Nowadays, M-Quadrature Amplitude Modulation (M-QAM) techniques are widely used to modulate information by bit packets due to their ability to increase transfer rates. These techniques require more power when increasing the modulation index M to avoid interference between symbols. This article proposes a technique that does not suffer from interference between symbols, but instead uses memory elements to store the modulation symbols. In addition, the aim of this paper is to implement a four-dimensional reconfigurable chaotic oscillator that generates 16-Chaotic Phase Shift Keying (16-CPSK) modulation–demodulation carriers. An encryption and modulation transmitter module, a reception module, and a master–slave Hamiltonian synchronization module make up the system. A 16-CPSK modulation scheme implemented in Field Programmable Gate Array (FPGA) and applied to a red-green-blue (RGB) and grayscale image encryption system are the main contributions of this work. Matlab and Vivado were used to verify the modulation–demodulation scheme and synchronization. This proposal achieved excellent correlation coefficients according to various investigations, the lowest being −15.9×10−6 and 0.13×10−3 for RGB and grayscale format images, respectively. The FPGA implementation of the 16-CPSK modulation–demodulation system was carried out using a manufacturer’s card, Xilinx’s Artix-7 AC701 (XC7A200TFBG676-2).