@parados,
Thank you for that educated attempt but failed answer. While it might be plausible, you must assume that all of the information is contained in the fallout shelter, and that no networking was used. This fallout shelter, was top secret, and was self sufficient and not linked to any point in the outside world, after being built.
Thus the billions and billions of lines of binary computer code was retrieved from somewhere in the fallout shelter proper.
It should be noted, that there is a possibility that you have raised, that our descendants from millions of years in the future, might well be able to intercept this from the galactic cloud of information, at some point, as cyberspace may become timeless.
But please get back to the bomb shelter and finish the equation....