Forget that, what about time travel?
Conspiracy theories aside, a good rule of thumb is that if you hear the military is "considering research into something", they've long since completed the research, and either have the results ready to go or have decided it's not worth the trouble. Translating "physics experiments" into useful technology can be pretty difficult, but if there is any way at all to break public key encryption with current technology, brute force or otherwise, it has already been done and is in use. If you ran a major government, what would /you/ do? So, you should probably start with the assumption that asymmetric encryption is at least somewhat transparent to certain agencies, if you are important enough to warrant the expense, regardless of the published state of quantum computing or any other research.
And don't forget about time travel. We're all traveling forward in time at the speed of /normal time/. So, with the magic of archiving, your internet traffic can *travel through time to the future* and be decrypted using what, by then, will be cheap technology. The only thing protecting you is that archiving it is a pain, and it's really not worth the trouble. And of course you're not doing anything important enough to attract attention, right?