Year: 2019
Type: article
Abstract: In one-out-of-$m$ spacetime-constrained oblivious transfer (SCOT), Alice and Bob agree on $m$ pairwise spacelike separated output spacetime regions ${R}_{0},{R}_{1},...,{R}_{m\ensuremath{-}1}$ in an agreed reference frame in a spacetime that is Minkowski, or close to Minkowski; Alice inputs a message ${\mathbf{x}}_{i}$ in the causal past of a spacetime point ${Q}_{i}$ of ${R}_{i}$, for $i\ensuremath{\in}{0,1,...,m\ensuremath{-}1}$; Bob inputs $b\ensuremath{\in}{0,1,...,m\ensuremath{-}1}$ in the intersection of the causal pasts of ${Q}_{0},{Q}_{1},...,{Q}_{m\ensuremath{-}1}$ and outputs ${\mathbf{x}}_{b}$ in ${R}_{b}$; Alice remains oblivious to $b$ anywhere in spacetime; and Bob is unable to obtain ${\mathbf{x}}_{i}$ in ${R}_{i}$ and ${\mathbf{x}}_{j}$ in ${R}_{j}$ for any pair of different numbers $i,j\ensuremath{\in}{0,1,...,m\ensuremath{-}1}$. We introduce unconditionally secure one-out-of-$m$ SCOT protocols extending the one-out-of-two SCOT protocols of Pital\'ua-Garc\'{\i}a [Phys. Rev. A 93, 062346 (2016)] and Pital\'ua-Garc\'{\i}a and Kerenidis [Phys. Rev. A 98, 032327 (2018)], for arbitrary integers $m\ensuremath{\ge}2$. 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 ${\mathcal{P}}_{\text{CC}}$ 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 ${\mathcal{P}}_{\text{CC}}$, for arbitrary integers $m\ensuremath{\ge}2$. 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.
Source: Physical Review A
Author: Damián Pitalúa-García
Institution: University of Cambridge
Language: Latvian
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G2505040309
OpenAlex ID: W2953688188