Almost all network systems provide an authentication mechanism based on user ID and password. In such system, it is easy to obtain the user password using a sniffer program with illegal eavesdropping. The one-time password and challenge-response method are useful authentication schemes that protect the user passwords against eavesdropping. In client/server environments, the one-time password scheme using time is especially useful because it solves the synchronization problem. It is the stability that is based on Square Root Problem, and we would like to suggest PBI(password Based Identification), enhancing the stability, for all of the well-known attacks by now including Off-line dictionary attack, password file compromise, Server and so on. The PBI is also excellent in the aspect of the performance.