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EPJ Quantum Technology

A new quantum solution to blind millionaires’ problem without an honest third party

Gang Du, Yu Zhang, Xinyue Mao, Hongwei Sun, Lei Wang

Published Nov 25, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1140/epjqt/s40507-024-00293-3

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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.
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.
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.
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.
As a particular area of quantum security multiparty computation, quantum secure multiparty summation plays a critical role in modern cryptography. It is widely known that most of the existing quantum summation protocols are based on an honest or semi-honest third party (TP). However, the introduced TP makes the protocol difficult to implement in practice, as it may face a single-point-of-failure attack on TP. Although some TP-free protocols are proposed to mitigate this risk, the increased cost of communication reduces its efficiency. To address these issues, a novel quantum-secure multiparty summation protocol based on a cooperative random number distribution mechanism (QMS-CRM) is proposed in this paper for the first time. During it, this mechanism is designed using Shamir’s secret sharing scheme. Furthermore, this approach eliminates the requirement for random number exchange between participants without the help of TP, enhancing the efficiency of the protocol. The security analysis demonstrates that the proposed protocol can resist both external attacks and collusion attacks by up to n−2n - 2n−2 participants. Finally, we simulated the protocol on the IBM Quantum Cloud platform, confirming its feasibility.
The quantum secure multiparty multiplication (QSMM) protocol aims to leverage the advantages of quantum computing to ensure data privacy and security in multiparty computation, preventing information from being leaked and protecting privacy against malicious attacks. However, current QSMM protocols suffer from high resource consumption and computation complexity in particle preparation and participant computation stages. In view of this, a QSMM protocol based on single particles is proposed in this paper. The proposed protocol utilizes high-dimensional single particles as information carriers, and the optimized quantum multiplication circuit is employed to embed the participants’ secret message and perform the multiplication. All participants collaboratively generate a blind matrix, and each column product of the blind matrix acts as the participant’s private key for the blinding of the secret value. Unlike other protocols that use decoy particles for eavesdropping detection, the proposed protocol leverages the properties of mutually unbiased basis particles to ensure its security, while reducing quantum resource consumption and the quantum capabilities required from the participants. Security analysis demonstrates that the proposed protocol can effectively resist attacks from external eavesdroppers and internal participants, and performance analysis shows that the proposed protocol achieves superior execution efficiency compared to other similar protocols.