In-app user identification with Apple ID

Hello, everyone! Hope somebody is familiar with this issue. There is an app an d related web service. The registration on the back-end requires login (email or username) and password. During Appstore review process we were informed that we are not allowed to ask appstore users to go through our registration form. And there we are stuck, what to do next? It is known that there is no way to get any unique key from Apple ID (forbidden due to privacy terms again) nor email.

So the questions is how to identify user of app if he changed on another device?