一种基于离散分数阶混沌系统和DNA序列运算的新型彩色图像加密算法

陈立平; 尹昊; 袁利国; António M. LOPES; J. A. Tenreiro MACHADO; 吴然超

doi:10.1631/FITEE.1900709

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一种基于离散分数阶混沌系统和DNA序列运算的新型彩色图像加密算法

用于信息科学的分数阶积分新趋势专题 | Updated：2022-05-19

- 一种基于离散分数阶混沌系统和DNA序列运算的新型彩色图像加密算法
- A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations
- 信息与电子工程前沿（英文） 2020年21卷第6期页码：866-879
- Affiliations：
  
  School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China
  College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
  UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal
  Department of Electrical Engineering, Polytechnic Institute of Porto, R. Dr. António Bernardino de Almeida, 431, Porto 4249-015, Portugal
  School of Mathematical Sciences, Anhui University, Hefei 230601, China
- Author bio：
  
  Li-ping CHEN, lip_chenhut@126.com
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 11971032) and the Science and Technology Program of Guangzhou, China (No. 201707010031)
- DOI：10.1631/FITEE.1900709
  中图分类号： TP37
- 收稿：2019-12-18，
  
  修回：2020-;4-16，
  
  纸质出版：2020-06
- Accepted：
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陈立平, 尹昊, 袁利国, 等. 一种基于离散分数阶混沌系统和DNA序列运算的新型彩色图像加密算法[J]. 信息与电子工程前沿（英文）, 2020,21(6):866-879.

Li-ping CHEN, Hao YIN, Li-guo YUAN, et al. A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 866-879.
陈立平, 尹昊, 袁利国, 等. 一种基于离散分数阶混沌系统和DNA序列运算的新型彩色图像加密算法[J]. 信息与电子工程前沿（英文）, 2020,21(6):866-879. DOI： 10.1631/FITEE.1900709.

Li-ping CHEN, Hao YIN, Li-guo YUAN, et al. A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 866-879. DOI： 10.1631/FITEE.1900709.

摘要

提出一种基于动态DNA编码和混沌的新型彩色图像加密算法。将一个三神经元分数阶离散Hopfield神经网络作为伪随机混沌序列发生器。其初值由外部输入的五位密钥以及明文图像的哈希值计算得来。外部密钥包含分数阶离散Hopfield神经网络的离散步长和阶次。哈希值由SHA-2函数计算得到。在保证较大密钥空间的同时，提高了算法对明文图像的敏感性。在此基础上，提出一种新型三维投影置乱方法，置乱图像红、绿、蓝信号通道中像素位置。DNA编码以及扩散被用于扩散图像信息。使用离散分数阶Hopfield神经网络生成的伪随机数序列确定每个像素的编码规则，用以保证编码方式的多样性。最后，运用置乱II和XOR提升算法的安全性。实验结果和安全性分析表明，该算法具有较好安全性，能够抵御多种典型攻击。

Abstract

A novel color image encryption algorithm based on dynamic deoxyribonucleic acid (DNA) encoding and chaos is presented. A three-neuron fractional-order discrete Hopfield neural network (FODHNN) is employed as a pseudo-random chaotic sequence generator. Its initial value is obtained with the secret key generated by a fiveparameter external key and a hash code of the plain image. The external key includes both the FODHNN discrete step size and order. The hash is computed with the SHA-2 function. This ensures a large secret key space and improves the algorithm sensitivity to the plain image. Furthermore

a new three-dimensional projection confusion method is proposed to scramble the pixels among red

green

and blue color components. DNA encoding and diffusion are used to diffuse the image information. Pseudo-random sequences generated by FODHNN are employed to determine the encoding rules for each pixel and to ensure the diversity of the encoding methods. Finally

confusion Ⅱ and XOR are used to ensure the security of the encryption. Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.

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references

T Abdeljawad , , , S Banerjee , , , GC Wu . . Discrete tempered fractional calculus for new chaotic systems with short memory and image encryption . . Optik, in press , , 2019 . . DOI: 10.1016/j.ijleo.2019.163698 http://doi.org/10.1016/j.ijleo.2019.163698 . .

RP Agarwal , , , AMA El-Sayed , , , SM Salman . . Fractional-order Chua's system: discretization, bifurcation and chaos . . Adv Differ Equat , , 2013 . . 2013 320 DOI: 10.1186/1687-1847-2013-320 http://doi.org/10.1186/1687-1847-2013-320 . .

