How to secure a doggy door from intruders?
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).