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A generalized Arnold’s Cat Map transformation for image scrambling

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Abstract

This study presents a new approach to generate the transformation matrix for Arnold’s Cat Map (ACM). Matrices of standard and modified ACM are well known by many users. Since the structure of the possible matrices is known, one can easily select one of them and use it to recover the image with several trials. However, the proposed method generates a larger set of transform matrices. Thus, one will have difficulty in estimating the transform matrix used for scrambling. There is no fixed structure for our matrix as in standard or modified ACM, making it much harder for the transform matrix to be discovered. It is possible to use different type, order and number of operations to generate the transform matrix. The quality of the shuffling process and the strength against brute-force attacks of the proposed method is tested on several benchmark images.

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Acknowledgments

The authors declare that they have equally participated in all parts of the manuscript. Also, they would like to thank Mr. P. Danesh from the Atilim University Academic Writing and Advisory Centre for his help in the preparation of the manuscript.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Atilim University, Ankara, Turkey

    Hakan Tora

  2. Department of Software Engineering, Atilim University, Ankara, Turkey

    Erhan Gokcay

  3. Department of Mathematics, Atilim University, Ankara, Turkey

    Mehmet Turan

  4. Graduate School of Natural and Applied Sciences, Atilim University, Ankara, Turkey

    Mohamed Buker

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  1. Hakan Tora
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  2. Erhan Gokcay
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  3. Mehmet Turan
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  4. Mohamed Buker
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Correspondence to Hakan Tora.

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Tora, H., Gokcay, E., Turan, M. et al. A generalized Arnold’s Cat Map transformation for image scrambling. Multimed Tools Appl 81, 31349–31362 (2022). https://doi.org/10.1007/s11042-022-11985-2

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  • DOI: https://doi.org/10.1007/s11042-022-11985-2

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