AO Ahgue , , , JD de Nkapkop , , , JY Effa , , , 等 . . A DNA-based chaos algorithm for an efficient image encryption application . . Int Symp on Electronics and linebreak Telecommunications , , 2018 . . p.1 - - 4 . . DOI: 10.1109/ISETC.2018.8583850 http://doi.org/10.1109/ISETC.2018.8583850 . .

OM Al-Hazaimeh , , , MF Al-Jamal , , , N Alhindawi , , , 等 . . Image encryption algorithm based on Lorenz chaotic map with dynamic secret keys . . Neur Comput Appl , , 2019 . . 31 ( ( 7 ): ): 2395 - - 2405 . . DOI: 10.1007/s00521-017-3195-1 http://doi.org/10.1007/s00521-017-3195-1 . .

CN Angstmann , , , BI Henry , , , BA Jacobs , , , 等 . . Discretization of fractional differential equations by a piecewise constant approximation . . Math Model Nat Phenom , , 2017 . . 12 ( ( 6 ): ): 23 - - 36 . . DOI: 10.1051/mmnp/2017063 http://doi.org/10.1051/mmnp/2017063 . .

FM Atıcı , , , S Şengül . . Modeling with fractional difference equations . . J Math Anal Appl , , 2010 . . 369 ( ( 1 ): ): 1 - - 9 . . DOI: 10.1016/j.jmaa.2010.02.009 http://doi.org/10.1016/j.jmaa.2010.02.009 . .

XL Chai , , , XL Fu , , , ZH Gan , , , 等 . . A color image cryptosystem based on dynamic DNA encryption and chaos . . Signal Process , , 2019 . . 155 44 - - 62 . . DOI: 10.1016/j.sigpro.2018.09.029 http://doi.org/10.1016/j.sigpro.2018.09.029 . .

GR Chen , , , YB Mao , , , KC Charles . . A symmetric image encryption scheme based on 3D chaotic cat maps . . Chaos Sol Fract , , 2004 . . 21 ( ( 3 ): ): 749 - - 761 . . DOI: 10.1016/j.chaos.2003.12.022 http://doi.org/10.1016/j.chaos.2003.12.022 . .

JL Chen , , , C Lei , , , SL Lin , , , 等 . . Preparation and structural characterization of a partially depolymerized beta-glucan obtained from Poria cocos sclerotium by ultrasonic treatment . . Food Hydrocoll , , 2015 . . 46 1 - - 9 . . DOI: 10.1016/j.foodhyd.2014.12.005 http://doi.org/10.1016/j.foodhyd.2014.12.005 . .

JX Chen , , , ZL Zhu , , , C Fu , , , 等 . . An image encryption scheme using nonlinear inter-pixel computing and swapping based permutation approach . . Commun Nonl Sci Numer Simul , , 2015 . . 23 ( ( 1-3 ): ): 294 - - 310 . . DOI: 10.1016/j.cnsns.2014.11.021 http://doi.org/10.1016/j.cnsns.2014.11.021 . .

JX Chen , , , ZL Zhu , , , LB Zhang , , , 等 . . Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption . . Signal Process , , 2018 . . 142 340 - - 353 . . DOI: 10.1016/j.sigpro.2017.07.034 http://doi.org/10.1016/j.sigpro.2017.07.034 . .

LP Chen , , , RC Wu , , , YG He , , , 等 . . Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties . . Appl Math Comput , , 2015 . . 257 274 - - 284 . . DOI: 10.1016/j.amc.2014.12.103 http://doi.org/10.1016/j.amc.2014.12.103 . .

LP Chen , , , JD Cao , , , RC Wu , , , 等 . . Stability and synchronization of fractional-order memristive neural networks with multiple delays . . Neur Netw , , 2017 . . 94 76 - - 85 . . DOI: 10.1016/j.neunet.2017.06.012 http://doi.org/10.1016/j.neunet.2017.06.012 . .

SJ Deng , , , YP Zhan , , , D Xiao , , , 等 . . Analysis and improvement of a hash-based image encryption algorithm . . Commun Nonl Sci Numer Simul , , 2011 . . 16 ( ( 8 ): ): 3269 - - 3278 . . DOI: 10.1016/j.cnsns.2010.12.016 http://doi.org/10.1016/j.cnsns.2010.12.016 . .

