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

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.

New Quantum Private Comparison Using Four-Particle Cluster State

“…This protocol also needs a QKD protocol to share secret keys before the protocol begins. In 2024, Hou and Wu [ 54 ] designed a protocol for equality comparison using single photons and unitary operations. To prevent the disclosure of private inputs to the parties, QKD protocols are used to share secret keys for encrypting confidential information.…”

Quantum private comparison for the socialist millionaire problem

“…However, [17] pointed out that [16] is susceptible to intercept resend attacks, and some suggestions are provided to enhance the security of private information. After that, some researchers focus on using different quantum states, such as single photons [18,19], Bell states [20], multi-qubit states [21][22][23][24], and highdimensional quantum states [25][26][27][28], and various encoding methods to develop the QPC protocol. Additionally, semiquantum private comparison (SQPC) protocols [29][30][31][32][33][34][35][36] have been proposed to alleviate the burden on quantum resources.…”