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

Abstract

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.

A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer

“…where the estimates of variablesŵ 1 andŵ 2 are calculated according to Equation (11). So, the receiver MATLAB/Simulink model structure according to model (5), (19) has the form shown in Figure 11.…”

“…where the estimates of variables and are calculated according to Equation (11). So, the receiver MATLAB/Simulink model structure according to model (5), (19) has the form shown in Figure 11. Figure 11 displays our MATLAB/Simulink model of the receiver with the two-channel synergetic observer and implements the initial model and observer equations from Subsection 3.5.…”

“…We obtain the observer Equation (19) taking into account the found functions for the reduction Equation (11).…”

“…For simulation, the resulting closed-loop system can be represented in a form suitable for numerical simulation. FPGA implementation techniques for chaotic systems are described by Tlelo-Cuautlea, et al [20], by Guillen-Fernandezb et al [19] and in other related papers. Notably, Tlelo-Cuautlea, et al [20] demonstrate the implementation of Forward Euler and Runge-Kutta numerical methods on an FPGA.…”

“…To compare the obtained results, the chaotic system was estimated using the least squares method in Section 3.7. In Section 4.1, some hardware system implementation options on an Arduino, Raspberry Pi and FPGAs are discussed based on examples from other studies described earlier [14][15][16][17][18][19][20]. Besides Section 4 provides examples of system software implementation, including an example of digital data software transmission (Section 4.2) and secured image transmission via the designed system in Section 4.3.…”