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Advanced Quantum Technologies

Verifiable Privacy‐Preserving Quantum Protocol for Blind Millionaire Problem and Its Application in Privacy Computing

Xiao‐Qiu Cai, Yu‐Guang Yang, Tian‐Yin Wang, Guang‐Bao Xu, Dong‐Huan Jiang

Published Oct 13, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1002/qute.202500600

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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.
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.
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.
Abstract Semi‐quantum secure summation allows multiple parties with limited quantum capabilities to perform collective calculations under the premise of protecting privacy. However, current approaches are confined to low‐dimensional quantum states as information carriers and are restricted to scenarios involving two or three parties. This limitation hinders their universality and ability to fulfill the requirements of practical secure multiparty computations. To address these challenges, a novel semi‐quantum secure multiparty summation (SQSMS) protocol is proposed based on high‐dimensional entangled states and single‐particle states. The protocol leverages the entanglement correlation to guarantee the security of the transmission, enabling resistance against various potential attacks. Then, by utilizing the IBM Qiskit platform, corresponding quantum circuits and simulation results are presented to validate the feasibility and correctness of the protocol. Furthermore, building upon the foundation of the SQSMS protocol, semi‐quantum anonymous auction and anonymous ranking protocols are further constructed. Compared with previous approaches, the designed protocols cater to the requirements of their respective counterparts. Consequently, the approach may have broad applications in semi‐quantum secure multiparty computation scenarios.
In this paper, a protocol for quantum millionaire problem with continuous variables is proposed. In the protocol, two participants can compare the values of their fortune with the assistance of a semi-trusted third party (STTP). Only EPR states are exploited in our protocol while most other protocols exploited d-dimensional Bell states. Two participants are just required to perform single particle operations, which makes our protocol more efficiently. Our protocol can ensure fairness, correctness, security and high efficiency as well. In our protocol, only the two participants can deduce the results of comparisons, others include STTP will learn no information. Our protocol can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the STTP.
The socialist millionaires' problem, emanating from the millionaires’ problem, allows two millionaires to determine whether they happen to be equally rich while remaining their riches undisclosed to each other. Most of the current quantum solutions to the socialist millionaires’ problem have lower efficiency and are theoretically feasible. In this paper, we introduce a practical quantum secure protocol for the socialist millionaires’ problem based on single photons, which can be easily implemented and manipulated with current technology. Our protocol necessitates the involvement of a semi-honest third party (TP) responsible for preparing the single-photon sequences and transmitting them to Alice who performs Identity or Hadamard operations on the received quantum sequences via her private inputs and the secret keys, producing new quantum sequences that are subsequently sent to Bob. Similarly, Bob encodes his private inputs into the received quantum sequences to produce new quantum sequences, which are then sent to TP. By conducting single-particle measurements on the quantum sequences received from Bob, TP can ascertain the equality of private inputs between Alice and Bob, and subsequently communicate the comparison result to them. To assess the feasibility, the proposed protocol is simulated on IBM Quantum Cloud Platform. Furthermore, security analysis demonstrates that our protocol can withstand attacks from outsiders, such as eavesdroppers, and from insider participants attempting to grab the private input of another participant.