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Advanced Quantum Technologies

A Distributed Quantum Blind Millionaire Protocol Based on Quantum Walks

Ran Zhang, Xue Zhang, Jiarui He, Long Zhang, Kejia Zhang

Published Sep 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT The quantum blind millionaire (QBM) problem is a fundamental primitive in quantum secure multi‐party computation. It enables two groups to compare aggregated private sums while protecting individual data, and is widely adopted in privacy‐preserving collaborative decision‐making. However, most existing QBM protocols either rely on semi‐honest third parties or adopt sophisticated quantum states. These approaches lead to high resource overhead and operational complexity, which restricts practical deployment. In this paper, we apply the one‐directional quantum walks on a circle (ODQWC) to the QBM problem for the first time and develop a new distributed QBM protocol. This scheme employs only a single quantum walker and requires no trusted third party. Moreover, the proposed protocol achieves higher qubit efficiency than most existing mainstream QBM protocols, with an efficiency exceeding . According to our analysis, the protocol passes the verification of both correctness and security, and its feasibility is confirmed via IBM Qiskit simulations. The proposed scheme solves the QBM problem efficiently and can serve as a building block for broader multi‐party collaborative computation tasks.

DOI
10.1002/qute.70443

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ABSTRACT The quantum blind millionaire (QBM) problem is a fundamental primitive in quantum secure multi‐party computation. It enables two groups to compare aggregated private sums while protecting individual data, and is widely adopted in privacy‐preserving collaborative decision‐making. However, most existing QBM protocols either rely on semi‐honest third parties or adopt sophisticated quantum states. These approaches lead to high resource overhead and operational complexity, which restricts practical deployment. In this paper, we apply the one‐directional quantum walks on a circle (ODQWC) to the QBM problem for the first time and develop a new distributed QBM protocol. This scheme employs only a single quantum walker and requires no trusted third party. Moreover, the proposed protocol achieves higher qubit efficiency than most existing mainstream QBM protocols, with an efficiency exceeding . According to our analysis, the protocol passes the verification of both correctness and security, and its feasibility is confirmed via IBM Qiskit simulations. The proposed scheme solves the QBM problem efficiently and can serve as a building block for broader multi‐party collaborative computation tasks.
Abstract The quantum blind millionaires’ (QBM) problem is an expanded version of the millionaires’ problem in a quantum environment. For any two sets with different members, the QBM problem represents the quantum solution of the private summation in each set and the private comparison of the results simultaneously. During it, the secrets of any participant should be protected. As a new topic in quantum secure multiparty computation (QSMC), current solutions to QBM problems usually require an honest third party to resist some potential attack strategies. However, the assumptions will affect their applicability in practical cooperative security systems. In this paper, we propose a new solution to the quantum blind millionaires’ (QBM) problem without the help of an honest third party for the first time. In our solution, the shift operations are applied to the d -dimensional 2-particle entangled states to encode the secrets of the participants. According to our analysis, the proposed solution can effectively resist typical internal and external attacks by applying the detection methods generated by the participants. We hope that the research will make positive developments for QSMC.
Blind millionaire (BM) problem is an extended version of the initial millionaire problem required to compare the sum of the participants’ secrets between different groups. As a new topic of quantum secure multiparty computing, existing protocols with some special entangled states may not be easily achieved in practice. This study proposes a non-entangled method of solving the quantum blind millionaire (QBM) problem with special d-level single-particle states for the first time. To protect the confidentiality of transmission secrets, this protocol exploits the property of randomly generated d-level single-particle states. Furthermore, simple shift operations are used to encode the respective secrets. Detailed security analysis demonstrates that this protocol is impervious to internal and external threats. The presented methods can not only be used to solve the blind millionaire problem but also be used as a basic module to solve other secure multiparty computing problems.
In order to compare the size relationship and the equality of private integers from two users without any risk of leaking their secrets, we put forward a novel two-round two-party quantum private comparison (QPC) protocol with a third party (TP) based on one-direction quantum walks on a circle (ODQWC). Here, TP is allowed to launch all kinds of possible attacks except the collusion attack. This protocol adopts quantum walk (QW) states as the initial quantum resource, which are actually a kind of two-particle product states. This protocol doesn’t need any pre-shared secret key or quantum entanglement swapping operation, and only adopts unitary operations andd-dimensional single particle measurements. Security analysis validates the security of the proposed protocol against both the outside attacks and the participant attacks. Compared with previous QPC protocols based on QW, this protocol is more efficient under certain conditions. Moreover, we construct quantum circuits for this protocol and reveal its correctness and feasibility by IBM Qiskit simulator.
We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks. With the help of one direction quantum walk, we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result, which improves the qubit efficiency and the maximum quantity of the participants’ secret messages. Besides, our protocol can judge the size of the secret messages, not only equality. Furthermore, the quantum walks particle is disentangled in the initial state. It only requires a quantum walks operator to move, making our proposed protocol easy to implement and reducing the quantum resources. Through security analysis, we prove that our protocol can withstand well-known attacks and brute-force attacks. Analyses also reveal that our protocol is correct and practical.
Abstract Blind millionaire (BM) problem aims to privately compare the summation result of secrets of participants from one group with that from another group without compromising their respective secrets. Although several quantum BM protocols are presented, it is pointed out that the correctness of these quantum BM protocols is not ensured. Then, a mechanism of permuting the embedding orders of all the participants in an anonymous manner is provided. Furthermore, a new quantum BM protocol based on the proposed anonymous embedding mechanism is proposed. It is shown that this protocol possesses the properties of privacy, self‐comparing, verifiability and fairness at the same time, and satisfies the security requirement of a quantum BM protocol in theory. In addition, the use of single‐particle states and simple shift operations makes the proposed protocol feasible with current technology. To demonstrate the scalability of the designed protocol, its applications in several privacy computing problems in real‐world scenarios such as joint bidding and preference survey are illustrated.
The socialist millionaire problem seeks to determine the equality relationship between the inputs of two users while ensuring that these inputs remain undisclosed to each other and to potential attackers. Current quantum protocols encounter challenges related to practicality and efficiency in addressing this issue. To overcome these challenges, we propose a quantum secure protocol specifically designed to effectively solve the socialist millionaire problem. In this protocol, a semihonest third party (TP) generates and distributes single photons to the participants. After securely receiving the photons, the participants encode their secret data using local quantum operations. The encoded photons are then returned to TP, which extracts the result via quantum measurement. By employing a circular photon transmission mode, the protocol reduces resource redundancy and achieves higher qubit efficiency. Security analysis confirms the protocol’s robustness against external quantum attacks—such as intercept‐resend, measurement‐resend, and entangle‐measure attacks—as well as against the curiosity of semihonest participants. Finally, using accessible quantum components (single photons, Pauli gates, and Bell measurements), we simulate the protocol on IBM Qiskit to verify its feasibility.