When a network connection request is sent from a user's personal computer (2) to a server (1) on the Internet (5), the server (1) sends an authentication confirmation number generated by a random number generating unit (13) to the personal computer (2) of the connection requester. The connection requester connects a portable telephone (3) to a modem (4) and enters the authentication confirmation number displayed on the personal computer (2) through operation of keys of the portable telephone (3). An authentication unit (16) authenticates the connection request of the connection requester to set up connection to the network if the telephone number of the portable telephone (3) stored in a user information storage unit (12) agrees with the telephone number sent to the modem (4) and if the authentication confirmation number entered through the portable telephone (3) is correct.