It's not a "hard problem" it's impossible, it would be a typical trying to solve a social issue with technical solution. Bad actors encrypt their comms anyway so only the unaware layman gets caught in the net.

> A mission to secure the people whilst not infringing personal rights in today's world is a really really hard problem.

The problem is that the NSA violates everyone's privacy without a care in the world.

This makes it pretty easy for them. Stockpile a bunch of vulnerabilities and go to town.

When you cannot even know what their budget is (since it's classified), can you even know what their capabilities are?

They don't sniff all the packets to find anything useful. Snowden showed that they intercept certain packets flowing between particular sources and destinations that might contain useful information. In Snowden's leaks, one such application was email inbox backup transfers for big Internet companies that did not (at that time) encrypt their WAN traffic, from which they mined the sender and recipient to build a social graph, a program that the leaks said had already been shut down.

Mining public forums like this one are likely fair game and seems not to be a secret, but it doesn't require anything in Room 641A.