Recently, Vaidyanathan et al. (Complex Systems and Their Applications, Springer, New York, USA, 2024 [16]) introduced a new 4-D highly chaotic system with a hyperbola of equilibrium points. In this work,we carry out a FPGA implementation of the Vaidyanathan chaotic system, which will be very useful for practical implementations. The FPGA implementation of the Vaidyanathan chaotic system is performed herein by applying the fourth-order Adams-Bashforth method. After observing the simulation of the chaotic system, the amplitudes of the state variables and can be processed by doing a computer arithmetic with 40-bit distributed in fixed-point format. The connection of a digital-to-analog (DAC) converter to the FPGA, leads us to observe experimental attractors on a Teledyne Lecroy oscilloscope, which are in good agreement with simulation results. Also, a new random number generator (RNG) based on a hyperchaotic system is designed on the Nvidia Jetson Nano development board. The generated random numbers have successfully passed the NIST 800-22, FIPS 140-1, and ENT statistical tests, demonstrating their suitability for use in the field of encryption. Additionally, an image encryption application based on these random numbers is successfully implemented on the Nvidia Jetson Nano platform. Finally, the reliability of the encryption process is convincingly demonstrated through histogram, correlation, NPCR-UACI, and entropy analyses. This study shows that the hyperchaotic system-based random number generator can be effectively and securely utilized in the field of encryption.