A conventional DHCP authentication system could not cope with a one-phase-two-messages DHCP sequence involved in a Rapid-Commit option. Further, in the conventional DHCP authentication system, it is possible to attack retransmission at lease renewal timing and, when information used in a retransmission system between a client and a server becomes the loss of synchronization, the conventional DHCP authentication system cannot detect the loss of synchronization and has such a problem that unnecessary traffics are continuously produced. A DHCP client device includes a means that stores a user ID, a secret key, and retransmission detection system (RDM) information. A DHCP server device includes a database that is available for the retrieval of a secret key and RMD information based on a user ID as a key or an access mechanism to an external DB with the same function as that of the database.