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arXiv:1702.01984

Experimental Quantum Solution to the Dining Cryptographers Problem

Alley Hameedi, Breno Marques, Muhammad, Sadiq, Marcin Wieśniak, Mohamed Bourennane

Published Feb 7, 2017• 2 citations
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Abstract

Quantum resources such as superposition and entanglement have been used to provide unconditional key distribution, secret sharing and communication complexity reduction. In this letter we present a novel quantum information protocol for dining cryptographers problem and anonymous vote casting by a group of voters. We successfully demonstrate the experimental realization of the protocol using single photon transmission. Our implementation employs a flying particle scheme where a photon passes by the voters who perform a sequence of actions (unitary transformations) on the photonic state at their local stations.

DOI
10.48550/arxiv.1702.01984

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Quantum resources such as superposition and entanglement have been used to provide unconditional key distribution, secret sharing and communication complexity reduction. In this letter we present a novel quantum information protocol for dining cryptographers problem and anonymous vote casting by a group of voters. We successfully demonstrate the experimental realization of the protocol using single photon transmission. Our implementation employs a flying particle scheme where a photon passes by the voters who perform a sequence of actions (unitary transformations) on the photonic state at their local stations.
This paper presents an innovative entanglement-based protocol to address the Dining Cryptographers problem, utilizing maximally entangled |GHZn⟩ tuples as its core. This protocol aims to provide scalability in terms of both the number of cryptographers n and the amount of anonymous information conveyed, represented by the number of qubits m within each quantum register. The protocol supports an arbitrary number of cryptographers n, enabling scalability in both participant count and the volume of anonymous information transmitted. While the original Dining Cryptographers problem focused on a single bit of information—whether a cryptographer paid for dinner—the proposed protocol allows m, the number of qubits in each register, to be any arbitrarily large positive integer. This flexibility allows the transmission of additional information, such as the cost of the dinner or the timing of the arrangement. Another noteworthy aspect of the introduced protocol is its versatility in accommodating both localized and distributed versions of the Dining Cryptographers problem. The localized scenario involves all cryptographers gathering physically at the same location, such as a local restaurant, simultaneously. In contrast, the distributed scenario accommodates cryptographers situated in different places, engaging in a virtual dinner at the same time. Finally, in terms of implementation, the protocol accomplishes uniformity by requiring that all cryptographers utilize identical private quantum circuits. This design establishes a completely modular quantum system where all modules are identical. Furthermore, each private quantum circuit exclusively employs the widely used Hadamard and CNOT quantum gates, facilitating straightforward implementation on contemporary quantum computers.
A novel quantum anonymous communication scheme is proposed on the basis of Dining Cryptographers (DC) Problem and nonmaximally entangled qubit pair. The scheme takes advantage of quantum-mechanical impossibility of local unitary transformation between certain nonmaximally entangled states to provide truly random number which can be brightly used in anonymous communication protocols based on DC-Nets. The analysis and discussions demonstrate that the proposed quantum anonymous communication scheme can be performed securely with high capacity and untraceability. The scheme can also be extended to a (2, 2) quantum secret sharing (QSS) scheme.
Quantum information protocols offer significant advantages in properties such as security, anonymity, and privacy for communication and computing tasks. An application where guaranteeing the highest possible security and privacy is critical for democratic societies is electronic voting. As computational power continues to evolve, classical voting schemes may become increasingly vulnerable to information leakage. In this work, we present the experimental demonstration of an information-theoretically secure and efficient electronic voting protocol that, crucially, does not rely on election authorities, leveraging the unique properties of quantum states. Our experiment is based on a high-performance source of Greenberger-Horne-Zeilinger (GHZ) states and realizes a proof-of-principle implementation of the protocol in two scenarios: a configuration with four voters and two candidates employing privacy enhancement techniques and an election scenario supporting up to eight voters and sixteen candidates. The latter is particularly well-suited for secure board-level elections within organizations or small-scale governmental contexts.
Abstract Anonymous voting is often one decision-making choice in many democracies. Facing the security threats from quantum computers, classical anonymous voting protocols based on computational complexity hypothesis have innovated to quantum anonymous voting protocols based on quantum mechanics. In this paper, we propose a quantum anonymous voting protocol by using high-dimension single particles. With the help of EA and T , the construction of our protocol makes each legitimate voter cast only one ballot, and all ballots open in a quite random rearrangement. Each voter can anonymously trace his/her vote by a private position index, thus our protocol achieving the precious properties of eligibility, privacy, no-reusability, verifiability and fairness. We also analyze that the protocol can successfully resist attacks from external eavesdroppers and internal participants, ensuring that our voting protocol is secure under ideal conditions. Designing mature quantum anonymous voting protocols is challenging.
Ensuring security and integrity of elections constitutes an important challenge with wide-ranging societal implications. Classically, security guarantees can be ensured based on computational complexity, which may be challenged by quantum computers. We show that the use of quantum networks can enable information-theoretic security for the desirable aspects of a distributed voting scheme in a resource-efficient manner. In our approach, ballot information is encoded in quantum states that enable an exponential reduction in communication complexity compared to classical communication. In addition, we provide an efficient and secure anonymous queuing protocol based on a distributed secure sum. As a result, our scheme only requires modest quantum memories with size scaling logarithmically with the number of voters. This intrinsic efficiency together with certain noise-robustness of our protocol paves the way for its physical implementation in realistic quantum networks.
Quantum communication protocols seek to leverage the unique properties of quantum systems for coordination or communication tasks, usually with guarantees of security or anonymity that exceed what is possible classically. One promising domain of application is elections, where strong such guarantees are essential to ensure legitimacy. We experimentally implement a recently proposed election protocol from Centrone et al. such that no one, including a potential central authority, can know the preferred candidate of any voter other than themself. We conduct a four-party election, generating and distributing four-partite GHZ states with ≈89%\approx 89\%≈89% fidelity and successfully recording voters' intentions ≈87%\approx 87\%≈87% of the time.