Spacetime-constrained oblivious transfer

TL;DR

This paper introduces spacetime-constrained oblivious transfer (SCOT), a relativistic cryptographic task where Bob must output a secret within a specific spacetime region, and demonstrates its security limitations and a quantum protocol in Minkowski spacetime.

Contribution

It formalizes SCOT in Minkowski spacetime, proves the impossibility of unconditionally secure classical and Galilean quantum protocols, and presents a secure quantum protocol in Minkowski spacetime.

Findings

Classical SCOT is impossible to secure unconditionally.

Quantum SCOT can be unconditionally secure in Minkowski spacetime.

Spacetime constraints fundamentally affect cryptographic protocol security.

Abstract

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.