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

Document Type : Research Paper


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.


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.


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Volume 12, Special Issue
December 2021
Pages 903-921
  • Receive Date: 02 September 2020
  • Revise Date: 17 August 2021
  • Accept Date: 04 September 2021