This paper continues the study of password-based protocols for
authenticated key exchange (AKE).
In 2000, Bellare, Pointcheval, and Rogaway
proposed the formal model on AKE.
In this paper, we propose the new security notions on AKE, 
based on the non-malleability of session keys.
Then we prove that this security notion is equivalent to that proposed by 
Bellare, Pointcheval, and Rogaway.
Furthermore, we show that there is a protocol secure in the random oracle model 
not always secure in the standard model with collision-resistant hash functions.