  In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x_0, x_1, Bob
inputs a bit b and outputs x_b. Secure OT requires that Alice and Bob learn
nothing about b and x_{\bar{b}}, respectively. We define spacetime-constrained
oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output
x_b within R_b, where R_0 and R_1 are fixed spacelike separated spacetime
regions. We show that unconditionally secure SCOT is impossible with classical
protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in
Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime,
and we show it unconditionally secure.
