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In this paper, we propose a hybrid password-based authenticated key exchange protocol (BPAKE) with stronger security using bilinear pairings. The proof of security for BPAKE is in the random oracle model and based on hardness of the Gap Diffie-Hellman problem and Gap Bilinear Diffie-Hellman problem. We also prove that BPAKE can resist password-compromise impersonation (PCI) attacks. The proposed protocol requires two communication steps, which is more efficient than previous solutions in terms of communication complexity. Due to its acceptable computation cost and low communication cost, our protocol is particularly suitable for implementation in the public wireless LANs.