New methods for constructing 2n / 2n+1-dimensional conservative chaotic systems and FPGA implementation

Conservative chaotic systems (CCS) show better applicability in chaos-based secure communication compared to dissipative chaotic systems (DCS). In this paper, two new approaches to design 2n-dimensional and 2n+1-dimensional Hamiltonian Conservative Chaotic Systems (HCCS) are given to generate systems with unique dynamic properties. Three HCCS instances validate the effectiveness of the proposed framework. Through a comprehensive analysis of 4D/5D-HCCSs, including equilibrium points, Lyapunov exponents, phase diagrams, bifurcation diagrams, and Hamiltonian energy evolutions, it is found that they exhibit different phenomena when the parameters of the system are varied. Moreover, the 4D-SDMCCS and 4D-MDMCCS are proposed by introducing a new segmentation function (named Sin-IPC) in 4D-HCCS, and the dynamical analyses of the systems demonstrate that have a controllable number of scrolls. Differently, the proposed 5D-HCCS has a multistability phenomenon and nested phenomenon under the Hamiltonian energy control, and the Lyapunov exponents of the system increase with the increase of Hamiltonian energy. Finally, to verify the practicability of the proposed methods, a novel pseudorandom number generator (PRNG) based on type 1.1 4D-MDMCCS and 5D-HCCS is designed and implemented in hardware by using FPGA, the experiments prove that the designed PRNG has a large key space and a good randomness of the output sequence, it can reasonably utilize hardware resources, has high throughput, and ensures the output of high-quality pseudo-random sequences, which can be used in the fields of random number generation, confidential communication and nonlinear control.