Authentication method and system for use thereof

An authentication method (20) for an authentication system (10) includes executing an application program in a host device (100); the application program obtaining a first service code; the application program determining whether the host device (100) is legal according to a check information; the application program transmitting an authentication request to an electronic device (102) obtaining a first validation value when the application program determines the host device (100) is legal; and the application program performing an encryption computation according to the first validation value, the first service code, and an authentication private key, and generating a response value for the electronic device (102); wherein the electronic device (102) performs a decryption computation corresponding to the encryption computation according to the authentication private key and the response value to obtain the second validation value and the second service code to determine whether to open a service.