A new quantum-inspired solution to blind millionaires' problem

The blind millionaires' problem is an expansion of the millionaires' problem, comparing the secrets belonging to two different sets. When each set has only one participant, it corresponds to the original millionaires' problem. In this paper, we propose a new solution to quantum blind millionaires' (QBM) problem based on d-level n-particle entangled states |chi(sic)(n) for the first time. In our solution, the summation of the secrets held by the participants from two sets can be compared successfully; here, each participant may have one or multiple secrets. Specially two different cases for overall and local comparison are discussed, respectively. During the QBM solution for overall comparison, it can be seen that the summation of all the secrets in each set can compare its value with the other set. Accordingly, during the QBM solution for local comparison, any one participant in one set can compare his secret with the summation of all the secrets in the other set. Moreover, the security analysis shows that the present solutions can prevent secrets leakage even if participants collude. Finally, the efficiency and some further discussions of our solutions are also proposed. As a new attempt, we hope these work may make positive effects to the development of quantum secure multiparty computation in future.