Controlled mutual quantum entity authentication with an untrusted third party

We propose a quantum control entity mutual authentication protocol that can be executed in environments involving an untrusted third party. In general, the third party, referred to as Charlie, can be an entity such as a telephone company, server, financial company, or login webpage for a portal service. Most communication protocols controlled by third parties are vulnerable to internal attacks. In this study, we present two solutions that make use of an entanglement correlation checking method and random numbers against an internal attack by an untrusted third party.