FPGA implementation and voice encryption application of a new hyperchaotic system with high complexity

This research work describes a new 4-D hyperchaotic system with high complexity. The proposed 4-D system is hyperchaotic as it has a bounded attractor set with two positive Lyapunov exponents. The large positive Lyapunov exponents of the new 4-D hyperchaotic system exhibit the high complexity of the proposed system. We also show that two nearly identical trajectories quickly separate, with significant differences emerging within just 0.6 seconds, which illustrates the high sensitivity of the state trajectories of the proposed hyperchaotic systems to initial conditions and significant unpredictability. Multistability for the newly proposed hyperchaotic system is illustrated by plotting two different coexisting hyperchaotic attractors for the identical values of the system's parameters, but for non-identical initial conditions. We also explore offset boosting, a control strategy that allows us to convert the bipolar signal into a unipolar signal without changing the dynamics, which makes the proposed system more adaptable for a range of applications. The electronic implementation of the new system with high complexity is done herein by applying the well-known Euler's method, which is implemented on a field-programmable gate array (FPGA). In this 4-D system, the nonlinear terms are the multiplication of two state variables that appear in each ordinary differential equation. The FPGA design for the newly developed hyperchaotic system with high complexity is implemented on the Zybo Z7-20 development board with xc7z020clg400-1. In this study, the potential of the new 4D hyperchaotic system in the field of information security was investigated and encryption of voice data was performed using the newly developed hyperchaotic system with high complexity. The variables of the system were evaluated with differential entropy analysis and high randomness levels were verified. The XOR-based encryption algorithm developed using these variables obtained with numerical solutions provides effective protection at time, frequency and statistical levels and allows lossless recovery of data.