I see talk in this thread that uses the term 'private key'. Which makes me think about using a literal cryptographic private / public key combo for this sort of thing.
Say I have a private key, and I want a business to have a way to ID me. They give me a key associated with me in their database, and I encrypt it with my private key, and give the results back. Now when someone wants to do business with them in my name they must turn those results back into what the business has in their database. So long as I keep my key safe the business can leak data all they want.
This would shift all the work for security over to the citizens though, which could have mixed results...
Say I have a private key, and I want a business to have a way to ID me. They give me a key associated with me in their database, and I encrypt it with my private key, and give the results back. Now when someone wants to do business with them in my name they must turn those results back into what the business has in their database. So long as I keep my key safe the business can leak data all they want.
This would shift all the work for security over to the citizens though, which could have mixed results...