How this works comes down to two things. First, a unique Tor identity is used for each input and each output, so they can't be linked at the network level. Second, some magic math: keyed-verification anonymous credentials. It lets the coordinator issue you so-called credentials; mathematical objects that you can then do interesting things with, like re-randomizing them or splitting them into several smaller ones.
The magic lies in this: when the coordinator receives your re-randomized credentials, it can verify that it issued them, but it can't tell which input they came from.
So throughout the whole process, the coordinator is essentially a blind man.
No, the coordinator doesn't.
How this works comes down to two things. First, a unique Tor identity is used for each input and each output, so they can't be linked at the network level. Second, some magic math: keyed-verification anonymous credentials. It lets the coordinator issue you so-called credentials; mathematical objects that you can then do interesting things with, like re-randomizing them or splitting them into several smaller ones.
The magic lies in this: when the coordinator receives your re-randomized credentials, it can verify that it issued them, but it can't tell which input they came from.
So throughout the whole process, the coordinator is essentially a blind man.