FPGA Realization of Spherical Chaotic System with Application in Image Transmission

Abstract

This paper considers a three-dimensional nonlinear dynamical system capable of generating spherical attractors. The main activity is the realization of a spherical chaotic attractor on Intel and Xilinx FPGA boards, with a focus on implementation of a secure communication system. The first major contribution is the successful synchronization of two chaotic spherical systems, in VHDL program, in a master-slave topology using Hamiltonian forms. The synchronization errors show that the two spherical chaotic systems synchronize in a very short time after which the error signals become zero. The second major contribution is the FPGA realization of a spherical chaotic attractor-based secure communication system, which involves encrypting both grayscale and RGB images with chaos and diffusion key at the transmitting system, sending the encrypted image via the state variables, and reconstructing the encrypted image at the receiving system. The Intel Stratix III and Xilinx Artix-7 AC701 results are the same as those of MATLAB. The statistical analyses of the encrypted and received images show that the implemented system is very effective, as it reveals high degree of randomness in the encrypted images with the entropy test, and the obtained correlation coefficient, which is zero, removes relativity between the original and encrypted images. Finally, the transmission system fully recovers the original grayscale and RGB images without loss of information.

A Novel Chaotic System with Wide Spectrum, its Synchronization, Circuit Design and Application to Secure Communication

“…A chaotic system has complex nonlinear behaviors and characteristics like sensitivity to initial conditions, long-term aperiodic behavior, and a wideband spectrum of Fourier transform (1) . Such features are observed in the real system (2) , Chemical reactor system (3) , Ecological system (4) , Communication system (5) and Complex Network (6) , etc. Several novel chaotic systems have been reported and designed to date, given the first three-dimensional (3D) autonomous chaotic system reported by Lorenz (7) , such as Rossler system (8) , Chen system (9) , Chua system (10) , Liu system (11) , Lu system (12) , other novel chaotic systems (13)(14)(15)(16)(17)(18)(19)(20)(21) , etc.…”

“…Simultaneously, the reported chaotic systems have disadvantages during communication security, and the possible reasons are (1) the value of first Lyapunov Exponent (LE) is small so that the disordered degree of chaotic signal is not high. (2) the bandwidth of the chaotic signals is very low. First LE of a dissipative dynamic gives quantitative measure as positive nature of first LE implies chaos, and its value reflects disorder in chaos behavior.…”

Optimizing the Maximum Lyapunov Exponent of Fractional Order Chaotic Spherical System by Evolutionary Algorithms

“…Hence, the need to maximize the MLE is imperative, for example, as seen in [6,[14][15][16], whereby the task was performed as an optimization problem using evolutionary algorithms (EAs). It is believed that maximizing the MLE of a chaotic oscillator brings about better performance in chaos-based secure communication system [17]. Therefore, the motivation behind our work is the need to develop more complex and unpredictable chaotic systems for cryptosystems, secure communication systems, and random number generators.…”

A Unified FPGA Realization for Fractional-Order Integrator and Differentiator

“…FPGAs have an important role in digital communications and complicated systems because of their characteristics such as flexibility due to the predesigned configurable logic blocks (CLB) and a high speed, up to hundreds of megahertz (MHz) [16]. Unlike application specific integrated circuits (ASIC), the design-implement-test-debug cycle may take only hours on an FPGA while on ASIC it can take months.…”