Abstract: An authentication system giving little load for the user at the time of authentication and retaining high security is realized. A management part 107 of a server apparatus 106 memorizes a password of a character queue of a plurality of digits. A random number generating part 108 generates a random number for each digit of a password. A communication part 111 transmits a plurality of random numbers to a terminal apparatus 101. A calculation part 109 calculates an authentication value used for authentication, with using a random number and a sign of a password, for each digit of the password. In the terminal apparatus 101, a display part 102 displays a random number for each digit of the password, and an input part inputs an input numerical value in response to the random number, for each digit of the password. The input numerical value of each digit is transmitted to the server apparatus 106 through a communication part 105.