ZF El Raheem , , , SM Salman . . On a discretization process of fractional-order logistic differential equation . . J Egypt Math Soc , , 2014 . . 22 ( ( 3 ): ): 407 - - 412 . . DOI: 10.1016/j.joems.2013.09.001 http://doi.org/10.1016/j.joems.2013.09.001 . .

R Enayatifar , , , AH Abdullah , , , IF Isnin . . Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence . . Opt Lasers Eng , , 2014 . . 56 83 - - 93 . . DOI: 10.1016/j.optlaseng.2013.12.003 http://doi.org/10.1016/j.optlaseng.2013.12.003 . .

R Enayatifar , , , HJ Sadaei , , , AH Abdullah , , , 等 . . A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata . . Opt Lasers Eng , , 2015 . . 71 33 - - 41 . . DOI: 10.1016/j.optlaseng.2015.03.007 http://doi.org/10.1016/j.optlaseng.2015.03.007 . .

M Essaid , , , I Akharraz , , , A Saaidi , , , 等 . . A novel image encryption scheme based on permutation/diffusion process using an improved 2D chaotic system . . Int Conf on Wireless Technologies, Embedded and Intelligent Systems , , 2019 . . p.1 - - 6 . . DOI: 10.1109/WITS.2019.8723717 http://doi.org/10.1109/WITS.2019.8723717 . .

C Goodrich , , , AC Peterson . . Discrete Fractional Calculus , , : : New York, USA Springer , , 2015 . . DOI: 10.1007/978-3-319-25562-0 http://doi.org/10.1007/978-3-319-25562-0 . .

GA Gottwald , , , I Melbourne . . A new test for chaos in deterministic systems . . Proc R Soc Lond Ser A , , 2004 . . 460 ( ( 2042 ): ): 603 - - 611 . . DOI: 10.1098/rspa.2003.1183 http://doi.org/10.1098/rspa.2003.1183 . .

RM Gray . . Entropy and Information Theory (2 nd Ed.) , , : : New York, USA Springer , , 2011 . . DOI: 10.1007/978-1-4419-7970-4 http://doi.org/10.1007/978-1-4419-7970-4 . .

ZH Guan , , , FJ Huang , , , WJ Guan . . Chaos-based image encryption algorithm . . Phys Lett A , , 2005 . . 346 ( ( 1-3 ): ): 153 - - 157 . . DOI: 10.1016/j.physleta.2005.08.006 http://doi.org/10.1016/j.physleta.2005.08.006 . .

R Guesmi , , , MAB Farah , , , A Kachouri , , , 等 . . A novel chaos-based image encryption using DNA sequence operation and secure Hash algorithm SHA-2 . . Nonl Dynam , , 2016 . . 83 ( ( 3 ): ): 1123 - - 1136 . . DOI: 10.1007/s11071-015-2392-7 http://doi.org/10.1007/s11071-015-2392-7 . .

S Hanis , , , R Amutha . . A fast double-keyed authenticated image encryption scheme using an improved chaotic map and a butterfly-like structure . . Nonl Dynam , , 2019 . . 95 ( ( 1 ): ): 421 - - 432 . . DOI: 10.1007/s11071-018-4573-7 http://doi.org/10.1007/s11071-018-4573-7 . .

JJ Hopfield . . Neural networks and physical systems with emergent collective computational abilities . . Proc Natl Acad Sci USA , , 1982 . . 79 ( ( 8 ): ): 2554 - - 2558 . . DOI: 10.1073/pnas.79.8.2554 http://doi.org/10.1073/pnas.79.8.2554 . .

GY Hu , , , WL Kou , , , JE Dong , , , 等 . . A novel image encryption algorithm based on cellular neural networks hyper chaotic system . . IEEE 4 th Int Conf on Computer and Communications , , 2018 . . p.1878 - - 1882 . . DOI: 10.1109/CompComm.2018.8780725 http://doi.org/10.1109/CompComm.2018.8780725 . .

ZY Hua , , , YC Zhou , , , HJ Huang . . Cosine-transform-based chaotic system for image encryption . . Inform Sci , , 2019 . . 480 403 - - 419 . . DOI: 10.1016/j.ins.2018.12.048 http://doi.org/10.1016/j.ins.2018.12.048 . .

