Through constructing and utilizing non-malleable, extractable, and weak simulation-sound trapdoor commitment schemes and corresponding smooth projective hash function familes, this paper proposes an efficient two-party password authenticated key exchange (PAKE) protocol within the universal composable (UC) framework, which is the optimal two-round PAKE protocol in this setting. Rigorous security proofs based on standard assumptions in the presence of static corruption adversary are then given out. Comparisons with previously proposed protocols show that, this protocol avoids the use of zero-knowledge protocols, and achieves a higher performance in terms of communication efficiency while attaining a comparable computational complexity.