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Fresnelet approach for image encryption in the algebraic frame

Author

Listed:
  • Farwa, Shabieh
  • Muhammad, Nazeer
  • Bibi, Nargis
  • Haider, Sajjad A.
  • Naqvi, Syed R.
  • Anjum, Sheraz

Abstract

In this manuscript, a novel, more efficient method to encrypt an image in the Fresnelet domain is proposed. The uniqueness of the presented algorithm depends on the Fresnelet transform based image decomposition in conjunction with an algebraically synthesized substitution box. The high- nonlinearity induced by the eccentrically designed S-box boosts the security of proposed scheme. In this two-steps encryption algorithm, firstly, we apply the Fresnelet transform to propagate information with desired wavelength at a specified distance. This results in the decomposition of the secret image data into four complex subbands. These complex sub-bands are further partitioned into real subband data and imaginary subband data. At second step, the net subband data, produced at the first level, is diffused by a unique iterative substitution approach based on the algebraic structure of Galois field F28. In the diffusion process, the permuted image is substituted via algebraic substitution algorithm. We prove through significant analysis techniques that the proposed scheme offers a highly elevated security level in encryption.

Suggested Citation

  • Farwa, Shabieh & Muhammad, Nazeer & Bibi, Nargis & Haider, Sajjad A. & Naqvi, Syed R. & Anjum, Sheraz, 2018. "Fresnelet approach for image encryption in the algebraic frame," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 343-355.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:343-355
    DOI: 10.1016/j.amc.2018.03.105
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    References listed on IDEAS

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    1. Nazeer Muhammad & Nargis Bibi & Zahid Mahmood & Tallha Akram & Syed Rameez Naqvi, 2017. "Reversible integer wavelet transform for blind image hiding method," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-17, May.
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    Cited by:

    1. Nasir Siddiqui & Fahim Yousaf & Fiza Murtaza & Muhammad Ehatisham-ul-Haq & M Usman Ashraf & Ahmed M Alghamdi & Ahmed S Alfakeeh, 2020. "A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-16, November.

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