an error occurred during authentication

Messages - If you can‘t sign in to your iMessage account or FaceTime on your Mac.    

Message activation error.      

Have someone else attempt to sign in using their Apple ID. If they can successfully sign in and use Messages/FaceTime, it may be your Apple ID. Someone I know had this happen and I was able to sign in using my Apple ID. After a call to Apple Support and then being elevated to a tier 2 support person, it turned out it was a problem with their Apple ID. It took the software engineers 3-4 days to fix the problem. When calling Apple, make sure you tell them it is an Apple ID problem so you don't get charged.

You can also try signing in on another device/computer. There have been a couple of posts where people's device/computer was blocked. You will need to contact Apple for that problem also.

There is a contact link.

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (The link doesn’t always load)

Get Support     Work through the screens to get a chat option. 

https://twitter.com/AppleSupport

Or fill out and submit  iTunes Store - Contact Us - Official Apple Support   The form is for iTunes, but will get passed to the ID Support section. 

See If you get an error when trying to activate iMessage or FaceTime  https://support.apple.com/en-us/HT201422