Proposals for a password-based authenticated key exchange protocol that have been published so far almost concentrated on the provable security. But in a real environment such as mobile one, efficiency is a critical issue as security. In this paper we discuss the efficiency of PAK which is secure in the random oracle model ［l］. Among 4 hash functions in PAK the instantiation for $H_1$, which outputs a verifier of the password, has most important effect on the computational efficiency. We analyze two different methods for $H_1$ suggested in ［1］ and we show that $H_{lq}$ has merits in transforming to EC or XTR variants as well as in the efficiency. As an efficient variant. we propose PAK2-EC and PAK2-XTR which do not require any additional step converting a hash output into a point of elliptic curve or XTR subgroup when compared to the previous work on the PAK［2］. Finally we compare PAK2 with the password-based authenticated key exchange protocols such as SPEKE, SRP, and AMP