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A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems

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Abstract

In this paper, a secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems is proposed. In this scheme, a fractional-order modified-Hénon map is considered as a transmitter, the system parameters and fractional orders are considered as secret keys. As a receiver, a step-by-step delayed observer is used, and based on this one, an exact synchronization is established. To make the transmission scheme secure, an encryption function is used to cipher the original information using a key stream obtained from the chaotic map sequences. Moreover, to further enhance the scheme security, the ciphered information is inserted by inclusion method in the chaotic map dynamics. The first contribution of this paper is to propose new results on the observability and the observability matching condition of nonlinear discrete-time fractional-order systems. To the best of our knowledge, these features have not been addressed in the literature. In the second contribution, the design of delayed discrete observer, based on fractional-order discrete-time hyperchaotic system, is proposed. The feasibility of this realization is demonstrated. Finally, different analysis are introduced to test the proposed scheme security. Simulation results are presented to highlight the performances of our method. These results show that, our scheme can resist different kinds of attacks and it exhibits good performance.

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Authors and Affiliations

  1. Laboratoire de Conception et Conduite des Systèemes de Production (L2CSP), UMMTO, BP 17 RP, 15000, Tizi-Ouzou, Algeria

    Sarah Kassim, Hamid Hamiche & Saïd Djennoune

  2. Department of Electrical/Electronics and Computer Engineering, University of Sharjah, Sharjah, UAE

    Maâmar Bettayeb

Authors
  1. Sarah Kassim
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  2. Hamid Hamiche
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  3. Saïd Djennoune
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  4. Maâmar Bettayeb
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Correspondence to Sarah Kassim.

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Kassim, S., Hamiche, H., Djennoune, S. et al. A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems. Nonlinear Dyn 88, 2473–2489 (2017). https://doi.org/10.1007/s11071-017-3390-8

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