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.
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.
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.
The socialist millionaire problem aims to compare the equality of two inputs from two users while keeping their inputs undisclosed to anyone. Quantum private comparison (QPC), whose security relies on the principles of quantum mechanics, can solve this problem and achieve the information-theoretic security of information processing. The current QPC protocols mainly utilize the bitwise XOR operation to implement the comparison, leading to insufficient security. In this paper, we propose a rotation operation-based QPC protocol to solve the socialist millionaire problem, which utilizes Bell states as quantum resources and rotation operations for classical calculations. The proposed protocol only utilizes easy-to-implement technologies such as Bell states, rotation operations, and Bell-basis measurements, making it more practical. The analysis demonstrates that our protocol can meet both the correctness and security requirements. Compared with the existing QPC protocols, our protocol has improved performance in terms of practicability and security.
This paper presents a quantum protocol for the secure privacy-preserving equality comparison of private arrays. The design overcomes the scalability limitations of conventional quantum private comparison schemes, which are typically restricted to single integers. In the proposed approach, each array element is encoded into the amplitude of a single-photon state. Participants then encrypt the received states via local rotation operations with privately chosen random angles. A circular transmission mode is employed, whereby the encrypted states are sequentially exchanged among all parties, including a semi-honest third party. The TP performs single-particle measurements to determine the equality of the arrays and broadcasts the result simultaneously to ensure fairness. The protocol's functionality and practicality were validated through quantum circuit simulations on the IBM Qiskit platform. Security analysis confirms its robustness against both external eavesdropping attacks and internal privacy threats from honest-but-curious participants. By utilizing single-photon encoding, rotation-based encryption, and single-particle measurement, the protocol achieves enhanced scalability and practical feasibility for multi-element comparisons, advancing beyond the scope of existing single-integer comparison schemes.
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.
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.
This study proposes a multiparty single-photon semi-quantum secret sharing (SQSS) protocol to simultaneously improve quantum bit (qubit) efficiency and practical feasibility. Existing quantum secret sharing protocols typically assume that all participants possess full quantum capabilities, which limits their deployment in real-world environments. To address this issue, the proposed protocol was designed using a semi-quantum model, allowing N agents with limited quantum capabilities to participate in the secret-sharing process. In terms of efficiency, the proposed protocol employs single photons as quantum resources and is analyzed under a unified definition of qubit efficiency. The results show that the qubit efficiency of the proposed protocol reaches 2N1 , which is comparable to the best recent quantum secret sharing protocols and outperforms most existing SQSS methods. Unlike certain protocols in which qubit efficiency decreases exponentially with the number of participants, the quantum resource consumption of the proposed protocol increases linearly with the number of agents. Consequently, its qubit efficiency decreases proportionally to N1 , rather than exponentially, providing better scalability as the number of agents increases. In terms of security, the protocol is analyzed against several attack models, including intercept-resend, entangle-and-measure, collective, and collusion attacks. The analysis shows that an adversary cannot obtain useful information without detection under these attacks, demonstrating the robustness of the proposed protocol.