Handgun Licensing and Registration Act of 2003 - Amends the Federal criminal code to require the Attorney General to establish a Federal system for the licensing and registration of all handguns owned, possessed, or controlled in the United States, which shall include a method for easily retrieving information to identify: (1) each State resident who owns, possesses, or controls a handgun; and (2) the handgun.Makes it unlawful for any person to own, possess, or control a handgun in a State to which this Act applies unless the person is licensed under the system and has registered the handgun with a Federal, State, or local law enforcement agency.Makes such requirements inapplicable to a State which has in effect a system for the licensing and registration of handguns which includes such identifying information (as certified by the Attorney General).Provides criminal penalties for violations under this Act.