So, let me see if I got the idea: it's possible to accumulate random numbers in such a way that:
Am I getting closer?
- Prevents observers from knowing which individual numbers were accumulated.
- Allows the one who knows one particular number to prove he knows it without having to reveal the number itself. Or if you do have to reveal it, it's still impossible to know which particular addition to the accumulator had put that number there, thus creating no link between the addition and the revealing of the number.
Am I getting closer?
Yes thats pretty much it. Technically the coin is c=g^s*h^r and c is seen by everyone when it is added to the accumulator (though s and r are not seen by anyone). But when it is spent s the coin serial number becomes disclosed and is stored in the doble spend db, c is hidden because of the ZKP and r is still not revealed).
Adam