Nonlinear Dynamics

, Volume 88, Issue 4, pp 2473–2489 | Cite as

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

  • Sarah Kassim
  • Hamid Hamiche
  • Saïd Djennoune
  • Maâmar Bettayeb
Original Paper

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.

Keywords

Private communication Chaotic synchronization Fractional-order systems Image encryption Modified-Hénon map Step-by-step observer Robustness 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Sarah Kassim
    • 1
  • Hamid Hamiche
    • 1
  • Saïd Djennoune
    • 1
  • Maâmar Bettayeb
    • 2
  1. 1.Laboratoire de Conception et Conduite des Systèemes de Production (L2CSP)UMMTOTizi-OuzouAlgeria
  2. 2.Department of Electrical/Electronics and Computer EngineeringUniversity of SharjahSharjahUAE

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