Digital data is increasing rapidly in the world day by day. Information security is important during data exchange over the Internet. The way to securely transmit images over the network is through the image encryption technique. In the proposed cryptography system, the hybridization of Lorenz-Rossler chaotic systems is used, and a random number sequence is generated. The security analyses such as histogram, correlation, differential attack, information entropy, and duration analysis of the study are performed. It is seen that the proposed system performs well, especially in terms of correlation. Additionally, the performance of the developed embedded system platforms is compared after testing on Nvidia Jetson Nano and Xilinx PYNQ Z1 boards. The Nvidia Jetson Nano board is more performant than the Xilinx PYNQ Z1 board. The safety and feasibility of the proposed system have been demonstrated.