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Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram

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Abstract

A novel four-image encryption scheme based on the quaternion Fresnel transforms (QFST), computer generated hologram and the two-dimensional (2D) Logistic-adjusted-Sine map (LASM) is presented. To treat the four images in a holistic manner, two types of the quaternion Fresnel transform (QFST) are defined and the corresponding calculation method for a quaternion matrix is derived. In the proposed method, the four original images, which are represented by quaternion algebra, are processed holistically in a vector manner by using QFST first. Then the input complex amplitude, which is constructed by the components of the QFST-transformed plaintext images, is encoded by Fresnel transform with two virtual independent random phase masks (RPM). In order to avoid sending entire RPMs to the receiver side for decryption, the RPMs are generated by utilizing 2D–LASM, which results that the amount of the key data is reduced dramatically. Subsequently, by using Burch’s method and the phase-shifting interferometry, the encrypted computer generated hologram is fabricated. To improve the security and weaken the correlation, the encrypted hologram is scrambled base on 2D–LASM. Experiments demonstrate the validity of the proposed image encryption technique.

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Acknowledgments

This work is partly supported by the Natural Science Foundation of Guangdong Province (No. 2014A030310038), the Educational Commission of Guangdong Province (No. 2013KJCX0127, No. 2015KTSCX089), the Fundamental Research Funds for the Central Universities (No. 20720160016), the Science and Technology Planning Project of Chaozhou (No. 2013G01), and the Research Fund of Hanshan Normal University (No. LT201201).

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Authors and Affiliations

  1. School of physics and electronic engineering, Hanshan Normal University, Chaozhou, China

    Chuying Yu

  2. College of mathematics and statistics, Hanshan Normal University, Chaozhou, China

    Jianzhong Li

  3. School of Software, Fujian Normal University, Fuzhou, China

    Xuan Li

  4. Department of Physics and Mechanical & Electrical Engineering, Xiamen University, Xiamen, China

    Xuechang Ren

  5. National Institute of Technology Kurukshetra, Kurukshetra, India

    B. B. Gupta

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  1. Chuying Yu
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  2. Jianzhong Li
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  3. Xuan Li
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  4. Xuechang Ren
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  5. B. B. Gupta
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Correspondence to Jianzhong Li.

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Yu, C., Li, J., Li, X. et al. Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram. Multimed Tools Appl 77, 4585–4608 (2018). https://doi.org/10.1007/s11042-017-4637-6

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  • DOI: https://doi.org/10.1007/s11042-017-4637-6

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