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arXiv:1609.08487

Fully general device-independence for two-party cryptography and position verification

Jérémy Ribeiro, Gláucia Murta, Stephanie Wehner

Published Sep 27, 2016• 8 citations
arXivHTMLPDF

Abstract

Device-independent quantum cryptography allows security even if the devices used to execute the protocol are untrusted - whether this is due to unknown imperfections in the implementation, or because the adversary himself constructed them to subvert the security of the protocol. While device-independence has seen much attention in the domain of quantum key distribution, relatively little is known for general protocols. Here we introduce a new model for device-independence for two-party protocols and position verification in the noisy-storage model. For the first time, we show that such protocols are secure in the most general device-independent model in which the devices may have arbitrary memory, states and measurements. In our analysis, we make use of a slight modification of a beautiful new tool developed in [arXiv:1607.01796] called "Entropy Accumulation Theorem". What's more, the protocols we analyze use only simple preparations and measurements, and can be realized using any experimental setup able to perform a CHSH Bell test. Specifically, security can be attained for any violation of the CHSH inequality, where a higher violation merely leads to a reduction in the amount of rounds required to execute the protocol.

DOI
10.48550/arxiv.1609.08487

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Device-independent quantum cryptography allows security even if the devices used to execute the protocol are untrusted - whether this is due to unknown imperfections in the implementation, or because the adversary himself constructed them to subvert the security of the protocol. While device-independence has seen much attention in the domain of quantum key distribution, relatively little is known for general protocols. Here we introduce a new model for device-independence for two-party protocols and position verification in the noisy-storage model. For the first time, we show that such protocols are secure in the most general device-independent model in which the devices may have arbitrary memory, states and measurements. In our analysis, we make use of a slight modification of a beautiful new tool developed in [arXiv:1607.01796] called "Entropy Accumulation Theorem". What's more, the protocols we analyze use only simple preparations and measurements, and can be realized using any experimental setup able to perform a CHSH Bell test. Specifically, security can be attained for any violation of the CHSH inequality, where a higher violation merely leads to a reduction in the amount of rounds required to execute the protocol.
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Quantum communication has demonstrated its usefulness for quantum cryptography far beyond quantum key distribution. One domain is two-party cryptography, whose goal is to allow two parties who may not trust each other to solve joint tasks. Another interesting application is position-based cryptography whose goal is to use the geographical location of an entity as its only identifying credential. Unfortunately, security of these protocols is not possible against an all powerful adversary. However, if we impose some realistic physical constraints on the adversary, there exist protocols for which security can be proven, but these so far relied on the knowledge of the quantum operations performed during the protocols. In this work we improve the device-independent security proofs of Kaniewski and Wehner [New J. Phys. 18, 055004 (2016)] for two-party cryptography (with memoryless devices) and we add a security proof for device-independent position verification (also memoryless devices) under different physical constraints on the adversary. We assess the quality of the devices by observing a Bell violation, and, as for Kaniewski and Wehner [New J. Phys. 18, 055004 (2016)], security can be attained for any violation of the Clauser-Holt-Shimony-Horne inequality.
The goal of two-party cryptography is to enable two parties, Alice and Bob, to solve common tasks without the need for mutual trust. Examples of such tasks are private access to a database, and secure identification. Quantum communication enables security for all of these problems in the noisy-storage model by sending more signals than the adversary can store in a certain time frame. Here, we initiate the study of device-independent (DI) protocols for two-party cryptography in the noisy-storage model. Specifically, we present a relatively easy to implement protocol for a cryptographic building block known as weak string erasure and prove its security even if the devices used in the protocol are prepared by the dishonest party. DI two-party cryptography is made challenging by the fact that Alice and Bob do not trust each other, which requires new techniques to establish security. We fully analyse the case of memoryless devices (for which sequential attacks are optimal) and the case of sequential attacks for arbitrary devices. The key ingredient of the proof, which might be of independent interest, is an explicit (and tight) relation between the violation of the Clauser–Horne–Shimony–Holt inequality observed by Alice and Bob and uncertainty generated by Alice against Bob who is forced to measure his system before finding out Alice's setting (guessing with postmeasurement information). In particular, we show that security is possible for arbitrarily small violation.
Abstract Position-based cryptography allows a party to prove its geographic location by responding to challenges from verifiers. Classical position verification is impossible against entangled adversaries. Quantum position verification overcomes this but requires trusted measurement devices at the verifi cation locations. We introduce Device-Independent Position Verification using the Mermin-Ardehali Belinskii-Klyshko four-party Bell inequality. Our protocol uses four verifiers at the corners of a square and a single prover. The MABK inequality has classical bound BMABK ≤ 4, while quantum mechan ics achieves BMABK = 4√2 ≈ 5.657 using the four-qubit Greenberger-Horne-Zeilinger state. We prove security against general quantum adversaries using relativistic no-go theorems and the entropy accumulation theorem. Using realistic experimental parameters (four-photon GHZ state fidelity F = 0.85, detector efficiency η = 0.65), we predict a Bell violation BMABK = 4.25, exceeding the classical bound by 0.25. The protocol tolerates up to 15% noise and achieves verification distances up to 30 km with current technology. This work provides the first practical path to location verification on untrusted hardware.
Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally. Here we present a property of entropy, termed "entropy accumulation", which asserts that the total amount of entropy of a large system is the sum of its parts. We use this property to prove the security of cryptographic protocols, including device-independent quantum key distribution, while achieving essentially optimal parameters. Recent experimental progress, which enabled loophole-free Bell tests, suggests that the achieved parameters are technologically accessible. Our work hence provides the theoretical groundwork for experimental demonstrations of device-independent cryptography.
The defining feature of one-sided device-independent quantum key distribution is its asymmetric trust model in which only one party is characterized. This scenario sets an interesting middle ground between high key rates achievable by characterizing devices and the security of full device-independence. Here, we provide new tools, methods, and benchmarks for calculating key rates in this setting. To achieve this, we develop and compare two extensions of the NPA hierarchy and derive finite-size security bounds against general attacks with arbitrary device memory. The latter is based on the Generalized Entropy Accumulation Theorem. We then investigate the performance of various protocols: the BB84 protocol both with and without losses, a qutrit mutually unbiased bases protocol, and protocols based on Bell inequalties such as CHSH and I3322I_{3322}I3322​. We find that the choice of which party is characterized can strongly affects the key rate, surprisingly without a universal ordering. Our work thus offers a general toolbox for calculating key rates for one-sided device-independent QKD protocols.