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Security of medical images based on special orthogonal group and Galois field

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Abstract

Security of medical images over an unsecured channel is a challenging task, and for this, several methods have been designed recently. The present paper is also in the same direction, and is an attempt to improve the security of the existing methods. In this paper, a cryptosystem is proposed, which performs encryption and decryption in the CBC (Cipher Block Chaining) mode of operation, and attains the confusion-diffusion properties using the PSN (Permutation-Substitution Network) of cryptography. The permutation is performed by a composite operation, consisting of rotation (via special orthogonal group), reflection, flipping, and pixel-wise shuffling, while substitution is performed by a composite operation of multiplication and multiplicative inverse over Galois field. The Archimedes’ constant is utilized for constructing Initialization Vector (IV) to be used in the CBC mode of encryption (and decryption). The proposed approach is able to encrypt monochrome (8-bit, 10-bit, 12-bit, and 16-bit), palette color, and 24-bit color medical images, simultaneously into noisy-like images from the human visual as well as the statistical point of view. The designed approach is empirically assessed via several statistical and security evaluation metrics, such as key sensitivity, chi-squared test, number of pixel change rate, avalanche effect, poker test, peak signal-to-noise ratio, etc. The results of these metrics support the objectives of our proposed approach. Moreover, a thorough comparison is also made with the recent state-of-the-art existing methods.

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Funding

This work was partially supported by UGC (University Grants Commission), New Delhi, India under grant No. [415024]

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  1. Department of Mathematics and Astronomy, University of Lucknow, Lucknow, –226 007, U.P., India

    Anand B. Joshi, Abdul Gaffar & Sonali Singh

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  1. Anand B. Joshi
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Correspondence to Anand B. Joshi.

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Joshi, A.B., Gaffar, A. & Singh, S. Security of medical images based on special orthogonal group and Galois field. Multimed Tools Appl 82, 44277–44308 (2023). https://doi.org/10.1007/s11042-023-15033-5

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