Quantum private comparison for the socialist millionaire problem

Abstract

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.