One-out-of- spacetime-constrained oblivious transfer
arXiv:1907.02475 · doi:10.1103/PhysRevA.100.012302
Abstract
In one-out-of- spacetime-constrained oblivious transfer (SCOT), Alice and Bob agree on pairwise spacelike separated output spacetime regions in an agreed reference frame in a spacetime that is Minkowski, or close to Minkowski; Alice inputs a message in the causal past of a spacetime point of , for ; Bob inputs in the intersection of the causal pasts of and outputs in ; Alice remains oblivious to anywhere in spacetime; and Bob is unable to obtain in and in for any pair of different numbers . We introduce unconditionally secure one-out-of- SCOT protocols extending the one-out-of-two SCOT protocols of Pitalúa-García [Phy. Rev. A 93, 062346 (2016)] and Pitalúa-García and Kerenidis [Phy. Rev. A 98, 032327 (2018)], for arbitrary integers . We define the task of one-out-of- distributed quantum access with classical memory (DQACM), which works as a subroutine to implement a class of one-out-of- SCOT protocols where distant agents only need to communicate classically. We present unconditionally secure one-out-of- DQACM protocols and one-out-of- SCOT protocols of the class , for arbitrary integers . We discuss various generalizations of SCOT. In particular, we introduce a straightforward extension of SCOT to a -out-of- setting, and suggest protocols where distant agents only need to communicate classically, while we leave the investigation of their security as an open problem.