Each time you want an encrypted session you need to make a request to the government third party key signing service that, with your public key, the public counterparty's key and a government generated key for your session, a new key for the session is produced.

It's possible but potentially expensive and has issues with who gets keys on international communication. And it's also dumb.

I think nanobots could accomplish this. The end result might be unexpected though...

It should be a square pie.