Nonlinear Dyn DOI 10.1007/s11071-017-3390-8 ORIGINAL PAPER A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems Sarah Kassim · Hamid Hamiche · Saïd Djennoune · Maâmar Bettayeb Received: 26 September 2016 / Accepted: 29 January 2017 © Springer Science+Business Media Dordrecht 2017 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 con- sidered 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 estab- lished. To make the transmission scheme secure, an encryption function is used to cipher the original infor- mation 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 S. Kassim (B )· H. Hamiche · S. Djennoune Laboratoire de Conception et Conduite des Systèemes de Production (L2CSP), UMMTO, BP 17 RP, 15000 Tizi-Ouzou, Algeria e-mail: kassim.sarah91@gmail.com H. Hamiche e-mail: hamid.hamiche07@gmail.com S. Djennoune e-mail: s_djennoune@yahoo.fr M. Bettayeb Department of Electrical/Electronics and Computer Engineering, University of Sharjah, Sharjah, UAE 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 intro- duced 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 syn- chronization · Fractional-order systems · Image encryption · Modified-Hénon map · Step-by-step observer · Robustness 1 Introduction Nowadays, information security is becoming an increasingly important topic due to the rapid progress of communication network and information technol- ogy [1], especially the security of images. Actually, images from various sources for various applications are required to be confidential between the transmit- ter and the receiver, such as medical imaging systems, architectural drawings, military image databases, and so on. Due to some intrinsic features of images, such as high correlation among adjacent pixels, bulk vol- ume of data, real-time requirement and high redun- 123