Good luck with that
But even if it were possible to create provably secure software (ah hae ma doots), all you'd need then would be provably secure hardware to run it on and provably secure people to operate it. As Bruce Schneier points out:
the mathematics are impeccable, the computers are vincible, the networks are lousy, and the people are abysmal. - Secrets and Lies: Digital Security in a Networked World
