# Coherent Chaotic Communication Using Generalized Runge-Kutta Method
###### Abstract
Another challenging problem is the lack of efficient techniques for modulating chaotic signals. Modulation is the process of varying one or more properties of a chaotic system, which generates the carrier signal, by following a separate sequence called the modulation signal that typically contains information to be transmitted and can be done in various ways, such as chaos shift keying [19], chaotic masking [20], parameter modulation [21; 22], symmetry coefficient modulation [22], and others. For non-coherent CCSs, one can mention differential chaos shift keying [23], quadrature chaos shift keying [24], and differential chaos shift keying code division multiple access [25]. Besides obvious robustness and easy implementation, non-coherent chaotic communication systems are not always able to provide high-level covertness for the transmitted information. Therefore, this study pays attention mainly to coherent communication systems. The choice of modulation scheme affects the performance and security level of the chaotic communication system as well as the complexity and cost of implementation. Modulation of chaotic signals requires high robustness to be able to change modulation parameters without breaking the desired oscillation mode and high resistivity to noise in the communication channel. Several secure communication schemes based on chaotic dynamics have been reported in the recent literature. [PERSON] et al. introduced a secure communication system based on extreme multistability [26]. [PERSON] et al. presented a chaotic secure communication scheme using a sliding-mode observer [27]. [PERSON] et al. [28] constructed a new six-dimensional Lorenz hyperchaotic system. The authors analyzed the equilibrium stability, dissipation, bifurcation, and Lyapunov exponent spectrum of the hyperchaotic system to verify its chaotic behavior. The simulation results indicate that the proposed scheme takes 0.45 s to synchronize, and the encryption method exhibits high security of transmission. [PERSON] et al. propose a new secure communications approach that is obtained by combining into one scheme the chaotic modulation, recursive encryption, and chaotic masking [20]. [PERSON] et al. [29] implemented a secure communication system for image encryption using the Raspberry Pi platform with MQTT for IoT protocol for transmission. Some other studies have been conducted on the use of chaotic oscillators in Internet of Things applications. [PERSON] et al. [30] analyzed the characteristics and operational aspects of chaos oscillators with a focus on low-power functionality, resilient chaotic oscillations, and resistance to parameter variations and noise. This analysis was aimed at advancing secure communication methodologies for wireless sensor networks in the Internet of Things and highlights the significance of chaotic dynamics for ensuring robust and secure data transmission. [PERSON] et al. presented a hyperchaos-based reconfigurable platform for real-time security of communicating embedded systems interconnected in networks following the Internet of Things (IoT) standards [31]. It should be noted that there are relatively few studies dedicated to hardware implementations of chaotic communication systems. [PERSON] et al. [32] developed a new optimal and simple approach for real-time implementation of continuous chaotic generator systems on a field programmable gate array (FPGA). The authors used the fourth-order Runge-Kutta method to obtain a discrete chaotic generator based on a well-known Chen system. [PERSON] et al. presented a memristor-based hyperchaotic circuit and implemented it in communication systems based on the same FPGA platform [33]. The signals obtained from the memristor-based hyperchaotic system have been utilized for both analog and digital communication schemes in this hardware solution and are a good demonstration of the nonlinearity of the memristor. [PERSON] et al. performed a comprehensive study on the effect of using different floating-point representations on the chaotic system's behavior [34].