Robust Image Transmission Scheme Based on Coupled Fractional-Order Chaotic Maps

Abstract

In this paper, we propose a novel image transmission scheme based on fractional-order discrete-time systems and on observers design. At the transmitter level, a grayscale original image is encrypted using chaotic signals generated from two different fractional-order chaotic systems. These signals should be available at the receiver level in order to recover this image at the reception end. This is why, two fractional-order observers are used to estimate the states of each fractional-order systems. In addition, in order to show the effectiveness of the proposed transmission system, simulation results will be illustrated and different analysis are given to illustrate and highlight the security and robustness of the proposed scheme.

Applying exponential unit for breaking symmetry of memristive maps

“…This uniform pattern observed in the histograms confirms the successful concealment of image intensity information. By applying the chi-square test [44,45], we get χ 2 = 261.35. It highlights the formidable challenge of extracting information from encrypted images and thereby emphasizes the robustness of the proposed encryption algorithm against statistical attacks.…”

A new synchronization result for fractional-order discrete-time chaotic systems via bandlimited channels

“…Additionally, the intricate geometric interpretation of the non-local effects of fractional derivatives in space or time adds another intriguing dimension to the use of fractional-order chaotic systems in secure transmission. Due to these compelling features, the application of fractional-order chaotic systems in secure communications poses a significant challenge in the field of data transmission when compared to integer-order chaotic systems [27][28][29][30][31][32]. For this, several synchronization methods have been proposed.…”

“…Motivated and instigated by the above pros of fractional-order chaotic systems in contrast to the integerorder ones, our purpose in [24] consisted in illustrating the transmission feasibility and efficiency over bandlimited sharing channel and using fractional-order chaotic maps. However, the synchronization occurring and establishment has not been deeply studied in such a case.…”

“…As far as the authors are aware, apart our former contribution in [24], the stability and synchronization analysis of discrete non-integer order chaotic maps with infinite dimensions and linked by bandlimited channels has not been yet surveyed.…”

“…The advantage of using discrete dynamics for secure transmission is mainly motivated by the simplicity of implementation of transmission schemes (digital systems and filters) on microcontroller boards. Still within this context, in [24], we have introduced a novel communication process by replacing the integer-order chaotic systems used by [23] for ciphering and dicephering by the ones whose dynamics are differentiated to fractional orders. This class of dynamics is most often called fractional-order chaotic systems.…”