No, you just need sufficiently advanced maths. You need a system where you can create a signature one time anonymously, the signature providing enough information for a merchant to prove it is valid. However, if you create a signature two or more times with the same key enough information is revealed to destroy your anonymity making the fraud traceable.
My understanding is that at least one system like this had been written up well over a decade ago, but I have no idea if the crypto has survived peer review and cannot cite anything. Anyone know details of a system such as I described?