A novel analysis and applications of an introduced hyperchaotic system

In this study, the new analysis of the introduced hyperchaotic equation set was handled. The equation set was firstly analyzed mathematically and then the results were proven by designing a more efficient circuit with active elements. The aim of the study is offering an effective secure communication application and random number generator application. Hence, based on the new analysis of equation set, secure communication system and random number generation application were proposed. Accordingly, creating a Pseudorandom Number Generator is the halfway house in this study. The signals received from the chaotic oscillator were sampled at low frequency and with a simple post-processing, a bit stream was created. The resulting bit stream passed the NIST test successfully. The other halfway of the study is creating a secure communication system by the synchronization of two chaotic oscillators that are in transmitter and receiver. An identical noise-like signals are generated in both transmitter and receiver parts. At the transmitter part adding a noise-like chaotic signal to the information is done. At the receiver, this same noise-like signal is subtracted from the perceived signal. Thus, the information can be transmitted securely. Spice simulations of both proposed applications have been made and it has been shown that they are compatible with mathematical analysis. The proposed circuits are suitable for realization with commercially available circuit elements.