An Efficient Image Encryption Scheme Based on S-Boxes and Fractional-Order Differential Logistic Map

In this work, an efficient image encryption based on S-boxes and fractional-order logistic map is proposed. The features of the fractional-order chaotic system in dynamical behaviors are exhibited. By simulation and comparison with the traditional logistic map, it is proved that the fractional-order logistic map contains larger key space and more parameters. Therefore, the fractional-order logistic system has better efficiency and security against cryptanalyst attacks. The S-boxes construction algorithm is proposed. By comparing with the S-boxes of the former schemes, the proposed S-boxes have good performance under Bits Independence Criterion (BIC), the Strict Avalanche Criterion (SAC) and the nonlinearity. Finally, the image encryption scheme is proposed for the verification. In the encryption process, the proposed S-boxes are used for scrambling and confusion. The simulation and experimental results indicate that the fractional-order method is a preferred approach to integer-order chaotic system.

[1]  Mohammad Reza Mosavi,et al.  A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos , 2013, Multimedia Tools and Applications.

[2]  Kehui Sun,et al.  Fractional-order simplest memristor-based chaotic circuit with new derivative , 2018 .

[3]  Xing-Yuan Wang,et al.  A new image encryption algorithm based on two-dimensional spatiotemporal chaotic system , 2018, Neural Computing and Applications.

[4]  Zhenfeng Zhang,et al.  Chaotic encryption algorithm based on alternant of stream cipher and block cipher , 2011 .

[5]  Zhongmeng Zhao,et al.  Chaotic image encryption based on circular substitution box and key stream buffer , 2014, Signal Process. Image Commun..

[6]  M. Baptista.  Cryptography with chaos , 1998 .

[7]  Yicong Zhou,et al.  Cosine-transform-based chaotic system for image encryption , 2019, Inf. Sci..

[8]  Xing-Yuan Wang,et al.  A novel color image encryption scheme using DNA permutation based on the Lorenz system , 2018, Multimedia Tools and Applications.

[9]  Jan Sher Khan,et al.  A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S8 permutation , 2017, J. Intell. Fuzzy Syst..

[10]  Tariq Shah,et al.  An efficient approach for the construction of LFT S-boxes using chaotic logistic map , 2012, Nonlinear Dynamics.

[11]  Rhouma Rhouma,et al.  On the security of a spatiotemporal chaotic cryptosystem. , 2007, Chaos.

[12]  Jan Sher Khan,et al.  TD-ERCS map-based confusion and diffusion of autocorrelated data , 2016, Nonlinear Dynamics.

[13]  Hejiao Huang,et al.  Image Encryption Using Josephus Problem and Filtering Diffusion , 2019, IEEE Access.

[14]  Irfan Younas,et al.  A New Efficient Digital Image Encryption Based on Inverse Left Almost Semi Group and Lorenz Chaotic System , 2018, Entropy.

[15]  Majid Khan,et al.  A Novel Digital Contents Privacy Scheme Based on Kramer’s Arbitrary Spin , 2019, International Journal of Theoretical Physics.

[16]  Tariq Shah,et al.  Construction of S-box based on chaotic Boolean functions and its application in image encryption , 2015, Neural Computing and Applications.

[17]  Yanfeng Wang,et al.  Memristor-Based Neural Network Circuit of Full-Function Pavlov Associative Memory With Time Delay and Variable Learning Rate , 2019, IEEE Transactions on Cybernetics.

[18]  Syeda Iram Batool,et al.  A novel image encryption scheme based on Arnold scrambling and Lucas series , 2019, Multimedia Tools and Applications.

[19]  Tariq Shah,et al.  A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems , 2012, Nonlinear Dynamics.

[20]  Giorgio Ausiello,et al.  The Making of a New Science , 2018, Springer International Publishing.

[21]  Xiaofeng Liao,et al.  A new color image encryption scheme based on logistic map over the finite field ZN , 2018, Multimedia Tools and Applications.

[22]  Jan Sher Khan,et al.  Chaos based efficient selective image encryption , 2018, Multidimensional Systems and Signal Processing.

[23]  Xing-yuan Wang,et al.  A novel image encryption algorithm based on genetic recombination and hyper-chaotic systems , 2015, Nonlinear Dynamics.

[24]  Tariq Shah,et al.  Image privacy scheme using quantum spinning and rotation , 2018, J. Electronic Imaging.

[25]  Yanfeng Wang,et al.  Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control , 2017 .

[26]  Fu-Rong Lin,et al.  A Runge–Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives , 2018, Int. J. Comput. Math..

[27]  Ana Dalia Pano-Azucena,et al.  Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators , 2016, Nonlinear Dynamics.

[28]  C. F. Li,et al.  Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations , 2010, Comput. Math. Appl..

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

[30]  Seyed Mohammad Seyedzadeh,et al.  A novel color image encryption algorithm based on spatial permutation and quantum chaotic map , 2015, Nonlinear Dynamics.

[31]  Devendra Kumar,et al.  Analysis of an El Nino-Southern Oscillation model with a new fractional derivative , 2017 .

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

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

[34]  X. Liao,et al.  An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps , 2007 .

[35]  Ljupco Kocarev,et al.  Theory and practice of chaotic cryptography , 2007 .

[36]  Vasily E. Tarasov,et al.  Lattice fractional calculus , 2015, Appl. Math. Comput..

[37]  Majid Khan,et al.  Construction of new S-boxes based on triangle groups and its applications in copyright protection , 2018, Multimedia Tools and Applications.

[38]  Majid Khan,et al.  A novel chaotic image encryption technique based on multiple discrete dynamical maps , 2019, Multimedia Tools and Applications.

