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arXiv:1811.07410 · Physical Review A

Practical and unconditionally secure spacetime-constrained oblivious transfer

Damián Pitalúa-García, Iordanis Kerenidis

Published Sep 24, 2018• 22 citations
arXivHTMLPDF

Abstract

Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location-oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We also show that our SCOT protocol can be used to implement unconditionally secure quantum relativistic bit commitment.

DOI
10.1103/physreva.98.032327

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Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location-oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We also show that our SCOT protocol can be used to implement unconditionally secure quantum relativistic bit commitment.
In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0,x1{x}_{0},{x}_{1}x0​,x1​, Bob inputs a bit bbb and outputs xb{x}_{b}xb​. Secure OT requires that Alice and Bob learn nothing about bbb and xb‾{x}_{\overline{b}}xb​, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output xb{x}_{b}xb​ within Rb{R}_{b}Rb​, where R0{R}_{0}R0​ and R1{R}_{1}R1​ 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.
We present a simple and practical quantum protocol involving two mistrustful agencies in Minkowski space, which allows Alice to transfer data to Bob at a space-time location that neither can predict in advance. The location depends on both Alice's and Bob's actions. The protocol guarantees unconditionally to Alice that Bob learns the data at a randomly determined location; it guarantees to Bob that Alice will not learn the transfer location even after the protocol is complete. The task implemented, transferring data at a space-time location that remains hidden from the transferrer, has no precise analog in nonrelativistic quantum cryptography. It illustrates further the scope for novel cryptographic applications of relativistic quantum theory.
In one-out-of-mmm spacetime-constrained oblivious transfer (SCOT), Alice and Bob agree on mmm 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 xi{\mathbf{x}}_{i}xi​ in the causal past of a spacetime point Qi{Q}_{i}Qi​ of Ri{R}_{i}Ri​, 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 xb{\mathbf{x}}_{b}xb​ in Rb{R}_{b}Rb​; Alice remains oblivious to bbb anywhere in spacetime; and Bob is unable to obtain xi{\mathbf{x}}_{i}xi​ in Ri{R}_{i}Ri​ and xj{\mathbf{x}}_{j}xj​ in Rj{R}_{j}Rj​ for any pair of different numbers $i,j\ensuremath{\in}{0,1,...,m\ensuremath{-}1}$. We introduce unconditionally secure one-out-of-mmm 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-mmm distributed quantum access with classical memory (DQACM), which works as a subroutine to implement a class PCC{\mathcal{P}}_{\text{CC}}PCC​ of one-out-of-mmm SCOT protocols where distant agents only need to communicate classically. We present unconditionally secure one-out-of-mmm DQACM protocols and one-out-of-mmm SCOT protocols of the class PCC{\mathcal{P}}_{\text{CC}}PCC​, for arbitrary integers $m\ensuremath{\ge}2$. We discuss various generalizations of SCOT. In particular, we introduce a straightforward extension of SCOT to a kkk-out-of-mmm setting, and suggest protocols where distant agents only need to communicate classically, while we leave the investigation of their security as an open problem.
We study the cryptographic primitive Oblivious Transfer; a composable construction of this resource would allow arbitrary multi-party computation to be carried out in a secure way, i.e. to compute functions in a distributed way while keeping inputs from different parties private. First we review a framework that allows us to analyze composability of classical and quantum cryptographic protocols in special relativity: Abstract Cryptography implemented with Causal Boxes. We then (1) explore and formalize different versions of oblivious transfer found in the literature, (2) prove that their equivalence holds also in relativistic quantum settings, (3) show that it is impossible to composably construct any of these versions of oblivious transfer from only classical or quantum communication among distrusting agents in relativistic settings, (4) prove that the impossibility also extends to multi-party computation, and (5) provide a mutual construction between oblivious transfer and bit commitment.
Oblivious transfer (OT) and bit commitment (BC) are two-party cryptographic protocols which play crucial roles in the construction of various cryptographic protocols. We propose three practical quantum cryptographic protocols in this paper. We first construct a practical quantum random oblivious transfer (R-OT) protocol based on the fact that non-orthogonal states cannot be reliably distinguished. Then, we construct a fault-tolerant one-out-of-two oblivious transfer ( O T 1 2 ) protocol based on the quantum R-OT protocol. Afterwards, we propose a quantum bit commitment (QBC) protocol which executes the fault-tolerant O T 1 2 several times. Mayers, Lo and Chau (MLC) no-go theorem proves that QBC protocol cannot be unconditionally secure. However, we find that computing the unitary transformation of no-go theorem attack needs so many resources that it is not realistically implementable. We give a definition of physical security for QBC protocols and prove that the practical QBC we proposed is physically secure and can be implemented in the real world.
Quantum physics allows for unconditionally secure communication between parties that trust each other. However, when the parties do not trust each other such as in the bit commitment scenario, quantum physics is not enough to guarantee security unless extra assumptions are made. Unconditionally secure bit commitment only becomes feasible when quantum physics is combined with relativistic causality constraints. Here we experimentally implement a quantum bit commitment protocol with relativistic constraints that offers unconditional security. The commitment is made through quantum measurements in two quantum key distribution systems in which the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. In each run of the experiment, a bit is successfully committed with less than 5.68×10(-2) cheating probability. This demonstrates the experimental feasibility of quantum communication with relativistic constraints.