I installed a doggy door so that our dog can go in/out when it has to go to the bathroom while we are at work/away. It lets him out into our fenced in backyard. The gates are deadlocked, but obviously this does not completely secure the house from determined intruders. If someone were to breach our fence, the intruder might easily fit into our doggy door. Other than the cover that was provided with the kit which I easily broke into, what is a good way to secure a doggy door from unwanted intrusions?
Forget securing the door, and install a security system with a motion sensor. Put labels up outside saying there is a security system (some people only put labels up, and don't have a real system).
Even if you have a door with a locking mechanism, if someone manages to defeat it (eg, kicks it open) or you forget to lock it, you still have the alarm go off.
Most motion sensors are "pet safe" in that it takes something over eg, 40 lbs or 80lbs to actually trigger (they have a rating and there are different sizes, so you can get a lower rating if you have a poodle and a bigger one if you have a great dane).
They make locks for the doors that only unlock when the collar worn by the dog is within a few feet.
There's this product: http://www.petdoors.com/cat-mate-electronic-cat-doors.html . It's a cat door, but it works on the same principle. Also, most of these you can set to 'allow onyl departures' or 'only arrivals' as well. - might not be applicable to your situation, but good to know.
Also, while I appreciate your plan for security, keep in mind that this is really only a deterrence against meddling kids - if people want in, they will get in regardless.
When I was growing up we had a simple system on the dog door into our garage, it was 1/4" thick steel plate that was slightly larger than the opening and a set of rails on two sides and the bottom of the door. When we were away and wanted to secure the door, we simply slid the plate into the slides with the handle that was on the back, and flipped a hasp down over it.
If your door is installed in a wall [ONLY] - go to home depot and get a metal pole about 2" thick and about 12" taller than the top of the dog door [to the floor]. Core a 2 1/2" thick hole into your slab approximately far enough away to allow your dog to get into and out of the dog door without a problem, but close enough that a person can't get their body around. Make sure you core the hole aligned with the middle of the dog door. Slide the pole into the hole and fill around it with quikcrete. You now have a barrier that your dog can easily maneuver around, but it is now impossible for a person to slide in and out of the dog door.
A variation of the pole in the floor is a little more elaborate but less likely to create a crack in the garage floor or other damage. I saw a neighbor of a friend's system, a police captain in Washington DC, who had installed a short 3/4 inch plywood wall parallel to the garage wall and just far enough from the original wall to allow the flap to open and the dog to squeeze in. The wall was about 1 1/2 times the height of the dog door and about twice the width and offset as described above. Then the wall was anchored to the original wall with "braces" of 2X4 anchored to the original wall in four places; top and bottom on both sides with lag screws to the original garage framing. It sounds all complicated but it is very simple and cheap and effective.
Interestingly, the neighborhood is bad and his dog passed away and the doggy door with the small chain link fence outside still apparently acts as an intrusion deterrent. I live in SW Virginia near a drug rehab place and have had drugged up characters wander onto my property and INTO my open garage several times. Once I put up a dog run attached to the house and a similar doggy door system, NO more weirdos in my garage. Adding the "maze" (as my granddaughter calls it) took about an hour and cost me used plywood, one 2X4 for less than two dollars and a handful of 1/2X3 lag screws. I think I paid another two or three dollars for at Lowe's.