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Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs

Author

Listed:
  • Achraf Daoui

    (National School of Applied Sciences, Sidi Mohamed Ben Abdellah-Fez University, Fez 30000, Morocco)

  • Haokun Mao

    (Information Countermeauser Technique Institute, School of Cyberspace Science, Faculty of Computing, Harbin Institute of Technology, Harbin 150001, China)

  • Mohamed Yamni

    (Dhar El Mahrez Faculty of Science, Sidi Mohamed Ben Abdellah-Fez University, Fez 30000, Morocco)

  • Qiong Li

    (Information Countermeauser Technique Institute, School of Cyberspace Science, Faculty of Computing, Harbin Institute of Technology, Harbin 150001, China)

  • Osama Alfarraj

    (Computer Science Department, Community College, King Saud University, Riyadh 11437, Saudi Arabia)

  • Ahmed A. Abd El-Latif

    (Information Countermeauser Technique Institute, School of Cyberspace Science, Faculty of Computing, Harbin Institute of Technology, Harbin 150001, China
    Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebeen El-Kom 32511, Egypt)

Abstract

The discrete Shmaliy moment transform (DST) is a type of discrete orthogonal moment transform that is widely used in signal and image processing. However, DST is not suitable for lossless image applications due to its non-integer reversible nature. To overcome this limitation, we introduce the integer discrete Shmaliy transform (IDST) that performs integer-to-integer encoding, leading to a perfect and unique reconstruction of the input image. Next, a new 1D chaotic system model, the 1D multiparametric piecewise linear chaotic map (M-PWLCM), is presented as an extension of the existing 1D PWLCM. The M-PWLCM includes eight control parameters defined over an unlimited interval. To demonstrate the relevance of IDST and M-PWLCM in reversible image processing applications, they are used in a new scheme for lossless compression and encryption of medical images in the internet of medical things (IoMTs). On the one hand, the simulation results show that our scheme offers a good compression ratio and a higher level of security to resist differential attacks, brute force attacks and statistical attacks. On the other hand, the comparative analysis carried out shows the overall superiority of our scheme over similar state-of-the-art ones, both in achieving a higher compression ratio and better security when communicating medical images over unsecured IoMTs.

Suggested Citation

  • Achraf Daoui & Haokun Mao & Mohamed Yamni & Qiong Li & Osama Alfarraj & Ahmed A. Abd El-Latif, 2023. "Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs," Mathematics, MDPI, vol. 11(16), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3619-:d:1221796
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    References listed on IDEAS

    as
    1. Li-bo Zhang & Zhi-liang Zhu & Ben-qiang Yang & Wen-yuan Liu & Hong-feng Zhu & Ming-yu Zou, 2015. "Medical Image Encryption and Compression Scheme Using Compressive Sensing and Pixel Swapping Based Permutation Approach," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, August.
    2. Achraf Daoui & Mohamed Yamni & Samia Allaoua Chelloug & Mudasir Ahmad Wani & Ahmed A. Abd El-Latif, 2023. "Efficient Image Encryption Scheme Using Novel 1D Multiparametric Dynamical Tent Map and Parallel Computing," Mathematics, MDPI, vol. 11(7), pages 1-29, March.
    3. Germán González & Rodrigo Nava & Boris Escalante-Ramírez, 2018. "A Comparative Study on Discrete Shmaliy Moments and Their Texture-Based Applications," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-17, August.
    4. Liu, Lingfeng & Wang, Jie, 2023. "A cluster of 1D quadratic chaotic map and its applications in image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 89-114.
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