In 2009, Abdalla et al. proposed a reasonably practical password-authenticated key exchange (PAKE) secure against adaptive adversaries in the universal composability (UC) framework. It exploited the Canetti-Fischlin methodology for commitments and the Cramer-Shoup smooth projective hash functions (SPHFs), following the Gennaro-Lindell approach for PAKE. In this paper, we revisit the notion of non-interactive commitments, with a new formalism that implies UC security. In addition, we provide a quite efficient instantiation. We then extend our formalism to SPHF-friendly commitments. We thereafter show that it allows a blackbox application to one-round PAKE and oblivious transfer (OT), still secure in the UC framework against adaptive adversaries, assuming reliable erasures and a single global common reference string, even for multiple sessions. Our instantiations are more efficient than the Abdalla et al. PAKE in Crypto 2009 and the recent OT protocol proposed by Choi et al. in PKC 2013. Furthermore, the new PAKE instantiation is the first one-round scheme achieving UC security against adaptive adversaries.