hm. Security policies is something you can break with one way or another. You cannot break mathematics that way.
The encryption tools you are using are written by people, and can have bugs. Being careless and blindly trusting them can get you into trouble.
You want math? How many combinations are afforded by your "long, carefully chosen password" in a symmetric system? How many core seconds per hour does a typical botnet scriptmonger control? Cryptanalysis of GPG doesn't even matter if Eve has enough time to brute force your symmetric key.