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A new hyperchaotic map and its application for image encryption

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Abstract.

Based on the one-dimensional Sine map and the two-dimensional Hénon map, a new two-dimensional Sine-Hénon alteration model (2D-SHAM) is hereby proposed. Basic dynamic characteristics of 2D-SHAM are studied through the following aspects: equilibria, Jacobin eigenvalues, trajectory, bifurcation diagram, Lyapunov exponents and sensitivity dependence test. The complexity of 2D-SHAM is investigated using Sample Entropy algorithm. Simulation results show that 2D-SHAM is overall hyperchaotic with the high complexity, and high sensitivity to its initial values and control parameters. To investigate its performance in terms of security, a new 2D-SHAM-based image encryption algorithm (SHAM-IEA) is also proposed. In this algorithm, the essential requirements of confusion and diffusion are accomplished, and the stochastic 2D-SHAM is used to enhance the security of encrypted image. The stochastic 2D-SHAM generates random values, hence SHAM-IEA can produce different encrypted images even with the same secret key. Experimental results and security analysis show that SHAM-IEA has strong capability to withstand statistical analysis, differential attack, chosen-plaintext and chosen-ciphertext attacks.

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Authors and Affiliations

  1. Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Hayder Natiq, M. R. M. Said & Adem Kilicman

  2. Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia

    M. R. M. Said

  3. Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia

    M. R. M. Said & Adem Kilicman

  4. The Branch of Applied Mathematics, Applied Science Department, University of Technology, Baghdad, Iraq

    Hayder Natiq & N. M. G. Al-Saidi

Authors
  1. Hayder Natiq
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  2. N. M. G. Al-Saidi
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  3. M. R. M. Said
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  4. Adem Kilicman
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Correspondence to Hayder Natiq.

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Natiq, H., Al-Saidi, N.M.G., Said, M.R.M. et al. A new hyperchaotic map and its application for image encryption. Eur. Phys. J. Plus 133, 6 (2018). https://doi.org/10.1140/epjp/i2018-11834-2

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  • DOI: https://doi.org/10.1140/epjp/i2018-11834-2

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