Key generation research of RSA public cryptosystem and Matlab implement

RSA is the asymmetric cryptography system. The security of RSA public key cryptosystem is based on the assumption that factoring of a large modulus is difficult. In RSA if someone can factor modulus into a product of two prime numbers, then the private key is also detected and hence the security of the cryptosystem is broken. So it is quite important to research the selection of prime and derive private key from public key. This paper introduces the basic number theories of RSA cryptosystem and applies t to key algorithm of RSA cryptosystem, such as Euclidean and its extension theorem, square-multiply algorithm and prime number testing. At last, provides a description of Matlab simulation of key algorithm and RSA encryption and decryption. The result shows that the whole simulation took 0.140176s, and solves the problem of key transmission.