Full Text:   <3757>

Summary:  <1448>

CLC number: TP391.4

On-line Access: 2020-06-12

Received: 2020-03-29

Revision Accepted: 2020-05-05

Crosschecked: 2020-05-20

Cited: 0

Clicked: 4716

Citations:  Bibtex RefMan EndNote GB/T7714


Zai-rong Wang


Babak Shiri


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.6 P.880-883


Discrete fractional watermark technique

Author(s):  Zai-rong Wang, Babak Shiri, Dumitru Baleanu

Affiliation(s):  Data Recovery Key Laboratory of Sichuan Province, School of Computer Science, Neijiang Normal University, Neijiang 641100, China; more

Corresponding email(s):   wangzr@njtc.edu.cn, shire_babak@yahoo.com, dumitru@cankaya.edu.tr

Key Words:  Discrete fractional calculus, Image encryption, Watermark

Zai-rong Wang, Babak Shiri, Dumitru Baleanu. Discrete fractional watermark technique[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 880-883.

@article{title="Discrete fractional watermark technique",
author="Zai-rong Wang, Babak Shiri, Dumitru Baleanu",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Discrete fractional watermark technique
%A Zai-rong Wang
%A Babak Shiri
%A Dumitru Baleanu
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 6
%P 880-883
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2000133

T1 - Discrete fractional watermark technique
A1 - Zai-rong Wang
A1 - Babak Shiri
A1 - Dumitru Baleanu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 6
SP - 880
EP - 883
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2000133

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.


汪在荣1,Babak Shiri2,Dumitru Baleanu3,4



Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Abdeljawad T, 2011. On Riemann and Caputo fractional differences. Comput Math Appl, 62(3):1602-1611.

[2]Anastassiou GA, 2011. About discrete fractional calculus with inequalities. In: Anastassiou GA (Ed.), Intelligent Mathematics: Computational Analysis. Springer, Berlin, Germany, p.575-585.

[3]Atici FM, Eloe P, 2009. Initial value problem in discrete fractional calculus. Proc Amer Math Soc, 137(3):981-989.

[4]Bai YR, Baleanu D, Wu GC, 2018. A novel shuffling technique based on fractional chaotic maps. Optik, 168:553-562.

[5]Bastos N, Ferreira R, Torres D, 2011. Discrete-time fractional variational problems. Signal Process, 91(3):513-524.

[6]Gao H, Gao TG, 2019. Double verifiable image encryption based on chaos and reversible watermarking algorithm. Multim Tools Appl, 78(6):7267-7288.

[7]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.

[8]Han H, 2020. A fractional-order decomposition model of image registration and its numerical algorithm. Comput Appl Math, 39:45.

[9]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.

[10]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. J Vibr Contr, 24(20):4797-4824.

[11]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.

[12]Ma CY, Shiri B, Wu GC, et al., 2020. New fractional signal smoothing equations with short memory and variable order. Optik, in press.

[13]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.

[14]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.

[15]Wu GC, Baleanu D, 2014. Discrete fractional logistic map and its chaos. Nonl Dynam, 75:283-287.

[16]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).

[17]Wu GC, Deng ZG, Baleanu D, et al., 2019. New variable-order fractional chaotic systems for fast image encryption. Chaos, 28(8):083103.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE