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arXiv:1102.2816 · Physical Review A

Location-oblivious data transfer with flying entangled qudits

Adrian Kent

Published Jul 22, 2011• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.84.012328

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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.
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.
Here we propose a general relativistic quantum framework for cryptography that exploits the fascinating connection of quantum non-locality and special theory of relativity with cryptography. The underlying principle of unconditional security is causality and two-fold quantum non-local correlations: first entanglement swapping and then teleportation over causally independent entangled systems. We show that the proposed framework has following remarkable and novel features in mistrustful cryptography: (i) It helps in defining a new notion of oblivious transfer where both the data transferred and the transfer position remains oblivious. (ii) The authenticity and integrity of the data transferred is guaranteed by the fundamental principles of quantum theory instead of computational complexity. (iii) It directly leads to unconditionally secure and deterministic two-sided two-party computation which is currently considered to be impossible. (iv) the proposed framework turns out to be asynchronous ideal coin tossing with zero bias which has not been achieved previously. (v) The same framework also implies unconditionally secure bit commitment. Finally, the combination of quantum non-locality and theory of relativity as discussed here can easily be generalized to multiparty setting that could be used to solve other mistrustful cryptographic tasks such as secret sharing and key agreement securely.
We present an unconditionally secure Oblivious Transfer protocol relying on two rounds of entanglement-free quantum communication. When played honestly, the protocol only requires the ability to measure a single qubit in a fixed basis, and to perform a coherent bit-flip (Pauli X) operation. We present a generalization to a "Private Data Sampling" protocol, where a player (Bob) can obtain a random sample of fixed size from a classical database of size N, while the database owner (Alice) remains oblivious as to which bits were accessed. The protocol is efficient in the sense that the communication complexity per query scales at most linearly with the size of the database. It does not violate Lo's "no-go" theorem for one-sided two-party secure computation, since a given joint input by Alice and Bob can result in randomly different protocol outcomes. Finally it could be used to implement a practical bit string commitment protocol, among other applications.
Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob's desired function choice and Bob should not learn any more than what is logically implied by the function value. While decent quantum protocols for this task are known, many become completely insecure if an adversary were to control the quantum devices used in the implementation of the protocol. In this work we give a fully device-independent quantum protocol for XOR oblivious transfer.
We propose a quantum protocol for 1-out-of-2, 1-out-of-n and k-out-of-n oblivious transfer. Oblivious transfer is a counter-intuitive cryptographic primitive in which the receiver receives only the information he is authorized for, while the sender does not know what information receiver received. In 1-out-of-2 oblivious transfer, Alice sends two bits to Bob who can choose only one of them to read, while Alice does not know which bit Bob read. k-out-of-n oblivious transfer is an extension of this idea. The proposed protocols do not require any classical communication, are practical, secure and can be implemented using current technology.