An image encryption algorithm based on a hidden attractor chaos system and the Knuth–Durstenfeld algorithm

Abstract Chaotic systems have been widely applied in digital image encryption due to their complex properties such as ergodicity, pseudo randomness and extreme sensitivity to their initial values and parameters. An image encryption algorithm based on a hidden attractor chaos system and Knuth–Durstenfeld algorithm is proposed. First, a hidden attractor chaos system is used to encrypt digital image. Compared to a self-excited attractor, the hidden attractor's attracting basin does not intersect with any small neighbourhoods of the equilibria. It is difficult for attackers to reconstruct the attractor by finding equilibrium points. Therefore, the hidden attractor chaotic system is difficult to decrypt. Meanwhile, the hidden attractor chaos system is very sensitive to initial values and parameters. Second, the Knuth–Durstenfeld algorithm has good randomness. In addition, the Knuth–Durstenfeld algorithm can reduce the time complexity and the space complexity of the permutation while achieving good permutation effects. Thus, Knuth–Durstenfeld algorithm is used to permutate the digital image. Finally, DNA sequence operations are used to diffuse image pixels values. Some experimental analyses have been applied to measure the new scheme, and the experimental results illustrate the scheme possesses better encryption performances. This method can be applied in secure image communication fields.

[1]  Xiaofeng Liao,et al.  Image encryption using 2D Hénon-Sine map and DNA approach , 2018, Signal Process..

[2]  Sajad Jafari,et al.  A new chaotic system with hidden attractor and its engineering applications: analog circuit realization and image encryption , 2018, Analog Integrated Circuits and Signal Processing.

[3]  Lilian Huang,et al.  A new color image encryption using combination of the 1D chaotic map , 2017, Signal Process..

[4]  Zengqiang Chen,et al.  A new image encryption algorithm based on hyper-chaos , 2008 .

[5]  Kevin M. Short,et al.  Steps Toward Unmasking Secure Communications , 1994 .

[6]  Qiang Liu,et al.  A novel image encryption algorithm based on chaos and Line map , 2015, Neurocomputing.

[7]  Xing-yuan Wang,et al.  A new image alternate encryption algorithm based on chaotic map , 2014, Nonlinear Dynamics.

[8]  Lu Xu,et al.  A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion , 2017 .

[9]  Xiaofeng Liao,et al.  Color image encryption based on chaotic systems and elliptic curve ElGamal scheme , 2017, Signal Process..

[10]  Marius-F. Danca,et al.  Hidden chaotic attractors in fractional-order systems , 2018, 1804.10769.

[11]  Chunhua Wang,et al.  A Novel Color Image Encryption Algorithm Based on Hyperchaotic System and Permutation-Diffusion Architecture , 2019, Int. J. Bifurc. Chaos.

[12]  Wei Zhang,et al.  An image encryption scheme using self-adaptive selective permutation and inter-intra-block feedback diffusion , 2018, Signal Process..

[13]  Lihua Gong,et al.  Quantum image encryption based on generalized Arnold transform and double random-phase encoding , 2015, Quantum Information Processing.

[14]  Chunhua Wang,et al.  Multiscroll Hyperchaotic System with Hidden Attractors and Its Circuit Implementation , 2019, Int. J. Bifurc. Chaos.

[15]  Lu Xu,et al.  A novel bit-level image encryption algorithm based on chaotic maps , 2016 .

[16]  Zenghui Wang,et al.  Hidden and self-excited coexisting attractors in a Lorenz-like system with two equilibrium points , 2018, Nonlinear Dynamics.

[17]  Vinod Patidar,et al.  A new substitution–diffusion based image cipher using chaotic standard and logistic maps , 2009 .

[18]  Yiran Chen,et al.  A novel image encryption scheme based on DNA sequence operations and chaotic systems , 2017, Neural Computing and Applications.

[19]  Guanrong Chen,et al.  A Novel Fast Image Encryption Scheme Based on 3D Chaotic Baker Maps , 2004, Int. J. Bifurc. Chaos.

[20]  Manish Kumar,et al.  A new RGB image encryption algorithm based on DNA encoding and elliptic curve Diffie-Hellman cryptography , 2016, Signal Process..

[21]  Christos Volos,et al.  Coexistence of hidden chaotic attractors in a novel no-equilibrium system , 2017 .

[22]  Zhiliang Zhu,et al.  An image encryption algorithm based on compound homogeneous hyper-chaotic system , 2017, Nonlinear Dynamics.

[23]  Yiran Chen,et al.  An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations , 2017, Signal Process. Image Commun..

[24]  Viet-Thanh Pham,et al.  Constructing a Chaotic System with an Infinite Number of Equilibrium Points , 2016, Int. J. Bifurc. Chaos.

[25]  J. Fridrich.  Symmetric Ciphers Based on Two-Dimensional Chaotic Maps , 1998 .

[26]  Yiran Chen,et al.  A color image cryptosystem based on dynamic DNA encryption and chaos , 2019, Signal Process..

[27]  Feng Xu,et al.  Image encryption based on non-affine and balanced cellular automata , 2014, Signal Process..

[28]  Kehui Sun,et al.  A fast image encryption algorithm based on chaotic map , 2016 .

[29]  Rongrong Wang,et al.  A new finding of the existence of hidden hyperchaotic attractors with no equilibria , 2014, Math. Comput. Simul..

[30]  R. Amutha,et al.  Double image compression and encryption scheme using logistic mapped convolution and cellular automata , 2017, Multimedia Tools and Applications.

[31]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[32]  T. Ha,et al.  A rule of seven in Watson-Crick base pairing of mismatched sequences , 2012, Nature Structural &Molecular Biology.

[33]  Yicong Zhou,et al.  Image encryption using binary bitplane , 2014, Signal Process..

[34]  Yingqian Zhang,et al.  A novel chaotic encryption scheme based on image segmentation and multiple diffusion models , 2018, Optics & Laser Technology.

[35]  Erdal Guvenoglu,et al.  An improvement for Knutt/Durstenfeld algorithm based image encryption , 2015, Signal Processing and Communications Applications Conference.

[36]  Sen Zhang,et al.  A novel simple no-equilibrium chaotic system with complex hidden dynamics , 2018 .

[37]  Chunhua Wang,et al.  A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion , 2018, Int. J. Bifurc. Chaos.

[38]  J. Fridrich.  Image encryption based on chaotic maps , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

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

[40]  Ling Zhou,et al.  A novel no‐equilibrium hyperchaotic multi‐wing system via introducing memristor , 2018, Int. J. Circuit Theory Appl..

[41]  Zhengjun Liu,et al.  Opto-digital image encryption by using Baker mapping and 1-D fractional Fourier transform , 2013 .

[42]  Lin Teng,et al.  A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive , 2012 .