The invention discloses an encryption and decryption hardware system based on RSA cryptographic algorithm, comprises an RSA main control module, a key generation module, an encryption control module,a decryption control module, a modulo exponentiation module, a modulo multiplication operation module and a large number multiplier module, wherein, the RSA main control module is used for calling theencryption control module and the decryption control module; The key generation module is used for generating a public key {e, N} and a private key {d, N} needed for encryption and decryption; The invention aims at the problems of large calculation amount, slow encryption and decryption operation speed and large area realized by hardware in the prior RSA hardware system, and under the condition of giving consideration to the hardware area and the realization speed, the improved Montgomery modular multiplication algorithm and the L-R modulo exponentiation algorithm are combined. The hardware system and the method of RSA encryption and decryption are designed, so the hardware system and the method can reduce the calculation amount in the process of RSA encryption and decryption, improve thespeed of RSA encryption and decryption, and reduce the area of the chip.