I absolutely understand not wanting a key access or even a knob on the outside. It is common in Detroit for side doors & basement doors to have no hardware at all on the outside. (And garage alley doors, too.)
Heck, my car has 5 doors and only one has a keyway. Handles, but no keyways.
Vertical dead bolts are very strong and very easy to install. You can get them one-sided (no hole through the door) or two-sided (keyed). The one pictured below has two pin loops, but you can get them with as many as six for more strength.
Use long screws in the loop plate to reach door jamb's studs.
If the door is solid core, the mechanism screws into the door. If it isn't solid core and is wood faced, you can use carriage bolts to install to the door. Put the bolt heads outside and acorn nuts on the inside so you don't brush your hand across the end of a bolt.
If the door is steel or fiberglass, use elevator bolts instead of carriage bolts. (They don't have to dent their way into the door like the hex on a carriage bolt does.)
Enjoy This Day!
Paul