FPGA realization of four chaotic interference cases in a terrestrial trajectory model and application in image transmission.

This article presents a technique to integrate two dynamical models, a four-wing spherical chaotic oscillator and the elliptical path described by the planet Earth during its translation movement around the sun. Four application cases are derived from the system by varying the dynamics of the chaotic oscillator and these can be applied in information encryption to transmit RGB and grayscale images modulated by CSK. Consequently, the three main contributions of this work are (1) the emulation of the trajectories of the planet Earth with chaotic interference, (2) the CSK modulation and image encryption in a master-slave synchronization topology, and (3) the CSK demodulation for decryption without loss of information with respect to the original information. The three contributions are based on VHDL code implementation. The results of the synchronization, encryption and decryption technique were verified by means of time series and the encrypted images showed a correlation less than - 0.000142 and - 0.0003439 for RGB and grayscale format, respectively, while the retrieved image shows a complete correlation with the image original. In this work, the co-simulations were performed between MATLAB/Simulink and Vivado, using the VHDL language on two FPGA boards from different manufacturers, namely, Xilinx Artix-7 AC701 and Intel Cyclone IV.

On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission.

Synchronizing chaotic oscillators has been a challenge to guarantee successful applications in secure communications. That way, three synchronization techniques are applied herein to twenty two chaotic oscillators, three of them based on piecewise-linear functions and nineteen proposed by Julien C. Sprott. These chaotic oscillators are simulated to generate chaotic time series that are used to evaluate their Lyapunov exponents and Kaplan-Yorke dimension to rank their unpredictability. The oscillators with the high positive Lyapunov exponent are implemented into a field-programmable gate array (FPGA), and afterwards they are synchronized in a master-slave topology applying three techniques: the seminal work introduced by Pecora-Carroll, Hamiltonian forms and observer approach, and open-plus-closed-loop (OPCL). These techniques are compared with respect to their synchronization error and latency that is associated to the FPGA implementation. Finally, the chaotic oscillators providing the high positive Lyapunov exponent are synchronized and applied to a communication system with chaotic masking to perform a secure image transmission. Correlation analysis is performed among the original image, the chaotic channel and the recovered image for the three synchronization schemes. The experimental results show that both Hamiltonian forms and OPCL can recover the original image and its correlation with the chaotic channel is as low as 0.00002, demonstrating the advantage of synchronizing chaotic oscillators with high positive Lyapunov exponent to guarantee high security in data transmission.