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Scale invariant digital image encryption using 3D modular chaotic map

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Abstract

Cryptography techniques are used to preserve the privacy and integrity of image media. Most proposed cryptographic images methods based on chaotic maps are dependent upon image sizes and most of them worked on square images. Tackling this problem, a scale invariant gray level image encryption method is proposed by means of 3D modular chaotic map. Initially, a 2D image with desirable size M × N is converted into a 3D image with m sub-images by size n × n. Optimizing the calculation, the parameters m and n should be appropriately selected. Having diffusion and confusion properties, two steps of 3D substitution and a 3D permutation step are used. In the 3D substitution steps, the pixels value of sub-images will be changed using the XOR operators and the circular shift. In the permutation step the pixels position of sub-images will be changed using 3D modular chaotic map, In this case, the m sub-images are divided into \( k=\left\lceil \frac{m}{n}\right\rceil \) equal size windows which each window has n sub-images with size n × n, and the 3D modular chaotic map is performed on any window with independent parameters. Depending upon the value of m, the number of windows is greater than or equal to 1; for k > 1, the last two windows may overlap to perform 3D chaotic map operation. Accelerating the proposed encryption method, the 3D chaotic map operations on windows can be implemented in parallel. The proposed method, in comparison with other methods of image encryption, improves the statistical parameters of cryptographic analysis, key space, and speed.

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Author information

Authors and Affiliations

  1. Islamic Azad University-South Tehran Branch, Tehran, Iran

    Ali Broumandnia

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  1. Ali Broumandnia
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Correspondence to Ali Broumandnia.

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Appendices

Appendix A

The reverse SI3DMCM is shown in Fig. 14.

Fig. 14
figure 14

Reverse scale invariant 3D modular chaotic map (RSI3DMCM) algorithm for digital image decryption with size M × N

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Appendix B

The reverse scale invariant image decryption is shown in Fig. 15.

Fig. 15
figure 15

The proposed scale invariant digital image decryption algorithm

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Appendix C

The reverse scale invariant image decryption is shown in block diagram Fig. 16.

Fig. 16
figure 16

The reverse scale invariant image decryption block diagram

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Broumandnia, A. Scale invariant digital image encryption using 3D modular chaotic map. Multimed Tools Appl 79, 11327–11355 (2020). https://doi.org/10.1007/s11042-019-08337-y

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  • DOI: https://doi.org/10.1007/s11042-019-08337-y

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