018.04.054
Bastos N, Ferreira R, Torres D, 2011. Discrete-time fractional variational problems. Signal Process, 91(3):513–524. https://doi.org/10.1016/j.sigpro.2010.05.001
Gao H, Gao TG, 2019. Double verifiable image encryption based on chaos and reversible watermarking algorithm. Multim Tools Appl, 78(6):7267–7288. https://doi.org/10.1007/s11042-018-6461-z
Ghose S, Das A, Bhunia AK, et al., 2020. Fractional local neighborhood intensity pattern for image retrieval using genetic algorithm. Multim Tools Appl, in press. https://doi.org/10.1007/s11042-020-08752-6
Han H, 2020. A fractional-order decomposition model of image registration and its numerical algorithm. Comput Appl Math, 39:45. https://doi.org/10.1007/s40314-020-1066-3
Li M, Xiao D, Liu H, et al., 2016. A recoverable chaos-based fragile watermarking with high PSNR preservation. Secur Commun Netw, 9(14):2371–2386. https://doi.org/10.1002/sec.1504
Liu ZY, Xia TC, Wang JB, 2017. Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography. JVibrContr, 24(20):4797–4824. https://doi.org/10.1177/1077546317734712
Liu ZY, Xia TC, Wang JB, 2018. Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem. Chin Phys B, 27(3):030502. https://doi.org/10.1088/1674-1056/27/3/030502
Ma CY, Shiri B, Wu GC, et al., 2020. New fractional signal smoothing equations with short memory and variable order. Optik, in press. https://doi.org/10.1016/j.ijleo.2020.164507
Podlubny I, 1999. Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press, San Diego, USA.
Pu YF, Wang WX, Zhou JL, et al., 2008. Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci Chin Ser F Inform Sci, 51(9):1319–1339. https://doi.org/10.1007/s11432-008-0098-x
Wu GC, Baleanu D, 2014. Discrete fractional logistic map and its chaos. Nonl Dynam, 75:283–287. https://doi.org/10.1007/s11071-013-1065-7
Wu GC, Zeng LG, Baleanu D, et al., 2014. Method for Generating Chaos Sequence Based on Fractional Order Discrete Mapping. CN Patent CN201 410 033 835 (in Chinese).
Wu GC, Deng ZG, Baleanu D, et al., 2019. New variableorder fractional chaotic systems for fast image encryption. Chaos, 28(8):083103. https://doi.org/10.1063/1.5096645
Author information
Authors and Affiliations
Contributions
Zai-rong WANG and Dumitru BALEANU designed the research. Zai-rong WANG introduced the algorithm. Babak SHIRI implemented the method and drafted the manuscript. Zai-rong WANG, Babak SHIRI, and Dumitru BALEANU revised and finalized the manuscript.
Corresponding author
Additional information
Compliance with ethics guidelines
Zai-rong WANG, Babak SHIRI, and Dumitru BALEANU declare that they have no conflict of interest.
Project supported by the Sichuan Science and Technology Support Program, China (No. 2018JY0120)
Rights and permissions
About this article
Cite this article
Wang, Zr., Shiri, B. & Baleanu, D. Discrete fractional watermark technique. Front Inform Technol Electron Eng 21, 880–883 (2020). https://doi.org/10.1631/FITEE.2000133
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.2000133