In machine translation (MT) mediated human-to-human communication, it is not an easy task to select the languages and translation services to be used as the users have various language backgrounds and skills. Our previous work introduced the best-balanced machine translation mechanism (BBMT) to automatically select the languages and translation services so as to equalize the language barriers of participants and to guarantee their equal opportunities in joining conversations. To assign proper languages to be used, however, the mechanism needs information of the participants' language skills, typically participants' language test scores. Since it is important to keep test score confidential, as well as other sensitive information, this paper introduces agents, which exchange encrypted information, and secure computation to ensure that agents can select the languages and translation services without destroying privacy. Our contribution is to introduce a multi-agent system with secure computation that can protect the privacy of users in multilingual communication. To our best knowledge, it is the first attempt to introduce multi-agent systems and secure computing to this area. The key idea is to model interactions among agents who deal with user's sensitive data, and to distribute calculation tasks to three different types of agents, together with data encryption, so no agent is able to access or recover participants' score.