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arXiv:1510.05044

Device-independent quantum secret sharing using Mermin-type contextuality

Stefano Gogioso

Published Oct 16, 2015• 1 citation
arXivHTMLPDF

Abstract

We present a new quantum secret sharing protocol based on recent advances in Mermin-type contextuality scenarios, which has some security guarantees against postquantum nonsignaling attackers. It is a fundamental assumption of secret sharing protocols that not all players are trusted parties, and that some may collude amongst themselves and with eavesdroppers to break confidentiality. To this extent, quantum secret sharing introduces a new layer of security, enabling eavesdropping detection via entangled states and noncommuting observables. A more thorough security analysis, however, becomes crucial if the protocol relies on untrusted devices for its implementation: for example, it cannot be excluded that some players may collude with the device supplier. In this paper, we put recent developments in Mermin-type contextuality to work in a new quantum secret sharing protocol. The maximal contextuality (aka maximal non-locality, or zero local fraction) demonstrated by the measurement scenarios results in some device-independent security guarantees against nonsignaling attackers -- be they classical, quantum or postquantum.

DOI
10.48550/arxiv.1510.05044

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We present a new quantum secret sharing protocol based on recent advances in Mermin-type contextuality scenarios, which has some security guarantees against postquantum nonsignaling attackers. It is a fundamental assumption of secret sharing protocols that not all players are trusted parties, and that some may collude amongst themselves and with eavesdroppers to break confidentiality. To this extent, quantum secret sharing introduces a new layer of security, enabling eavesdropping detection via entangled states and noncommuting observables. A more thorough security analysis, however, becomes crucial if the protocol relies on untrusted devices for its implementation: for example, it cannot be excluded that some players may collude with the device supplier. In this paper, we put recent developments in Mermin-type contextuality to work in a new quantum secret sharing protocol. The maximal contextuality (aka maximal non-locality, or zero local fraction) demonstrated by the measurement scenarios results in some device-independent security guarantees against nonsignaling attackers -- be they classical, quantum or postquantum.
Contextuality is a key resource in quantum information and the device-independent security of quantum algorithms. In this work, we show that the recently developed, operational Mermin non-locality arguments provide a large, novel family of quantum realisable All-vs-Nothing models. In particular, they result in a diverse wealth of quantum realisable models which are maximally contextual (i.e. lie on the faces of the no-signalling polytope with no local elements), and could be used as a resource for the security of a new class of quantum secret sharing algorithms.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes against eavesdroppers and dishonest participants remained unproven. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players, by utilizing ideas from the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate the practical feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.
Device-independent quantum secret sharing (DI-QSS) provides security against untrusted quantum devices. While device-independent quantum key distribution (DI-QKD) using Mermin-Peres magic square game [Zhen et al., Phys. Rev. Lett, 2023] has been proposed, we present the first DI-QSS protocol based on a pseudo-telepathy parity game without requiring dedicated rounds and specific basis configuration, unlike CHSH-based DI-QSS schemes [Zhang et al., Phys. Rev. A, 2024]. Our scheme simultaneously certifies device-independence and key generation using a single test, achieving optimal performance for a seven-qubit GHZ state configuration. Security against collective attacks is analyzed, and a positive key rate is obtained under white noise and photon loss. Moreover, we show a bitwise advantage over the previous protocol for producing the same raw key length.
Quantum secret sharing (QSS) enables a dealer to securely distribute keys to multiple players. Device-independent (DI) QSS can resist all possible attacks from practical imperfect devices and provide QSS the highest level of security in theory. However, DI QSS requires high-performance devices, especially for low-noise channels, which is a big challenge to demonstrate experimentally. We propose a DI QSS protocol with the advanced random key generation basis strategy, which combines the random key generation basis with the noise preprocessing and postselection strategies. We develop the methods to numerically simulate the key generation rate in an acceptable time. Our DI QSS protocol has some advantages. First, it can increase the noise tolerance threshold from an initial 7.147% to 9.231% (29.16% growth) and reduce the global detection efficiency threshold from 96.32% to 93.41%. The maximal distance between any two users increases to 1.43 km, which is about 5.5 times the initial value. Second, by randomly selecting two basis combinations to generate the key, our DI QSS protocol can reduce the entanglement resource consumption. Our protocol has potential for the experimental demonstration of DI QSS and application in the future.
Classical secret sharing proposed by Shamir used classical computational power in classical cryptography to achieve secret key sharing, but with the advent of quantum systems, computational power can be overruled. To ensure a secure secret sharing scheme independent of computational power, a scheme independent of computational complexity is needed to achieve security. This paper will provide a protocol dependent on inherent secure nature of quantum cryptography (quantum no cloning theorem and quantum measurement rule). A secure multiparty quantum secret sharing scheme has been proposed to ensure that no one can eavesdrop or extract any share of the secret message via inherent security provided by quantum entanglement swapping and quantum teleportation. Entanglement swapping is a process that allows two non-interacting quantum systems to be entangled. Whereas, Quantum teleportation allows a party to send a qubit to another entangled party without sending the qubit over the channel. Moreover, in order to ensure security against possible active attacks, sender himself will generate and distribute EPR pairs to be used in the scheme. Result will be a secure multiparty QSS scheme which will be secure against internal and external eavesdropping, masquerading and brute-force attacks.
Quantum secret sharing (QSS) is a cornerstone of multi-party quantum information security. However, traditional QSS protocols are vulnerable to detector side-channel attacks. Measurement-device-independent QSS (MDI-QSS) elegantly resolves this by outsourcing measurements to an untrusted third party. Building upon this, we propose a measurement-deviceindependent dynamic quantum secret sharing (MDI-DQSS) scheme based on hyperentanglement. Our protocol leverages simultaneous entanglement in both polarization and spatial degrees of freedom, which enhances the channel capacity and improves the key generation rate. The scheme is designed for practical implementation, relying on single-photon states that are feasible to prepare and manipulate. We present the complete protocol, from state preparation and distribution to cooperative decoding, and provide a comprehensive security analysis demonstrating its robustness.