A terminal identification method is provided which enables two-way communications between terminals and a network while identifying terminal IDs and protecting privacy. Also, authentication method and system are provided which require no complicated calculating process, less steps and smaller amount for wireless communications, and less power consumption. A server and terminal share a hash function and an initial value determined for each terminal, calculate the same temporary ID by hashing the initial value the same number of times with the hash function, and identify the terminal using the calculated temporary ID. The server and the terminal also hold a common hash function and authentication information, acquire an authenticating communication parameter from communication parameters temporarily common during communication, and generate an authentication key using the authentication information, the authenticating communication parameter, and the hash function. Then at least one of the server and terminal performs authentication using the generated authentication key.