There are backdoors to almost every “secure” type of online system if you were to listen to the conspiracy theorists. With that in mind, creating the ultimate backdoor system and defending against it are not that hard to do.
We already know the NSA wants to eavesdrop on the internet. It has secret agreements with telcos to get direct access to bulk internet traffic. It has massive systems like TUMULT, TURMOIL, and TURBULENCE to sift through it all. And it can identify ciphertext — encrypted information — and figure out which programs could have created it.
But what the NSA wants is to be able to read that encrypted information in as close to real-time as possible. It wants backdoors, just like the cybercriminals and less benevolent governments do.
And we have to figure out how to make it harder for them, or anyone else, to insert those backdoors.