Color image encryption using linear feedback shift registers by three dimensional permutation and substitution operations

Document Type : Research Paper

Authors

1 Departament of Computer Engineering, Qom Branch, Islamic Azad University, Qom, Iran.

2 Departament of Computer Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.

3 Department of Computer Engineering, Center Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

This study proposes a scale-invariant digital color image encryption method that includes three main steps the pre-substitution, the 3D scale-invariant modular chaotic map, and the post-substitution. 1) The pre-substitution: At the first stage, pixels of plain sub-images are XOR with different key patterns. By starting from one of the plain sub-images, the pixels of the selected plain sub-image is XOR with the initial key, and the result is used as the cipher sub-image and as the next key pattern for performing XOR operations on the next plain sub-image. In other words, the XOR result of each step is used as the next step key pattern, 2) the 3D permutation: At the second stage,  first the red, green, and blue components of a $M \times N$ color image is divided to m sub-images with size $n \times n$. Then m sub-images are partitioned into $k = \left\lceil {\frac{m}{n}} \right\rceil $ windows $W_1$ to $W_k$ with size $n \times n$ sub-images. The last two ï؟¼$W_k-1$ and ï؟¼$W_k$ windows may be overlap in several sub-images. Finally, the three-dimensional modular chaotic maps are performed on the $W_1$ï؟¼ to $W_k$ï؟¼ windows with MIPF keys and selected by LFSR, 3) the post-substitution: At the final stage, the $M \times N$ color image is initially divided into a set of color sub-images. Then, the 24-bit pixels of each sub-images are circularly shifted with several bits specified in the secret key. Modular arithmetic is used in the 3D scale-invariant chaotic maps to increase keyspace and enhance security parameters. With repeat at least one round of main steps, the proposed encryption scheme reaches optimum parameter values and it is highly sensitive to minor differences in both secret key and plain image. The proposed encryption method for images improves the standard parameters of evaluation such as entropy, adjacent pixel correlations, histogram, and expanded keyspace.