[39]  Debiao He,et al.  Cryptanalysis and improvement of an extended chaotic maps-based key agreement protocol , 2012, Nonlinear Dynamics.

[40]  G. Álvarez,et al.  Cryptanalysis of a discrete chaotic cryptosystem using external key , 2003 .

[41]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[42]  Iqtadar Hussain,et al.  Construction of chaotic quantum magnets and matrix Lorenz systems S-boxes and their applications , 2018, Chinese Journal of Physics.

[43]  X. Mou,et al.  Improving security of a chaotic encryption approach , 2001, Physics Letters A.

[44]  Jan Sher Khan,et al.  Visual Meaningful Encryption Scheme Using Intertwinning Logistic Map , 2018, Advances in Intelligent Systems and Computing.

[45]  Majid Khan,et al.  A new construction of confusion component of block ciphers , 2019, Multimedia Tools and Applications.

[46]  Majid Khan,et al.  Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps , 2019, International Journal of Theoretical Physics.

[47]  Guanrong Chen,et al.  Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[48]  Dongdong Lin,et al.  Cryptanalyzing an Image Encryption Algorithm Based on Autoblocking and Electrocardiography , 2017, IEEE MultiMedia.

[49]  Tariq Shah,et al.  A new implementation of chaotic S-boxes in CAPTCHA , 2016, Signal Image Video Process..

[50]  Majid Khan,et al.  A new approach to digital content privacy using quantum spin and finite-state machine , 2019, Applied Physics B.

[51]  Gonzalo Alvarez,et al.  Cryptanalysis of a chaotic secure communication system , 2003 .

[52]  Majid Khan,et al.  A novel image encryption scheme based on quantum dynamical spinning and rotations , 2018, PloS one.

[53]  Yang Li,et al.  A novel method to design S-box based on chaotic map and genetic algorithm , 2012 .

[54]  Yanfeng Wang,et al.  Dynamical Analysis of Memcapacitor Chaotic System and Its Image Encryption Application , 2020 .

[55]  Feng Hao,et al.  Cryptanalysis of a Chaotic Image Encryption Algorithm Based on Information Entropy , 2018, IEEE Access.

[56]  S. Salman,et al.  On a discretization process of fractional-order Logistic differential equation , 2014 .

[57]  Dumitru Baleanu,et al.  A hybrid computational approach for Klein–Gordon equations on Cantor sets , 2017 .

[58]  Yang Li,et al.  Optical image encryption technique based on compressed sensing and Arnold transformation , 2013 .

[59]  Junwei Sun,et al.  Autonomous memristor chaotic systems of infinite chaotic attractors and circuitry realization , 2018, Nonlinear Dynamics.

[60]  Iqtadar Hussain,et al.  A New Algorithm to Construct Secure Keys for AES , 2010 .

[61]  Tariq Shah,et al.  Construction of New S-box using a Linear Fractional Transformation , 2011 .

[62]  Arshad Ali,et al.  DNA Sequence Based Medical Image Encryption Scheme , 2018, 2018 10th Computer Science and Electronic Engineering (CEEC).

[63]  Noor Munir,et al.  A Generalization of Algebraic Expression for Nonlinear Component of Symmetric Key Algorithms of Any Characteristic p , 2018, 2018 International Conference on Applied and Engineering Mathematics (ICAEM).

[64]  L. Kocarev,et al.  Chaos and cryptography: block encryption ciphers based on chaotic maps , 2001 .

[65]  Devendra Kumar,et al.  An efficient analytical technique for fractional model of vibration equation , 2017 .

[66]  Majid Khan,et al.  Information Confidentiality Using Quantum Spinning, Rotation and Finite State Machine , 2018, International Journal of Theoretical Physics.

[67]  Yiran Chen,et al.  A novel chaos-based image encryption algorithm using DNA sequence operations , 2017 .

[68]  Yueping Li,et al.  A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation , 2017 .

[69]  Safya Belghith,et al.  A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization , 2016, Nonlinear Dynamics.

[70]  Jian Liu,et al.  Keyed Hash Function Using Hyper Chaotic System With Time-Varying Parameters Perturbation , 2019, IEEE Access.

[71]  Adil Masood Siddiqui,et al.  Chaotic substitution for highly autocorrelated data in encryption algorithm , 2014, Commun. Nonlinear Sci. Numer. Simul..

[72]  Mohd. Salmi Md. Noorani,et al.  Modified Baptista type chaotic cryptosystem via matrix secret key , 2008 .

[73]  Yi Shen,et al.  Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal sliding mode control , 2016, Nonlinear Dynamics.

[74]  Yingqian Zhang,et al.  Fractional Order Spatiotemporal Chaos with Delay in Spatial Nonlinear Coupling , 2018, Int. J. Bifurc. Chaos.

[75]  X. Liao,et al.  A block cipher with dynamic S-boxes based on tent map , 2009 .

[76]  Majid Khan,et al.  A novel image encryption scheme based on multiple chaotic S-boxes , 2015, Nonlinear Dynamics.

[77]  Rogelio Hasimoto-Beltrán,et al.  High-performance multimedia encryption system based on chaos. , 2008, Chaos.

[78]  Yangquan Chen,et al.  Computers and Mathematics with Applications Numerical Approximation of Nonlinear Fractional Differential Equations with Subdiffusion and Superdiffusion , 2022 .

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

[80]  Majid Khan,et al.  A Novel Image Encryption Technique Based on Generalized Advanced Encryption Standard Based on Field of Any Characteristic , 2019, Wireless Personal Communications.

[81]  Xiaofeng Liao,et al.  A novel method for designing S-boxes based on chaotic maps , 2005 .