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Protocols for password-based authenticated key exchange (PAKE) allow two users who share only a short, low-entropy password to agree on a cryptographically strong session key. One must ensure that protocols are immune to off-line dictionary attacks in which an adversary exhaustively enumerates all possible passwords in an attempt to determine the correct one. Recently Katz, et al.  gave a new framework for realizing PAKE without random oracles, in the common reference string model. In this paper, we instantiate the framework of  under the lattices assumptions. Specifically, we modified the lattice-based approximate projective hashing introduced in  and plug it into the framework of , and we prove our new PAKE is efficient and secure based on the security of GK's PAKE framework  in the standard model.