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A novel efficient image encryption algorithm based on affine transformation combine with linear fractional transformation

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Abstract

Algebraic structures and their hardware–software implementation gain considerable attention in the field of information security and coding theory. Research progress in the applications of arithmetic properties of algebraic structures is being frequently made. These structures are mostly useful in improvement of the cryptographic algorithms. A novel technique is given to design a cryptosystem responsible for lossless for image encryption. The proposed scheme is for the RGB image whose pixels are considered as 24 binary bits, accordingly a unique arrangement for the construction of S-boxes over a Galois field \( GF\left( {2^{9} } \right) \) is employed. Consequently, it generates multiple different S-boxes with excellent cryptographic characteristic and hence confusing process of the cryptosystem has been working. Whereas the diffusion process in this cryptosystem is based on Affine transformation over a unit elements of an integers modulo ring \( {\mathbb{Z}}_{n} \). The scrambling of the image data through the Affine transformation escalate the security asset, avoid computational effort and abbreviated the time complexity. In addition, the simulation test and comparative scrutinize illustrate that the proposed scheme is highly sensitive, large keyspace, excellent statistical properties and secure against differential attacks. Therefore, the proposed algorithm is valuable for confidential communication. Furthermore, due to the arithmetic properties of algebraic structures, the proposed scheme would be easily implemented, secure and fast enough to be utilized in real-world applications.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant Number R.G.P. 2/58/40.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Dawood Shah & Tariq Shah

  2. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Sajjad Shaukat Jamal

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  1. Dawood Shah
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  2. Tariq Shah
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  3. Sajjad Shaukat Jamal
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Correspondence to Dawood Shah.

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Shah, D., Shah, T. & Jamal, S.S. A novel efficient image encryption algorithm based on affine transformation combine with linear fractional transformation. Multidim Syst Sign Process 31, 885–905 (2020). https://doi.org/10.1007/s11045-019-00689-w

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  • DOI: https://doi.org/10.1007/s11045-019-00689-w

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