An authentication system includes one or more portable terminals and an electronic device. The electronic device includes a storage section, a terminal location acquiring section, a determining section, an authentication section, and a right granting section. The storage section stores authentication information of each of one or more users, usage right information of each user, and location information of the electronic device. The terminal location acquiring section acquires location information of each portable terminal. The determining section determines a first portable terminal that is located within a specific authentication distance from the electronic device, based on the location information. The authentication section performs authentication of a first user associated with the first portable terminal, based on the authentication information of the first user. The right granting section permits the first user to use the electronic device within a scope of usage right granted to the first user.