LL Huang , , , JH Park , , , GC Wu , , , 等 . . Variable-order fractional discrete-time recurrent neural networks . . J Comput Appl Math , , 2020 . . 370 112633 DOI: 10.1016/j.cam.2019.112633 http://doi.org/10.1016/j.cam.2019.112633 . .

E Kaslik , , , S Sivasundaram . . Nonlinear dynamics and chaos in fractional-order neural networks . . Neur Netw , , 2012 . . 32 245 - - 256 . . DOI: 10.1016/j.neunet.2012.02.030 http://doi.org/10.1016/j.neunet.2012.02.030 . .

CQ Li , , , DD Lin , , , JH Li . . Cryptanalyzing an image-scrambling encryption algorithm of pixel bits . . IEEE Multim , , 2017 . . 24 ( ( 3 ): ): 64 - - 71 . . DOI: 10.1109/MMUL.2017.3051512 http://doi.org/10.1109/MMUL.2017.3051512 . .

RZ Li , , , Q Liu , , , LF Liu . . Novel image encryption algorithm based on improved logistic map . . IET Image Process , , 2019 . . 13 ( ( 1 ): ): 125 - - 134 . . DOI: 10.1049/iet-ipr.2018.5900 http://doi.org/10.1049/iet-ipr.2018.5900 . .

Z Li , , , CG Peng , , , LR Li , , , 等 . . A novel plaintext-related image encryption scheme using hyper-chaotic system . . Nonl Dynam , , 2018 . . 94 ( ( 2 ): ): 1319 - - 1333 . . DOI: 10.1007/s11071-018-4426-4 http://doi.org/10.1007/s11071-018-4426-4 . .

HJ Liu , , , A Kadir . . Asymmetric color image encryption scheme using 2D discrete-time map . . Signal Process , , 2015 . . 113 104 - - 112 . . DOI: 10.1016/j.sigpro.2015.01.016 http://doi.org/10.1016/j.sigpro.2015.01.016 . .

JAT Machado . . Fractional order description of DNA . . Appl Math Model , , 2015 . . 39 ( ( 14 ): ): 4095 - - 4102 . . DOI: 10.1016/j.apm.2014.12.037 http://doi.org/10.1016/j.apm.2014.12.037 . .

JAT Machado . . Bond graph and memristor approach to DNA analysis . . Nonl Dynam , , 2017 . . 88 ( ( 2 ): ): 1051 - - 1057 . . DOI: 10.1007/s11071-016-3294-z http://doi.org/10.1007/s11071-016-3294-z . .

JAT Machado , , , AC Costa , , , MD Quelhas . . Entropy analysis of the DNA code dynamics in human chromosomes . . Comput Math Appl , , 2011 . . 62 ( ( 3 ): ): 1612 - - 1617 . . DOI: 10.1016/j.camwa.2011.03.005 http://doi.org/10.1016/j.camwa.2011.03.005 . .

KS Miller , , , B Ross . . Fractional difference calculus . . Proc Int Symp on Univalent Functions, Fractional Calculus and Their Applications , , 1988 . . p.139 - - 152 . . . .

B Norouzi , , , S Mirzakuchaki . . An image encryption algorithm based on DNA sequence operations and cellular neural network . . Multim Tools Appl , , 2017 . . 76 ( ( 11 ): ): 13681 - - 13701 . . DOI: 10.1007/s11042-016-3769-4 http://doi.org/10.1007/s11042-016-3769-4 DOI: 10.1007/s11042-016-3769-4 http://doi.org/10.1007/s11042-016-3769-4 . .

D Ravichandran , , , P Praveenkumar , , , JBB Rayappan , , , 等 . . DNA chaos blend to secure medical privacy . . IEEE Trans NanoBiosci , , 2017 . . 16 ( ( 8 ): ): 850 - - 858 . . DOI: 10.1109/TNB.2017.2780881 http://doi.org/10.1109/TNB.2017.2780881 DOI: 10.1109/TNB.2017.2780881 http://doi.org/10.1109/TNB.2017.2780881 . .

SL Sun . . A novel hyperchaotic image encryption scheme based on DNA encoding, pixel-level scrambling and bit-level scrambling . . IEEE Photon J , , 2018 . . 10 ( ( 2 ): ): 7201714 DOI: 10.1109/JPHOT.2018.2817550 http://doi.org/10.1109/JPHOT.2018.2817550 . .

