A Novel Image Encryption Algorithm Based on the Delayed Maps and Permutation-Confusion-Diffusion Architecture

To improve the dynamical behaviors of 1D chaotic maps, a new linear-delay-modulation method (LDM) is proposed. Derived from the Sine map, a delayed Sine map (DSM) is proposed based on the LDM. *en, we substitute the Sine map in the SIMM system with DSM and obtained a delayed SIMM system (DSIMM). Its chaotic performance is analyzed through the phase diagram, Lyapunov exponent spectrum, and complexity. *e results show that the delayed chaotic map can generate more complex dynamical behaviors and more random sequences. Hence, we apply the two delayed systems to a novel image encryption algorithm with the permutation-confusion-diffusion architecture. Firstly, to permutate the pixel of the image efficiently, the plainimage is scrambled by using a multilayer of the nonlinear index. Secondly, the image is confused by using the chaotic matrix generated with two chaotic sequences, and then, the ciphertext is transformed into a 1D sequence. Finally, to improve the plaintext sensitivity and facilitate key management, we enhance the sensitivity by applying a novel diffusion algorithm instead of using plaintext-related keystream. *e diffusion equation contains the sum of undiffused pixels and the operation of cyclic bit-shift. Simulation results for the gray image illustrate the effectiveness of the proposed encryption algorithm.

[1]  Zhiliang Zhu,et al.  Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption , 2018, Signal Process..

[2]  Ruisong Ye,et al.  A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism , 2011 .

[3]  Yi He,et al.  Color Image Encryption Using Three-Dimensional Sine ICMIC Modulation Map and DNA Sequence Operations , 2017, Int. J. Bifurc. Chaos.

[4]  Sun,et al.  Chaotic Image Encryption Algorithm by Correlating Keys with Plaintext , 2012 .

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

[6]  Bibhudendra Acharya,et al.  A novel multi-dimensional multiple image encryption technique , 2020, Multimedia Tools and Applications.

[7]  Kehui Sun,et al.  A fast image encryption algorithm based on compressive sensing and hyperchaotic map , 2019, Optics and Lasers in Engineering.

[8]  Congxu Zhu,et al.  An Efficient Image Encryption Scheme Based on the LSS Chaotic Map and Single S-Box , 2020, IEEE Access.

[9]  Atal Chaudhuri,et al.  A robust image encryption scheme using chaotic tent map and cellular automata , 2020, Nonlinear Dynamics.

[10]  K. Chon,et al.  Approximate entropy for all signals , 2009, IEEE Engineering in Medicine and Biology Magazine.

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

[12]  Alexander Marshak,et al.  Approximate Entropy and Sample Entropy: A Comprehensive Tutorial , 2019, Entropy.

[13]  Xiaofei Xu,et al.  Batch Image Encryption Using Generated Deep Features Based on Stacked Autoencoder Network , 2017 .

[14]  Yong Zhang,et al.  A plaintext-related image encryption algorithm based on chaos , 2017, Multimedia Tools and Applications.

[15]  Azman Samsudin,et al.  An image encryption scheme based on hybridizing digital chaos and finite state machine , 2019, Signal Process..

[16]  She-Xiang Jiang,et al.  Quantum image encryption algorithm based on Arnold scrambling and wavelet transforms , 2020, Quantum Inf. Process..

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

[18]  Xingyuan Wang,et al.  Image Encryption Based on Hash Table Scrambling and DNA Substitution , 2020, IEEE Access.

[19]  Hui Liu,et al.  A Color Image Encryption Scheme Based on Arnold Scrambling and Quantum Chaotic , 2017, Int. J. Netw. Secur..

[20]  Bibhudendra Acharya,et al.  Multiple grayscale image encryption using cross-coupled chaotic maps , 2020, J. Inf. Secur. Appl..

[21]  Congxu Zhu,et al.  Secure Image Encryption Algorithm Based on Hyperchaos and Dynamic DNA Coding , 2020, Entropy.