Keywords

[1] Sh. Agarwal, A Review of Image Scrambling Technique Using Chaotic Maps, International Journal of Engineering
and Technology Innovation, 8 (2) (2018) 77-98.
[2] X. Chai, X. Fu, Zh. Gan, Y. Lu and Y. Chen, A color image cryptosystem based on dynamic DNA encryption
and chaos, 155 (2019) 44-62.
[3] J. Chen, Z.L. Zhu, L.B. Zhang, Y. Zhang and B.Q. Yang, Exploiting self-adaptive permutation-diffusion and DNA
random encoding for secure and efficient image encryption, 142 (2018) 340-353.
[4] B. Chen, M. Yu, Y. Tian, L. Li4, D. Wang, X. Sun, Multiple-parameter fractional quaternion Fourier transform
and its application in color image encryption, IET Image Process., 12 (12) (2018) 2238-2249.
[5] R. Enayatifar, H.J. Sadaei, A.H. Abdullah, M. Lee and I.F. Isnin, A novel chaotic based image encryption using
a hybrid model of deoxyribonucleic acid and cellular automata, 71 (2015) 33-41.
[6] C. Fu, J. Chen, H. Zou, W. Meng, Y. Zhan and Y. Yu, A chaos-based digital image encryption scheme with an
improved diffusion strategy, Opt. Express 20 (3) (2012) 2363-2378.
[7] Zh. Hua, F. Jin, B. Xu and H. Huang, 2D Logistic-Sine-coupling map for image encryption, Elsevier, Signal
Processing 149 (2018) 148-161.
[8] Z. Hua and Y. Zhou, Design of image cipher using block-based scrambling and image filtering, 396 (2017) 97-113.
[9] D. Jiang, Y. Chen, X. GU, L. Xie and L. Chen, Efficient and universal quantum key distribution based on chaos
and middleware, 31 (2) (2017)1650264.
[10] A. Jolfaei and A. Mirghadri, An Image Encryption Approach using Chaos and Stream Cipher, Journal of Theoretical and Applied Information Technology, 117-123.
[11] M. Kumari, Sh. Gupta and P. Sardana, A Survey of Image Encryption Algorithms, Springer, 3D Research 8 (37)
(2017).
[12] A. R. Lan, J. He, Sh. Wang, T. Gu and X. Luo, Integrated chaotic systems for image encryption, 147 (2018)
133-145.
[13] C. Li, Y. Liu, T. Xie and M.Z.Q. Chen, Breaking a novel image encryption scheme based on improved hyperchaotic
sequences, 73 (3) (2013) 2083-2089.
[14] C. Li, Cracking a hierarchical chaotic image encryption algorithm based on permutation, 118 (2016) 203–210.
https://doi.org/10.1016/j.sigpro.2015.07.008.
[15] M. Liu, S. Zhang, Z. Fan, M. Qiu, H∞ state estimation for discrete-time chaotic systems based on a unified
model, IEEE Trans. Syst. Man Cybern, Part B 42 (4) (2012) 1053-1063.
[16] A. Momeni Asl, A. Broumandnia and S. J. Mirabedini, Scale-Invariant Digital Color Image Encryption Using a
3D Modular Chaotic Map, in IEEE Access, 9 (2021) 102433-102449, DOI: 10.1109/ACCESS.2021.3096224.
[17] M.A. Murillo-Escobar, C. Cruz-Hern´andez, F. Abundiz-P´erez, R.M. L´opez-Guti´errez and O.R. Acosta Del Campo,
A RGB image encryption algorithm based on total plain image characteristics and chaos, 109 (2015) 119-131.
[18] X. Wang and Zh. Li, A color image encryption algorithm based on Hopfield chaotic neural network, Optics and
Lasers in Engineering 115 (2019) 107-118.
[19] X. Wang, P. Li, Y. ZhangLi, Y. Liu, H. Zhang and X. Wang, A novel color image encryption scheme using DNA
permutation based on the Lorenz system, Multimedia Tools and Applications, 77 (5) (2018) 6243-6265.
[20] X. Wang, Y. Zhang and Xue-Mei Bao, A Colour Image Encryption Scheme Using Permutation-Substitution Based
on Chaos, 17 (2015) 3877-3897.
[21] E.Y. Xie, C. Li, S. Yu and J. L¨u, on the cryptanalysis of Fridrich’s chaotic image encryption scheme, 132 (2017)
150-154.
[22] L. Xu, Z. Li, J. Li and W. Hua, A novel bit-level image encryption algorithm based on chaotic maps, 78 (2016)
17-25.
[23] P. PING, J. YANG FAN, Y. CHI MAO, F. XU and Z. GAO A chaos-based image encryption scheme using
digit-level permutation and block diffusion, IEEE Access, 2019.[24] P. R. Sankpal and P. A. Vijaya, Image Encryption Using Chaotic Maps: A Survey, 2014.
[25] L. Skanderova and I. Zelinka, Arnold cat map and Sinai as chaotic numbers generators in evolutionary algorithms,
In: AETA 2013, Recent Advances in Electrical Engineering and Related Sciences, (2014) 381-9.
[26] B. Yang and X. Liao, A new color image encryption scheme based on the logistic map over the finite field ZN,
Multimedia Tools and Applications, 77 (16) (2018) 21803–21821.
[27] G. Ye and X. Huang, Spatial image encryption algorithm based on chaotic map and pixel frequency, Sci. China-Inf.
Sci. 61 (5) (2018) 058104.
[28] Y. Zhang and D. Xiao, An image encryption scheme based on rotation matrix bit-level permutation and block
diffusion, Communication Nonlinear Science Numer. Simul. 19 (1) (2014) 74-82.
[29] Y. Zhang, D. Xiao, Y. Shu and J. Li, A novel image encryption scheme based on a linear hyperbolic chaotic
system of partial differential equations, Signal Processing Image Communication. 28 (3) (2013) 292-300.
[30] Y.Q. Zhang and X.Y. Wang, A symmetric image encryption algorithm based on mixed linear–nonlinear coupled
map lattice, Inf. Sci. 273 (2014) 329-351.
[31] Y.Q. Zhang and X.Y. Wang, A new image encryption algorithm based on non-adjacent coupled map lattices, Appl.
Soft Comput. 26 (2015) 10-20.
[32] N. Zhou, Y. Hu, L. Gong and G. Li, Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations, Quantum Inf. Process. 16 (6) (2017) 164.
[33] Y. Zhou, K. Panetta, S. Agaian and C.L.P. Chen, Image encryption using P-Fibonacci transform and decomposition, 285 (5) (2012) 594-608.
[34] Y. Zhou, L. Bao and C.L.P. Chen, Image encryption using a new parametric switching chaotic system, 93 (11)
(2013) 3039-3052
[35] H. Zhu, Y. Zhao and Y. Song, 2D logistic-modulated-sine-coupling logistic chaotic map for image encryption,
IEEE Access, 7 (2019) 14081-14098.
Volume 12, Special Issue
December 2021
Pages 903-921
  • Receive Date: 02 September 2020
  • Revise Date: 17 August 2021
  • Accept Date: 04 September 2021