Abstract: As the core component of postquantum signature algorithm Falcon,Residual Number System (RNS) is of great significance for solving the NTRU equation in key generation module of algorithm.In this paper,FPGA implementation of RSN is introduced.Residual number generation,cyclic group inversion module and residual number reduction module are deeply studied.An efficient hardware design idea and structure is proposed,where main framework of the algorithm is designed using the parallel structure and cyclic iteration is adopted for optimization.Synthesis is performed on chip and an overall improvement scheme of the algorithm is presented.Applications of the RNS in 6-rounds lift ring are all realized and data volume is further increased.Hardware implementation of modular generation module application in 10-rounds lift ring is performed with less logical resource and higher operating speed.