[22]  Yide Ma,et al.  A Nonlinearly Modulated Logistic Map With Delay for Image Encryption , 2018, Electronics.

[23]  Cong Xu,et al.  A novel image encryption algorithm based on bit-plane matrix rotation and hyper chaotic systems , 2019, Multimedia Tools and Applications.

[24]  Yong Zhang,et al.  The unified image encryption algorithm based on chaos and cubic S-Box , 2018, Inf. Sci..

[25]  Kehui Sun,et al.  A visually secure asymmetric image encryption scheme based on RSA algorithm and hyperchaotic map , 2020, Physica Scripta.

[26]  Bibhudendra Acharya,et al.  An efficient colour image encryption scheme based on 1-D chaotic maps , 2019, J. Inf. Secur. Appl..

[27]  Gargi Bhattacharjee,et al.  A Hybridized Model for Image Encryption through Genetic Algorithm and DNA Sequence , 2018 .

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

[29]  Xingyuan Wang,et al.  Fractal sorting matrix and its application on chaotic image encryption , 2021, Inf. Sci..

[30]  B. B. Zaidan,et al.  New Comparative Study Between DES, 3DES and AES within Nine Factors , 2010, ArXiv.

[31]  Sos S. Agaian,et al.  Local Shannon entropy measure with statistical tests for image randomness , 2013, Inf. Sci..

[32]  Xingyuan Wang,et al.  Image encryption algorithm based on the matrix semi-tensor product with a compound secret key produced by a Boolean network , 2020, Inf. Sci..

[33]  Bibhudendra Acharya,et al.  A Simple, Secure, and Time-Efficient Bit-Plane Operated Bit-Level Image Encryption Scheme Using 1-D Chaotic Maps , 2019 .

[34]  Jun Zhou,et al.  Quantum Chaotic Image Encryption with One Time Running Key , 2014 .

[35]  Yicong Zhou,et al.  2D Sine Logistic modulation map for image encryption , 2015, Inf. Sci..

[36]  Bobby D. Gerardo,et al.  Enhancing IDEA Algorithm using Circular Shift and Middle Square Method , 2019, 2019 17th International Conference on ICT and Knowledge Engineering (ICT&KE).

[37]  Musheer Ahmad,et al.  Cryptanalysis of an Image Encryption Algorithm Based on Combined Chaos for a BAN System, and Improved Scheme Using SHA-512 and Hyperchaos , 2018, Symmetry.

[38]  Xue Ouyang,et al.  A color image encryption method based on memristive hyperchaotic system and DNA encryption , 2020 .

[39]  Bibhudendra Acharya,et al.  Dual-Layer DNA-Encoding–Decoding Operation Based Image Encryption Using One-Dimensional Chaotic Map , 2020 .

[40]  Xuan Li,et al.  Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram , 2017, Multimedia Tools and Applications.

[41]  Gaurav Bhatnagar,et al.  Biometric Inspired Multimedia Encryption Based on Dual Parameter Fractional Fourier Transform , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[42]  Xiaoyu Wang,et al.  An encrypted coverless information hiding method based on generative models , 2021, Inf. Sci..

[43]  Mario Aldape-Pérez,et al.  Substitution box generation using Chaos: An image encryption application , 2018, Appl. Math. Comput..

[44]  Yu Fu,et al.  A secure image encryption scheme with compression-confusion-diffusion structure , 2020, Multimedia Tools and Applications.

[45]  K. Briggs.  An improved method for estimating Liapunov exponents of chaotic time series , 1990 .

[46]  Chen Chen,et al.  An improved image encryption algorithm with finite computing precision , 2020, Signal Process..

[47]  Dawei Zhang,et al.  Optical image compression and encryption transmission-based ondeep learning and ghost imaging , 2020 .

[48]  Hongyu Zhao,et al.  Fast image encryption algorithm based on parallel computing system , 2019, Inf. Sci..