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arXiv:1701.01087 · Physical Review A

Device-independent quantum private query

Arpita Maitra, Goutam Paul, Sarbani Roy

Published Apr 28, 2017• 40 citations
arXivHTMLPDF

Abstract

In quantum private query (QPQ), a client obtains values corresponding to his or her query only, and nothing else from the server, and the server does not get any information about the queries. V. Giovannetti et al. [Phys. Rev. Lett. 100, 230502 (2008)] gave the first QPQ protocol and since then quite a few variants and extensions have been proposed. However, none of the existing protocols are device independent; i.e., all of them assume implicitly that the entangled states supplied to the client and the server are of a certain form. In this work, we exploit the idea of a local CHSH game and connect it with the scheme of Y. G. Yang et al. [Quantum Info. Process. 13, 805 (2014)] to present the concept of a device-independent QPQ protocol.

DOI
10.1103/physreva.95.042344

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In quantum private query (QPQ), a client obtains values corresponding to his or her query only, and nothing else from the server, and the server does not get any information about the queries. V. Giovannetti et al. [Phys. Rev. Lett. 100, 230502 (2008)] gave the first QPQ protocol and since then quite a few variants and extensions have been proposed. However, none of the existing protocols are device independent; i.e., all of them assume implicitly that the entangled states supplied to the client and the server are of a certain form. In this work, we exploit the idea of a local CHSH game and connect it with the scheme of Y. G. Yang et al. [Quantum Info. Process. 13, 805 (2014)] to present the concept of a device-independent QPQ protocol.
Abstract In this paper, we present a novel quantum private query (QPQ) scheme that is fully device-independent. As far as we know, this is the first QPQ scheme that uses EPR pairs and offers full device independence. Our approach takes into account the self-testing of shared EPR pairs and the self-testing of projective measurement operators in a mistrustful scenario where neither the client nor the server trusts each other. To achieve full device independence, we also exploit self-testing of a specific class of POVM operators used by the client in our scheme. Additionally, we evaluate the performance of our proposal formally and derive an upper limit of the maximum cheating probabilities (when the protocol does not terminate) for both the dishonest client and the dishonest server.
Quantum Private Query (QPQ) is an unconditional secure mistrustful cryptographic primitive which is assumed to be a probabilistic version of the Oblivious Transfer (OT) schemes or an imperfect version of Symmetric Private Information Retrieval (SPIR) schemes. Recently, Maitra et al. (Phys. Rev. A, 2017) identified that the B92 QKD-based QPQ scheme proposed by Yang et al. (Quant. Inf. Process., 2014) is vulnerable whenever the devices involved in that scheme are dubious and to improve the overall security, they suggested a semi-Device Independent (DI) proposal for that QPQ scheme by introducing a local test at the server's end. In this work, we overcome the limitation of the Maitra et al. proposal by removing trustworthiness from all the (involved) devices, and suggest a full DI proposal for the Yang et al. scheme, exploiting a proper self-testing mechanism of observables along with the local version of the tilted CHSH game. We compare the performance of our proposal with a recent full DI-QPQ scheme (arxiv 1901.03042) and discuss their relative advantages. Additionally, we present a DI proposal for a modified version of the Yang et al. scheme, enabling the client to retrieve maximum raw key bits during the oblivious key generation phase. We evaluate the security of all our proposals with a formal analysis.
In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Private Query (QPQ) protocols fail to maintain the database security if the entangled states shared between Alice and Bob are not of a certain form. So it is necessary to certify the states a priori. In this regard, the local CHSH test was proposed. However, the proposed scheme works perfectly for the asymptotic case when we have infinite number of qubits. In this brief report, we upgrade the protocol for finite number of qubits and connect the sample size to the success probability of CHSH test. We also perform a rigorous security analysis of the proposed protocol.
Measurement-Device-Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We compare the database security and client’s privacy in MDI QPQ for qubits with qutrits. For some instances, we observe that qutrit will provide better security for database than qubit. However, when it comes to the question of client’s privacy, we have to take additional measures in case of qutrit. Hence, we conclude that though in case of Quantum Key Distribution (QKD) higher dimension provides better security, in case of QPQ this is not obvious.
Symmetric private information retrieval (SPIR) protocol is proposed for users to retrieve items from a database holder without revealing the retrieval address, and meanwhile the users cannot learn any additional entries of the database. Quantum key distribution (QKD)-based quantum private queries (QPQs) are the most practical protocols for the SPIR problem. However, most existing protocols assume ideal devices. To overcome this drawback, we propose a device independent QPQ protocol based on QKD with imperfect sources and detectors. By constructing the semi-definite programming optimization problem, we give the CHSH test threshold and prove the correctness of our protocol. We use the shift and permutation post-processing technique to further improve the security. We compare the performance of our protocol with a recent full device-independent QPQ. and discuss their relative advantages. The simulation results show that our protocol improves database security, user privacy and efficiency. The number of final key bits that Alice knows is close to 1, and Bob’s guessing probability is below 0.15 in our protocol. Moreover, the proposed scheme can be used for any entanglement-based QPQ protocol to remove trust on the devices.
The first device-independent quantum private query protocol (MRT17) which is proposed by Maitra \emph{et al.} [Phys. Rev. A 95, 042344 (2017)] to enhance the security through the certification of the states and measurements. However, the MRT17 protocol works under an assumption of perfect detectors, which increases difficulty in the implementations. Therefore, it is crucial to investigate what would affect the security of this protocol if the detectors were imperfect. Meanwhile, Maitra \emph{et al.} also pointed out that this problem remains open. In this paper, we analyze the security of MRT17 protocol when the detectors are imperfect and then find that this protocol is under attack in the aforementioned case. Furthermore, we propose device-independent QPQ protocol without the assumption of perfect detectors. Compared with MRT17 protocol, our protocol is more practical without relaxing the security in the device-independent framework.