Round-optimal password-based authenticated key exchange

We show a general framework for constructing password-based authenticated key exchange protocols with optimal round complexity — one message per party, sent simultaneously — in the standard model, assuming a common reference string. When our framework is instantiated using bilinear-map cryptosystems, the resulting protocol is also (reasonably) efficient. Somewhat surprisingly, our framework can be adapted to give protocols in the standard model that are universally composable while still using only one (simultaneous) round.