One-out-of-m spacetime-constrained oblivious transfer
Abstract
In one-out-of-m spacetime-constrained oblivious transfer (SCOT), Alice and Bob agree on m pairwise spacelike separated output spacetime regions R0,R1,…, Rm-1 in an agreed reference frame in a spacetime that is Minkowski, or close to Minkowski; Alice inputs a message xi in the causal past of a spacetime point Qi of Ri, for i∈\0,1,…,m-1\; Bob inputs b∈\0,1,…,m-1\ in the intersection of the causal pasts of Q0,Q1,…,Qm-1 and outputs xb in Rb; Alice remains oblivious to b anywhere in spacetime; and Bob is unable to obtain xi in Ri and xj in Rj for any pair of different numbers i,j∈\0,1,…,m-1\. We introduce unconditionally secure one-out-of-m SCOT protocols extending the one-out-of-two SCOT protocols of Pital\'ua-Garc\'ia [Phy. Rev. A 93, 062346 (2016)] and Pital\'ua-Garc\'ia and Kerenidis [Phy. Rev. A 98, 032327 (2018)], for arbitrary integers m≥ 2. We define the task of one-out-of-m distributed quantum access with classical memory (DQACM), which works as a subroutine to implement a class PCC of one-out-of-m SCOT protocols where distant agents only need to communicate classically. We present unconditionally secure one-out-of-m DQACM protocols and one-out-of-m SCOT protocols of the class PCC, for arbitrary integers m≥2. We discuss various generalizations of SCOT. In particular, we introduce a straightforward extension of SCOT to a k-out-of-m setting, and suggest protocols where distant agents only need to communicate classically, while we leave the investigation of their security as an open problem.