AA is irrelevant for this scheme. I mentioned it in the talk only to introduce the "real" solution. AA lets you prove ownership of the passport over the internet by challenging it with a nonce that's signed, but it doesn't provide any way to hide data so it can be anonymous.
Thanks for the answer. I watched the video again and understand a bit better what you're aiming at. I think I get the interaction between elements now: AA prevents cloning, but we don't have that in practice. Also, ZKP wouldn't work with AA because AA checks a signature, but to do that you have to have a pubkey (something like that?)
But on the other hand ZKP + Skype seems to make no sense; I mean, yeah, *some* data might still be hidden but really it does destroy anonymity, in a very visceral way..
Looking at this combination of elements I can't see how it's going to work - assuming (a) AA destroys the possibility of anonymity and/or (b) AA isn't available, as is the case today for most countries(?)