Abstract: An authentication system of a portable electronic device is disclosed. The authentication system of a portable electronic device includes a first identity recognition module, a second identity recognition module, an application module, an authentication module and a near field communication (NFC) module. The application module enables the first identity recognition module or the second identity recognition module according to a setting. The authentication module is electrically connected to the first identity recognition module and the second identity recognition module. The authentication module authenticates the first identity recognition module or the second identity recognition module which is enabled. The NFC module is electrically connected to the first identity recognition module and the second identity recognition module. The NFC module executes a corresponding function according to the first identity recognition module or the second identity recognition module which is enabled and authenticated.

Abstract: A connection establishing method between two electronic devices is disclosed, which includes following steps: activating a connection establishing program in a first electronic device; searching at least one specified electronic device; reading a storage unit, wherein the storage unit includes a database, and the database stores a plurality of corresponding connection modes between a plurality of second electronic devices and the first electronic device; pairing the searched specified electronic device with the database. If the second electronic devices include the specified electronic device, a connection between the specified electronic device and the first electronic device is established according to the corresponding connection mode. If the second electronic devices do not include the specified electronic device, a connection mode between the specified electronic device and the first electronic device is established and the database is updated.