Very recently, Byun and Lee suggested two provably secure group Diffie-Hellman key exchange protocols using
participant’s distinct passwords. Unfortunately, the schemes were found to be flawed by Tang and Chen. They presented two password guessing attacks such as off-line and undetectable on-line dictionary attacks by malicious insider attacker. In this paper, we present concrete countermeasures for two malicious insider attacks, and modify the two group Diffie-Hellman key exchange protocols to be secure against malicious insider password guessing attacks. Our countermeasures do not require additional round costs, hence they are efficient.