A mediated semi-quantum protocol for millionaire problem based on high-dimensional Bell states

A mediated semi-quantum protocol allows the participants, who are mathematically equivalent to the classical communicators, to complete specific tasks with the help of a third party with quantum processing ability, which is conducive to the application of quantum communication network. In this paper, a novel mediated semi-quantum private comparison protocol based on high-dimensional Bell states is proposed. It allows two classical participants, Alice and Bob to compare the size of their private information with the help of a semi-honest quantum third party Charlie. So the protocol can be regarded as a semi-quantum solution of the original millionaire problem. It provides a way to solve the problem of secure multi-party computation in quantum resource constrained environment. In this protocol, Charlie establishes quantum channels by distributing high-dimensional Bell states to Alice and Bob. Through the established channels, Alice and Bob can encode private information and prevent information leakage by preparing new particles or reflecting the received particles. Ultimately, who is richer can be deduced with some simple calculations. In the security analysis of the protocol, we analyze that the proposed protocol can resist outside attack, participant attack and TP attack, so as to prove that the private information of the participants in the proposed protocol will not be leaked.