Re: The utter fools
A better way to work is to remember that when you're hunting criminals, you are not hunting super-intelligent encryption-geniuses, but rather the less-able twerps of this world. As such, you simply have to accept that some of their communications won't be accessible to you, and there isn't a magical McGuffin that will let you get around this.
This is the same thinking process that police had to go through when DNA evidence was first introduced; all DNA actually shows is that at some point, the person whose DNA is present was in contact with whatever the DNA was detected on. Thus the old criminal trick of picking up cigarette ends outside dodgy pubs, then scattering one or two in prominent places when committing a burglary only works if you have stupid policemen around.
Another example is of some burglars who targeted country houses and operated as a gang. Their modus operandi was to meet up at a motorway service station near the target, turn off all mobile phones then go out to rob the target. Only afterwards did they re-enable their phones. This meant they didn't leave an electronic trail to their crimes, but did mean that they left a huge great signal that they were about to commit a crime (for they never met up, turned off phones then sloped off down the pub lawfully to add distraction to the pattern).
As I say, we're dealing with criminals, not masterminds. Criminals always make mistakes, and police have the manpower to catch these mistakes.
So, forget the phoney prize of being able to break encryption. If it is seen as possible, people will use other methods to get around this problem; unbreakable one-time pads for instance. Or, use encryption known not to have been back-doored.