If you have a security key you should have a code that you were given, when the lock was fitted...if you have'nt got the code, nobody should cut you a spare key...
Basically it stops anyone from copying your key ...
Suppose you will need to change the cylinder in the door if you have'nt got the code...
When I get a key that is snapped off in the lock...I use a small pair of sharp nosed pliers to pull it out...or sometimes a coping saw blade will do to start to draw it out...then finish it off with pliers.
Check your buildings insurance...it often covers lost keys and the replacement of locks and cylinders.
Security keys are usually used in better quality locks..that in turn means more money...