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A new medical image encryption algorithm based on the 1D logistic map associated with pseudo-random numbers

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Abstract

A new, fast, and secure encryption algorithm for medical images based on the 1D logistic map associated with pseudo-random numbers has been proposed. Initial values and parameters of the logistic map play an important role (as secret keys) to generate key matrices for shuffling and substituting pixels in the image. The proposed algorithm has been designed to provide the user control over the level of security required by increasing or decreasing the number of rounds of the encryption process. During the encryption process, two pseudo-random rows and two pseudo-random columns have been inserted on each side of the original image to counter chosen and known plain-image attacks. The proposed algorithm has been tested for robustness and effectiveness using the standard tests available. Further, differential and noise attacks have also been analyzed. Cryptanalysis of the proposed algorithm has been performed by testing it against most of the frequently used attacks, such as known and chosen plain-image attacks. The run time for different images has been recorded to check the efficiency of the proposed algorithm. The tests were performed on 50 grayscale and 50 RGB images. The average entropy and NPCR of encrypted images were approximately 7.99 and 99.6%, respectively, for the selected images. Some medical images, such as the human brain, MRI, and lungs, have been selected to demonstrate the output of the proposed algorithm. Similarly, the proposed algorithm has been tested for a standard non-medical test image as well. The obtained results have also been compared with existing competing algorithms. The proposed algorithm can be apt for practical use.

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Notes

  1. Source: https://www.hlevkin.com/06testimages.htm

  2. Source: https://homepages.cae.wisc.edu/~ece533/images/

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Acknowledgments

The authors thank the anonymous reviewers for helpful and constructive comments that greatly contributed to improving this article.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Sciences-Pilani, Hyderabad Campus, Hyderabad, 500078, Telangana, India

    Manish Kumar & Prateek Gupta

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  1. Manish Kumar
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  2. Prateek Gupta
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Correspondence to Manish Kumar.

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Informed consent

The medical images (the human brain, MRI, and lungs) used in this paper fall under the category of x-ray and brain scans, which pose no threat to confidentiality and privacy. These medical images are available as open-source (https://www.hlevkin.com/06testimages.htm). The non-medical image (Lena) used in this paper is a standard test image available as open-source (https://homepages.cae.wisc.edu/~ece533/images/).

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Kumar, M., Gupta, P. A new medical image encryption algorithm based on the 1D logistic map associated with pseudo-random numbers. Multimed Tools Appl 80, 18941–18967 (2021). https://doi.org/10.1007/s11042-020-10325-6

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  • DOI: https://doi.org/10.1007/s11042-020-10325-6

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