S Toughi , , , MH Fathi , , , YA Sekhavat . . An image encryption scheme based on elliptic curve pseudo random and Advanced Encryption System . . Signal Process , , 2017 . . 141 217 - - 227 . . DOI: 10.1016/j.sigpro.2017.06.010 http://doi.org/10.1016/j.sigpro.2017.06.010 . .

A ur Rehman , , , XF Liao , , , R Ashraf , , , 等 . . A color image encryption technique using exclusive-OR with DNA complementary rules based on chaos theory and SHA-2 . . Optik , , 2018 . . 159 348 - - 367 . . DOI: 10.1016/j.ijleo.2018.01.064 http://doi.org/10.1016/j.ijleo.2018.01.064 . .

JS Wang , , , F Long , , , WH Ou . . CNN-based color image encryption algorithm using DNA sequence operations . . Int Conf on Security, Pattern Analysis, and Cybernetics , , 2017 . . p.730 - - 736 . . DOI: 10.1109/SPAC.2017.8304370 http://doi.org/10.1109/SPAC.2017.8304370 . .

XY Wang , , , HL Zhang , , , XM Bao . . Color image encryption scheme using CML and DNA sequence operations . . Biosystems , , 2016a . . 144 18 - - 26 . . DOI: 10.1016/j.biosystems.2016.03.011 http://doi.org/10.1016/j.biosystems.2016.03.011 . .

XY Wang , , , CM Liu , , , HL Zhang . . An effective and fast image encryption algorithm based on chaos and interweaving of ranks . . Nonl Dynam , , 2016b . . 84 ( ( 3 ): ): 1595 - - 1607 . . DOI: 10.1007/s11071-015-2590-3 http://doi.org/10.1007/s11071-015-2590-3 . .

GC Wu , , , D Baleanu , , , ZX Lin . . Image encryption technique based on fractional chaotic time series . . J Vibr Contr , , 2016 . . 22 ( ( 8 ): ): 2092 - - 2099 . . DOI: 10.1177/1077546315574649 http://doi.org/10.1177/1077546315574649 . .

GC Wu , , , T Abdeljawad , , , JL Liu , , , 等 . . Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique . . Nonl Anal Model Contr , , 2019a . . 24 ( ( 6 ): ): 919 - - 936 . . DOI: 10.15388/NA.2019.6.5 http://doi.org/10.15388/NA.2019.6.5 . .

GC Wu , , , ZG Deng , , , D Baleanu , , , 等 . . New variable-order fractional chaotic systems for fast image encryption . . Chaos , , 2019b . . 29 ( ( 8 ): ): 083103 DOI: 10.1063/1.5096645 http://doi.org/10.1063/1.5096645 . .

XJ Wu , , , HB Kan , , , J Kurths . . A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps . . Appl Soft Comput , , 2015 . . 37 24 - - 39 . . DOI: 10.1016/j.asoc.2015.08.008 http://doi.org/10.1016/j.asoc.2015.08.008 . .

XJ Wu , , , KS Wang , , , XY Wang , , , 等 . . Lossless chaotic color image cryptosystem based on DNA encryption and entropy . . Nonl Dynam , , 2017 . . 90 ( ( 2 ): ): 855 - - 875 . . DOI: 10.1007/s11071-017-3698-4 http://doi.org/10.1007/s11071-017-3698-4 . .

GD Ye , , , C Pan , , , XL Huang , , , 等 . . An efficient pixel-level chaotic image encryption algorithm . . Nonl Dynam , , 2018 . . 94 ( ( 1 ): ): 745 - - 756 . . DOI: 10.1007/s11071-018-4391-y http://doi.org/10.1007/s11071-018-4391-y . .

GJ Zhang , , , Q Liu . . A novel image encryption method based on total shuffling scheme . . Opt Commun , , 2011 . . 284 ( ( 12 ): ): 2775 - - 2780 . . DOI: 10.1016/j.optcom.2011.02.039 http://doi.org/10.1016/j.optcom.2011.02.039 . .

LM Zhang , , , KH Sun , , , WH Liu , , , 等 . . A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations . . Chin Phys B , , 2017 . . 26 ( ( 10 ): ): 100504 DOI: 10.1088/1674-1056/26/10/100504 http://doi.org/10.1088/1674-1056/26/10/100504 DOI: 10.1088/1674-1056/26/10/100504 http://doi.org/10.1088/1674-1056/26/10/100504 . .

