https://en.wikipedia.org/wiki/Turbulence_(NSA)
This is of course what an outfit like the STASI or Gestapo would do, isn't it? If you're actually trying to hide from surveillance, the best tactic is to hide in plain sight, maintaining a cover story consisting of bland normal online presence that doesn't draw extra attention.
Of course living in an authoritarian panopticon and having to hide in this manner is an undesirable situation, and the solution is not technological, but rather political in nature. One basic issue is transparency, i.e. the public should be able to see what the intelligence agencies and corporations are up to with their surveillance programs. This is why Snowden's exposure of PRISM, XKEYSCORE, TRAFFICTHIEF, etc. was in the public interest, i.e. legitimate whistleblowing.