Practical quantum protocols for blind millionaires’ problem based on rotation encryption and swap test

Millionaires’ problem, as the most fundamental problem in secure multiparty computation (SMC), has attracted much attention in recent years. Blind millionaires’ problem, an extension of millionaires’ problem, enables to determine the size relationship of the secrets sum. In this paper, two practical quantum protocols based on rotation encryption and swap test are proposed, which can essentially solve the blind millionaires’ problem. To verify the correctness and feasibility, the proposed protocols are simulated on IBM Quantum Platform by designing the corresponding quantum circuits. Compared with the existing quantum solutions for the blind millionaires’ problem, the proposed protocols demonstrate improved performance in terms of feasibility and security, as they utilize Bell states, single-particle measurements, rotation operations and swap tests without necessitating the preparation of d-dimensional quantum states, the shift operation of d-dimensional quantum states, quantum Fourier transform, or the measurement of computational basis and Fourier basis. Security analysis demonstrates that the private data of each participant and the secrets sum remain confidential and undisclosed.