If the national security agencies are determined to eavesdrop on you, as far as I know there is currently no browser setup that can with very high confidence prevent it. Let's for example posit that Tor is successful in obscuring your IP address from the destination activity 80% of the time. Then if you send 10 transactions and or mining shares (over time perhaps not in the same Tor session), then your chance of being non-anonymous has declined to 0.8^10 = 11%. Not good odds, especially if the cost of being non-anonymous is very great, e.g. you break some Orwellian capital controls in 2017 and end up in a SuperMax prison.
Some argue that hiding in plain sight is best, i.e. not drawing attention to yourself by using Tor. However, if you are accessing the nodes of a crypto-currency network, I assume the national security agencies are (will be in 2017!) tracking you if you agree with the theory that the G20 is going to be hunting down (to confiscate) all wealth as the bankrupt global economy forces them to. This is couched in propaganda themes such as "go after tax avoiders" and "prevent money laundering and funding for terrorism". Others might argue this is a paranoid view.
I believe there exist algorithms to attain higher levels of confidence, that can be described and analyzed mathematically, but as far I know such algorithms are not implemented for any browser setup nor anonymous coin.
Very pessimistic view of the future. I am a little bit more optimistic.
To enforce the rules globally, they will need to have the resources and consensus of all nations and their own population. I do not believe people will give up their right of privacy so easily.
If the economic of the existing power really going down the sink, they will no longer have the influence and infrastructure in place to enforce the rules.