Synchronization of chaotic-type delayed neural networks and its application

Our proposed image encryption is based on synchronization of chaotic fuzzy cellular neural networks (FCNNs) with different time delays and uses sampled-data controller. (i) It is known that the chaotic system plays a vital role in secure communication. (ii) FCNNs are more suitable for image processing due to its local connectedness. (iii) There are some results derived on theory part for the problem of synchronization of chaotic delayed FCNNs. (iv) We raise the following question: Is it possible to utilize these obtained chaotic values via FCNNs to image encryption? (v) Finally, we tried the above and succeed. Moreover, numerical instance and comparison results show that the proposed scheme works well and is resistant to differential attack.

[1]  David J. Hill,et al.  Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Leon O. Chua,et al.  Fuzzy cellular neural networks: applications , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[3]  Liping Chen,et al.  Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays , 2011, Expert Syst. Appl..

[4]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[5]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[6]  Zengyun Wang,et al.  Synchronization analysis of linearly coupleddelayed neural networks with discontinuous activations , 2015 .

[7]  Zhigang Zeng,et al.  Lag Synchronization of Switched Neural Networks via Neural Activation Function and Applications in Image Encryption , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[9]  Pagavathigounder Balasubramaniam,et al.  Stationary oscillation of interval fuzzy cellular neural networks with mixed delays under impulsive perturbations , 2012, Neural Computing and Applications.

[10]  Tao Xie,et al.  Breaking a novel image encryption scheme based on improved hyperchaotic sequences , 2012, Nonlinear Dynamics.

[11]  Chang'e Dong,et al.  Color image encryption using one-time keys and coupled chaotic systems , 2014, Signal Process. Image Commun..

[12]  Rajinder Kaur Rajinder Kaur,et al.  Image Encryption Techniques:A Selected Review , 2012 .

[13]  Xingyuan Wang,et al.  A novel color image encryption scheme using alternate chaotic mapping structure , 2016 .

[14]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[15]  Qintao Gan,et al.  Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control , 2012, J. Frankl. Inst..

[16]  Xiaodi Li,et al.  Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations , 2011, J. Frankl. Inst..

[17]  S. M. Lee,et al.  Secure communication based on chaotic synchronization via interval time-varying delay feedback control , 2011 .

[18]  Safwan El Assad,et al.  A new chaos-based image encryption system , 2016, Signal Process. Image Commun..

[19]  Xiangjun Wu,et al.  A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps , 2015, Appl. Soft Comput..

[20]  Abdul Hanan Abdullah,et al.  A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata , 2015 .

[21]  Jian-Feng Zhao,et al.  A novel image encryption scheme based on an improper fractional-order chaotic system , 2015, Nonlinear Dynamics.

[22]  Qing Zhu,et al.  Design of exponential state estimator for neural networks with distributed delays , 2009 .

[23]  Paul M. Chau,et al.  Image encryption for secure Internet multimedia applications , 2000, 2000 Digest of Technical Papers. International Conference on Consumer Electronics. Nineteenth in the Series (Cat. No.00CH37102).

[24]  Zhidong Teng,et al.  Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control , 2012, Math. Comput. Simul..

[25]  Jinhu Lu,et al.  On Cryptanalysis of Fridrich's chaotic image encryption scheme , 2016, ArXiv.

[26]  Mohammad Hossein Moattar,et al.  Color image encryption based on hybrid hyper-chaotic system and cellular automata , 2017 .

[27]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[28]  Rui Xu,et al.  Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control☆ , 2012 .

[29]  Shiguo Lian,et al.  A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system , 2012, J. Syst. Softw..

[30]  Pagavathigounder Balasubramaniam,et al.  Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays , 2011, Circuits Syst. Signal Process..

[31]  Fatih Özkaynak,et al.  Brief review on application of nonlinear dynamics in image encryption , 2018, Nonlinear Dynamics.

[32]  Huaguang Zhang,et al.  Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays , 2009, Neurocomputing.

[33]  Wei Zhang,et al.  Chaotic synchronization and secure communication based on descriptor observer , 2009 .

[34]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[35]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[36]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[37]  Xingyuan Wang,et al.  A color image encryption with heterogeneous bit-permutation and correlated chaos , 2015 .

[38]  Dongdong Lin,et al.  Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits , 2016, IEEE MultiMedia.

[39]  Nan Li,et al.  Synchronization for general complex dynamical networks with sampled-data , 2011, Neurocomputing.

[40]  Lili Yu,et al.  The application of hybrid encryption algorithm in software security , 2013, 2013 3rd International Conference on Consumer Electronics, Communications and Networks.

[41]  Geoff Boeing,et al.  Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction , 2016, Syst..

[42]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays , 2011, Math. Comput. Model..

[43]  Alexey A. Koronovskii,et al.  Generalized synchronization of chaos for secure communication: Remarkable stability to noise , 2010, 1302.4067.

[44]  Hongjun Liu,et al.  Asymmetric color image encryption scheme using 2D discrete-time map , 2015, Signal Process..