I know that a fresh Ubuntu install can wipe Windows files completely. 

But I've heard that Windows writes random hidden data everywhere without your permission. Can there be remains of Windows after a clean install of Ubuntu that can be potentially used by *malicious software* against your data or passwords?

I had a nasty malware attack recently and left Windows for good, but the software service installed Windows again. So will a fresh Ubuntu install by me over Windows wipe it for good?