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arXiv:2103.01662 · Physical Review A

Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game

Ricardo Faleiro, Manuel Goulão

Published Feb 26, 2021• 4 citations
arXivHTMLPDF

Abstract

In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with nonlocality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly. The authorization levels are encoded in the nonlocal resources distributed to the users and subsequently confirmed by their ability to win Clauser-Horne-Shimony-Holt games using such resources. We formalize the protocol, prove its security, and frame it in a device-independent setting employing the notion of Clauser-Horne-Shimony-Holt self-testing via simulation. Finally, we provide a proof-of-concept implementation using the Qiskit open-source framework.

DOI
10.1103/physreva.103.022430

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In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with nonlocality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly. The authorization levels are encoded in the nonlocal resources distributed to the users and subsequently confirmed by their ability to win Clauser-Horne-Shimony-Holt games using such resources. We formalize the protocol, prove its security, and frame it in a device-independent setting employing the notion of Clauser-Horne-Shimony-Holt self-testing via simulation. Finally, we provide a proof-of-concept implementation using the Qiskit open-source framework.
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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.
In the Quantum Computing field, the CHSH (Clauser-Horne-Shimony-Holt) game plays a vital role in determining whether a system is in classical or quantum domain. This quantum advantage property is applied in determining the security of the quantum systems, especially in quantum cryptography, in the form of Device-Independent (DI) secure Quantum Key Distribution (QKD). The traditional CHSH game is designed for a system with two players, where each player has access to one entangled qubit from the Bell’s state. In 2024, Hamza Jaffali and Frédéric Holweck proposed a new three-qubit CHSH game by extending the traditional CHSH game to three players using the three-qubit Greenberger–Horne–Zeilinger (GHZ) state and W state.In this paper, first, we present our findings of new CHSH quantum games with quantum advantage in the four-qubit and five-qubit systems. These CHSH quantum games, when played using their quantum strategy, are found to outperform any classical strategy. Second, we apply the quantum advantage property of the existing three-qubit game to develop the corresponding three party DIQKD protocol. Third, we then apply the quantum advantage property of the newly developed four-qubit and five-qubit games to develop their corresponding four party and five party DIQKD protocols.
Recently there were many proposals on device-independent (DI) quantum key distribution protocol whose security is based on the violation of the Clauser-Horne-Shimony-Holt inequality. However, as a statistical law, a certain extent of fluctuation has to be allowed. We show that the eavesdropper can make use of this property to obtain a remarkable part of the secret key by replacing some of the DI nonlocal boxes with local ones. On the contrary, the same cheating strategy does not apply to the device-dependent (DD) version of the protocol. Thus such kind of DI protocol is less secure than its DD counterpart.
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.
Can a classical system command a general adversarial quantum system to realize arbitrary quantum dynamics? If so, then we could realize the dream of device-independent quantum cryptography: using untrusted quantum devices to establish a shared random key, with security based on the correctness of quantum mechanics. It would also allow for testing whether a claimed quantum computer is truly quantum. Here we report a technique by which a classical system can certify the joint, entangled state of a bipartite quantum system, as well as command the application of specific operators on each subsystem. This is accomplished by showing a strong converse to Tsirelson's optimality result for the Clauser-Horne-Shimony-Holt (CHSH) game: the only way to win many games is if the bipartite state is close to the tensor product of EPR states, and the measurements are the optimal CHSH measurements on successive qubits. This leads directly to a scheme for device-independent quantum key distribution. Control over the state and operators can also be leveraged to create more elaborate protocols for reliably realizing general quantum circuits.