What makes you think the government has a polynomial prime factoring algorithm?
What makes you think they don't? What makes you think they even need one? What makes you think they don't hire, and utilize, some of the most powerful math-heads out there? What makes you think that something that can't be broken today won't bring you to the vale of tears days, months, even years later, if that's what it takes? What makes you think they don't have, or won't have, some kind of quantum computing device that obviates encryption entirely? What makes you think they didn't log every keystroke you typed, thus making encryption a complete non-issue? Wait, what, your system is "pure"? You know they can tell what you're typing by the sound, right? Finally, what makes you think they won't come right to your home or place of business or your favorite club, hustle you into a dank basement somewhere, and waterboard you or pound your toes to mush with a hammer or actually, eventually, read your mind electronically and get what they want that way? Got any relatives you treasure? What about the recipient(s)? Now there are (at least) two points of human weakness.
And... you do know that "they" have access to quite a few technologies that "we" do not, right?
I would seriously bet on the idea that if you demonstrate you think you need to encrypt your stuff by simply doing so, all you've managed to accomplish is get on a list of "we'll get back to this suspicious character later."
Right now, if you've got something secret that you don't want the government to become aware of, just don't say it or otherwise communicate it. That's your very best chance of actually keeping it a secret. It may be your only chance.