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

This study proposes a scale-invariant digital color image encryption method that includes three main steps the pre-substitution, the ۳D scale-invariant modular chaotic map, and the post-substitution. ۱) 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, ۲) the ۳D 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_۱ to W_k with size n \times n sub-images. The last two ï؟¼W_k-۱ and ï؟¼W_k windows may be overlap in several sub-images. Finally, the three-dimensional modular chaotic maps are performed on the W_۱ï؟¼ to W_kï؟¼ windows with MIPF keys and selected by LFSR, ۳) 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 ۲۴-bit pixels of each sub-images are circularly shifted with several bits specified in the secret key. Modular arithmetic is used in the ۳D 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:

Image encryption , ۳D chaotic map , Modular arithmetic , LFSR , Keyspace