Efficient Quantum-Secure Protocol for the Socialist Millionaire Problem With Pauli Operators

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.