A battery-powered trigger-locking device, which is configured to be disposed on a gun with a trigger for firing, includes a data receiver, a data memory and a logic device for determining whether data received by the receiver is the same, or substantially the same, as data stored in the memory. If a data match is indicated, the logic device causes an electromagnetic device to move a trigger-locking member to an unlocked position, permitting the gun to be fired. A separate electronic gun key is provided to transmit gun unlock data to the data receiver of the trigger-locking device. This gun unlock data may be a password, a long pseudo-random number or biologic data identifying the gun owner or some other person who is licensed or otherwise authorized to fire the gun.