LY Zhang , , , CQ Li , , , KW Wong , , , 等 . . Cryptanalyzing a chaos-based image encryption algorithm using alternate structure . . J Syst Softw , , 2012 . . 85 ( ( 9 ): ): 2077 - - 2085 . . DOI: 10.1016/j.jss.2012.04.002 http://doi.org/10.1016/j.jss.2012.04.002 . .

Q Zhang , , , XP Wei . . A novel couple images encryption algorithm based on DNA subsequence operation and chaotic system . . Optik , , 2013 . . 124 ( ( 23 ): ): 6276 - - 6281 . . DOI: 10.1016/j.ijleo.2013.05.009 http://doi.org/10.1016/j.ijleo.2013.05.009 . .

Q Zhang , , , LL Liu , , , XP Wei . . Improved algorithm for image encryption based on DNA encoding and multi-chaotic maps . . AEU Int J Electron Commun , , 2014 . . 68 ( ( 3 ): ): 186 - - 192 . . DOI: 10.1016/j.aeue.2013.08.007 http://doi.org/10.1016/j.aeue.2013.08.007 . .

R Zhang , , , DW Qi , , , YZ Wang . . Dynamics analysis of fractional order three-dimensional Hopfield neural network . . Proc 6 th Int Conf on Natural Computation , , 2010 . . p.3037 - - 3039 . . DOI: 10.1109/ICNC.2010.5582371 http://doi.org/10.1109/ICNC.2010.5582371 . .

Y Zhang . . The unified image encryption algorithm based on chaos and cubic S-Box . . Inform Sci , , 2018 . . 450 361 - - 377 . . DOI: 10.1016/j.ins.2018.03.055 http://doi.org/10.1016/j.ins.2018.03.055 . .

YQ Zhang , , , XY Wang . . A new image encryption algorithm based on non-adjacent coupled map lattices . . Appl Soft Comput , , 2015 . . 26 10 - - 20 . . DOI: 10.1016/j.asoc.2014.09.039 http://doi.org/10.1016/j.asoc.2014.09.039 . .

YQ Zhang , , , XY Wang , , , J Liu , , , 等 . . An image encryption scheme based on the MLNCML system using DNA sequences . . Opt Lasers Eng , , 2016 . . 82 95 - - 103 . . DOI: 10.1016/j.optlaseng.2016.02.002 http://doi.org/10.1016/j.optlaseng.2016.02.002 . .

YS Zhang , , , D Xiao . . Self-adaptive permutation and combined global diffusion for chaotic color image encryption . . AEU Int J Electron Commun , , 2014 . . 68 ( ( 4 ): ): 361 - - 368 . . DOI: 10.1016/j.aeue.2013.10.002 http://doi.org/10.1016/j.aeue.2013.10.002 . .

XD Zheng , , , J Xu , , , W Li . . Parallel DNA arithmetic operation based on n -moduli set . . Appl Math Comput , , 2009 . . 212 ( ( 1 ): ): 177 - - 184 . . DOI: 10.1016/j.amc.2009.02.011 http://doi.org/10.1016/j.amc.2009.02.011 . .

YC Zhou , , , L Bao , , , CLP Chen . . A new 1D chaotic system for image encryption . . Signal Process , , 2014 . . 97 172 - - 182 . . DOI: 10.1016/j.sigpro.2013.10.034 http://doi.org/10.1016/j.sigpro.2013.10.034 . .

YC Zhou , , , ZY Hua , , , CM Pun , , , 等 . . Cascade chaotic system with applications . . IEEE Trans Cybern , , 2015 . . 45 ( ( 9 ): ): 2001 - - 2012 . . DOI: 10.1109/TCYB.2014.2363168 http://doi.org/10.1109/TCYB.2014.2363168 . .

ZL Zhu , , , W Zhang , , , KW Wong , , , 等 . . A chaos-based symmetric image encryption scheme using a bit-level permutation . . Inform Sci , , 2011 . . 181 ( ( 6 ): ): 1171 - - 1186 . . DOI: 10.1016/j.ins.2010.11.009 http://doi.org/10.1016/j.ins.2010.11.009 . .

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