Three-party EKE was proposed to establish a session key between two clients through a server However, three-party EKE is insecure against undetectable on-line and off-line password guessing attacks In this paper, we first propose an enhanced three-party EKE to withstand the security risk in three-party EKE We also propose a verifier-based three-party EKE that is more secure than a plaintext-equivalent mechanism in which a compromise of the server's database will not result in success in directly impersonating clients