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Frontiers in Physics

Single-photon-based quantum secure protocol for the socialist millionaires’ problem

Min Hou, Yue Wu

Published Mar 6, 2024• 20 citations
Publisher

Abstract

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.

DOI
10.3389/fphy.2024.1364140

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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 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 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.
Quantum private comparison (QPC) represents a cryptographic approach that enables two parties to determine whether their confidential data are equivalent, without disclosing the actual values. Most existing QPC protocols utilizing single photons or Bell states are considered highly feasible, but they suffer from inefficiency. To address this issue, we present a novel QPC protocol that capitalizes on the entanglement property of Bell states and local operations to meet the requirements of efficiency. In the proposed protocol, two participants with private inputs perform local operations on shared Bell states received from a semi-honest third party (STP). Afterward, the modified qubits are returned to the STP, who can then determine the equality of the private inputs and relay the results to the participants. A simulation on the IBM Quantum Cloud Platform confirmed the feasibility of our protocol, and a security analysis further demonstrated that the STP and both participants were unable to learn anything about the individual private inputs. In comparison to other QPC protocols, our proposed solution offers superior performance in terms of efficiency.
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.
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.
In this paper,a quantum private comparison protocol based on d dimensional single-particle states is proposed. In the protocol,a semi-honest third party transfers a sequence of n particles to one participant w ho encodes n secret keys by performing n local unitary operations. Then these particles are sent to the other participant w ho also by the same w ay encodes n secret keys and returns these particles back to the semi-honest party. Finally after the participants broadcast the results of encrypting their secrets w ith secret keys,the semi-honest third party can help the tw o participants compare the size relationships of their n pair corresponding secrets w ithout disclosing them to any other people. In addition,the security of the protocol is also discussed in detail. It is show n that the protocol is secure in theory. Moreover,since only single-particle states are used,as compared w ith other quantum private comparison protocols,the presented protocol is more feasible under the current technical conditions.