A new quantum solution to blind millionaires’ problem without an honest third party

The quantum blind millionaires’ (QBM) problem is an expanded version of the millionaires’ problem in a quantum environment. For any two sets with different members, the QBM problem represents the quantum solution of the private summation in each set and the private comparison of the results simultaneously. During it, the secrets of any participant should be protected. As a new topic in quantum secure multiparty computation (QSMC), current solutions to QBM problems usually require an honest third party to resist some potential attack strategies. However, the assumptions will affect their applicability in practical cooperative security systems. In this paper, we propose a new solution to the quantum blind millionaires’ (QBM) problem without the help of an honest third party for the first time. In our solution, the shift operations are applied to the d-dimensional 2-particle entangled states to encode the secrets of the participants. According to our analysis, the proposed solution can effectively resist typical internal and external attacks by applying the detection methods generated by the participants. We hope that the research will make positive developments for QSMC.