The invention discloses an RSA key pair fast generation system and an RSA key pair fast generation method. The system comprises a CPU core, a cipher coprocessor, a prime number generator, and a memory. The prime number generator is used for filtering composite numbers, is implemented in hardware form, supports 256-bit, 512-bit, 1024-bit, 2048-bit and 4096-bit composite number filtering, and completes modular redundancy, calculation and identification table setting. According to the RSA key pair fast generation method, in order to realize fast key pair retrieving, filtering and judging in an asymmetric algorithm, a hardware-based composite number filtering scheme is adopted, optimized modular exponentiation and improved Montgomery modular multiplication are employed, and the existing prime number decision algorithm is optimized. Thus, efficient prime number screening is realized, the key pair generation speed is increased, and the problem that the generation of an RSA key pair takes long in the existing encryption and decryption technology is solved.