Since they see everyone as a potential threat, taint their data so that everyone appears to be that threat. Millions of us could increase the signal-to-noise ratio in their collected data by using a bot to perform random human-like web searches and visits.
If 100 people are searching for , the government has actionable surveillance data. If 100 thousand or 10 million are searching for it in ways that are indistinguishable from a human, then that data becomes unreliable and is no longer actionable.
Adding email to this would strike a fatal blow. Someone could figure a way to create a secure layer to inform a client when a given email being sent was fake, and thus suppress it visually. Soon from the government perspective everyone would be cheating on their spouses and spouting extremist views and plotting this or that.
This would result in an increase in liberty by proving to the government that it should fear its people, if only because its sophisticated surveillance tools now confirm that all the people are evil.