Re: perhaps itself encrypted with a key known only to law enforcement
The big assumption of course is that GCHQ have to be at least as good at keeping their private key secret as Alice and Bob are
No - you've made two assumptions :-
- The one you mention
- That the message sent to GCHQ is indeed the same as the one you sent to Alice
The first of these we know to be false straight off the bat - look at the CIA and NSA leaks to show how they actually aren't all that good at keeping secrets. And it gets worse once you need international cooperation - because that means giving all the keys to the Russians, the Syrians, the Iranians, the North Koreans, etc. Failure to do so would mean you don't get their cooperation - and guess where all the traffic goes instead.
The second is a fundamental flaw in that it requires the bad guys to play by the rules in order to catch them - so Bob sends a message to Alice that says "Attack at Dawn", whereas GCHQ gets one that says "Mary had a little lamb". Bob *swears* both messages have the same content.
So what we're left with is a system that is fundamentally less secure for everyone and no use whatsoever for catching bad guys.
Vic.