SIMPLE QUANTUM PROTOCOLS FOR THE MILLIONAIRE PROBLEM WITH A SEMI-HONEST THIRD PARTY

Recently there were many quantum protocols devoted to solve the millionaire problem and private comparison problem by adding a semi-honest third party. They all require complicated quantum methods, while still leak a non-trivial amount of information to at least one of the parties. But it will be shown here that once the third party is introduced, there can be protocols which is very simple in the sense that they require quantum key distribution as the only quantum resource. Meanwhile, the amount of information leaked can be made arbitrarily small. Furthermore, in most previous protocols the third party can spoil the protocols without being detected. In our protocol such cheating can also be avoided, so that the only constraint left is that the third party should not conspire with another participant. Thus our solutions surpass all existing protocols on both feasibility and security.