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Digital image scrambling based on outer totalistic cellular automaton and gray code pixels substitution

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Abstract

A digital image is scrambled by rearranging the pixels of an image, so that the original information contents are indistinguishable visually and relationships between initially adjacent pixels are disturbed. Cellular Automata (CA) are dynamic and discrete systems capable of generating complex behaviors based on simple rules. This characteristic makes CA an ideal candidate for developing effective image scrambling techniques. In spite of evidence that CA techniques have demonstrated effectiveness in image scrambling related literature, an original image content can still be identified from a database of scrambled images by contrasting the histograms of the suspected images and the scrambled images’ histogram. This problem is addressed in the paper by replacing pixel intensities with their Gray Code equivalent values as part of resolving pixels. The Gray Code pixel substitution provides robustness of the proposed scrambling method as seen in the results. With regard to the scrambling technique itself, an image is scrambled using a 2D lattice created using different generations of lattices derived from the same randomly generated lattice by Conway’s Game of Life (CGL) Outer Totalistic Cellular Automaton (OTCA) rule. Using the proposed method, the key space required to decrypt images by brute force is increased by 푢u (2size(original lattice)), where u is the number of generations of unique pairs. Comparing this method with other image scrambling techniques, it shows superior results with higher Gray Difference Degree (GDD) for the same image experimentation samples.

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Data availability

The datasets analyzed in this study are available publically, from University of Waterloo image repository, [https://links.uwaterloo.ca/Repository.html] and University of South California SIPI Institute miscellaneous volume, [https://sipi.usc.edu/database/database.php?volume=misc&image=2#top].

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Author notes

  1. Eimad Abusham and Kashif Zia contributed equally to this work.

Authors and Affiliations

  1. Faculty of Computing and Information Technology, Sohar University, Al Jamia Street, 311, Sohar, Oman

    Basil Ibrahim & Eimad Abusham

  2. University of Glasgow, Glasgow, UK

    Kashif Zia

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  1. Basil Ibrahim
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  2. Eimad Abusham
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  3. Kashif Zia
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Ibrahim, B., Abusham, E. & Zia, K. Digital image scrambling based on outer totalistic cellular automaton and gray code pixels substitution. Multimed Tools Appl 82, 18811–18829 (2023). https://doi.org/10.1007/s11042-022-14184-1

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