Chrome Sync supports optional client-side encryption, and Firefox Sync always uses client-side encryption.
Do you honestly believe that if the NSA decided they wanted your browser history, the encryption used by Chrome or Firefox would stymie them for too long?
I guess I'm just not really clear on what folks are worried about happening with these history data. Is the concern that the data could be leaked, revealing potentially privacy-compromising information? Or that Google might mine it in an attempt to make a buck off of your metadata? Or that the government might use it to identify you as a potential political dissident?
Personally, I find the Google search history to be useful, though less useful lately since DDG is my primary search engine now. I don't quite get the knee-jerk "this is creepy" outrage and fear I see from some folks about this feature.
Yes, I do. But I also believe that they would more easily access my computer after I inserted the master password, or detain me with false accuses until I give up, and maybe more. We're talking about organizations that do not abide by the law. But one thing is to worry for the NSA coming after you, another is to keep your history hidden from Google.
I submit that if you don't want Google to know about your searches, you should not use Google (or at the very least, not use Google with a browser logged in to a Google service).
That said, I can imagine someone who wants to use a search engine that he doesn't trust (because the results are better but wants to keep his privacy): for example a girl may want to search for pregnancy tests but she may dislike to be later targeted by ads about that.
You are right that one could simply avoid the service or at least avoid to be logged in, but most people are oblivious of these things.
(And your point about hiding from the NSA vs. Google is what I was trying to get at in my comment above, which for some reason got downvoted quite heavily).
If they care about your browser history specifically, then in a battle between one individual and a government-level adversary, I'd bet on the latter; it's unlikely they'd try to break the encryption when they could use keyloggers, cameras, or any number of other methods that work fine on targeted individuals. (Or,
But if they care about doing blanket capture and analysis of everyone's history, then yes, I think the encryption used by Chrome and Firefox should work. Security bugs are always possible, of course, and browsers are quite notorious for them, but the more widely a security bug is exploited, the more rapidly it'll be detected and fixed.
The solution to this is not to turn off Google's search history, but to use a search engine (like DDG) who purportedly have security and anonymity built in.