The present invention provides a lock with an authenticated open and set function, by which the lock may be opened without any bothersome operation for inserting a key to open the lock. An IC card 3 sends user identification information stored in a memory 34 to an authenticated open and set function unit 1. The authenticated open and set function unit 1 sends the user identification information to a collator 15 under the control of a controller 11 on reception of it. The collator 15 collates the user identification information sent from the IC card 3 with that stored in a memory 16. When both of the user identification information are coincided with each other, the collator 15 sends the collation signal, which is indicative of the user being authenticated, to the controller 11. The controller 11 gives a controller 17 a command to open a lock installed in a door 2. The controller 17 opens the lock based on the command by the controller 11.