A quantum solution to blind millionaire problem with only single-particle states

Abstract

Blind millionaire (BM) problem is an extended version of the initial millionaire problem required to compare the sum of the participants’ secrets between different groups. As a new topic of quantum secure multiparty computing, existing protocols with some special entangled states may not be easily achieved in practice. This study proposes a non-entangled method of solving the quantum blind millionaire (QBM) problem with special d-level single-particle states for the first time. To protect the confidentiality of transmission secrets, this protocol exploits the property of randomly generated d-level single-particle states. Furthermore, simple shift operations are used to encode the respective secrets. Detailed security analysis demonstrates that this protocol is impervious to internal and external threats. The presented methods can not only be used to solve the blind millionaire problem but also be used as a basic module to solve other secure multiparty computing problems.