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 $R_0,R_1,\dots ,R_{m-1}$ in an agreed reference frame in a spacetime that is Minkowski, or close to Minkowski; Alice inputs a message $x_i$ in the causal past of a spacetime point $Q_i$ of $R_i$, for $i\in \{0,1,\dots ,m-1\}$; Bob inputs $b\in \{0,1,\dots ,m-1\}$ in the intersection of the causal pasts of $Q_0,Q_1,\dots ,Q_{m-1}$ and outputs $x_b$ in $R_b$; Alice remains oblivious to $b$ anywhere in spacetime; and Bob is unable to obtain $x_i$ in $R_i$ and $x_j$ in $R_j$ for any pair of different numbers $i,j\in \{0,1,\dots ,m-1\}$. We introduce unconditionally secure one-out-of-$m$ 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 $m\ge 2$. 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 $m\ge 2$. 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.

References in corpus (28)

• Unconditionally secure quantum bit commitment is impossible
• Is Quantum Bit Commitment Really Possible?
• Insecurity of Quantum Secure Computations
• Is Entanglement Monogamous?
• Preparation contextuality powers parity-oblivious multiplexing
• Unconditionally Secure Bit Commitment
• Why Quantum Bit Commitment And Ideal Quantum Coin Tossing Are Impossible
• Cryptography from Noisy Storage
• Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes
• A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography
• Entanglement assisted random access codes
• Complete Insecurity of Quantum Protocols for Classical Two-Party Computation
• Unconditionally Secure Bit Commitment with Flying Qudits
• The Impossibility Of Secure Two-Party Classical Computation
• (4,1)-Quantum Random Access Coding Does Not Exist
• Quantum Tasks in Minkowski Space
• Coin Tossing is Strictly Weaker Than Bit Commitment
• Practical relativistic bit commitment
• Summoning Information in Spacetime, or Where and When Can a Qubit Be?
• Spacetime-constrained oblivious transfer
• Location-Oblivious Data Transfer with Flying Entangled Qudits
• A Quantum Paradox of Choice: More Freedom Makes Summoning a Quantum State Harder
• A No-summoning theorem in Relativistic Quantum Theory
• Practical and unconditionally secure spacetime-constrained oblivious transfer
• Improved Classical and Quantum Random Access Codes
• Quantum information causality
• S-money: virtual tokens for a relativistic economy
• Unconstrained Summoning for relativistic quantum information processing

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• Quantum oblivious transfer: a short review
• Cryptanalysis and improvement of Wu-Cai-Wu-Zhang's quantum private comparison protocol