Interesting. The characters are readable but unfortunately, they are upside down. This is something I've never seen on a real Japanese sword; I suspect you've bought something else.
Here's a chance for someone who knows more than I do to jump in and tell us that the famous Damdifino school always signed upside down. Anyone out there have better news for the sword's owner?
And, by the way, rust should never be removed from a sword's nakago except by a competent restorer, if even then. Messed with nakagos seriously decrease a sword's value.
Grey