In wireless ad hoc networks environment, Bellovin and Merritt first developed a password-based Encrypted Key Exchange (EKE) protocol against offline dictionary attacks using both symmetric and public-key cryptography independent of the public key infrastructure (PKI). In this paper, we first discover that there exist some weaknesses in EKE protocol that is subjected to imposter attacks based on the analysis result of BAN logic that we apply in EKE protocol. In order to remedy the flaws, we propose an improved scheme--Provable Password-Authenticated Key Exchange (PPAKE) protocol that generates the session key's timestamp, and verifies the authenticity of public key against imposter attack without online trusted third parties. The proposed protocol is also proven to be secure and trustworthy by BAN logic analysis. In comparison with other schemes, our measurements show that our proposed PPAKE protocol is more safety and requires less computations cost suitable for wireless ad hoc n...