> The correct answer is probably a new government ID system based on public key encryptio

Check out Estonia

The interesting question is how to verify who someone is before issuing them a digital ID. Estonia verifies people using their Estonian ID cards, their mobile devices, or biometric data if they have it recorded.

The system is only as strong as its weakest link. ID cards can be faked and mobile devices can be stolen. Biometrics can't be easily faked, but they're horrible to have leaked because you can't change your fingerprints or eyeballs if compromised.