This paper gives a formal analysis on the authenticated key exchange protocol based on password using the theory of the strand space model.We introduce the ability on modeling the DH problem and the guessing attack

and then give a proof on secrecy of the password

authentication and the secrecy of the session key of the simplified DH-EKE protocol.Based on the analysis

we propose a basic condition of the key exchange protocol based on password on resisting the guessing attack.Extending the method to the three-party case

a necessary condition is concluded to guarantee the security of the three-party authenticated key exchange protocol based on the pure password.