  We present a new template for building oblivious transfer from quantum
information that we call the "fixed basis" framework. Our framework departs
from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the correct
choice of measurement basis used by each player, except for some hidden trap
qubits that are intentionally measured in a conjugate basis. We instantiate
this template in the quantum random oracle model (QROM) to obtain simple
protocols that implement, with security against malicious adversaries:
  1. Non-interactive random-input bit OT in a model where parties share EPR
pairs a priori.
  2. Two-round random-input bit OT without setup, obtained by showing that the
protocol above remains secure even if the (potentially malicious) OT receiver
sets up the EPR pairs.
  3. Three-round chosen-input string OT from BB84 states without entanglement
or setup. This improves upon natural variations of the CK88 template that
require at least five rounds.
  Along the way, we develop technical tools that may be of independent
interest. We prove that natural functions like XOR enable seedless randomness
extraction from certain quantum sources of entropy. We also use idealized (i.e.
extractable and equivocal) bit commitments, which we obtain by proving security
of simple and efficient constructions in the QROM.
