This is no longer the case. Any SSN issued after 2011 is fully randomized
Additionally, the following SSNs are always invalid:
That’s kinda backwards, isn’t it? If I want to verify my identity to a company, they would send me something that only I could decrypt. Some government agency provides all the public keys of all citizens, the company takes my public key, encrypts some secret with it, sends it to me, and asks me to decrypt and return it. If I’m able to do so, I must be who I say I am otherwise I would not be able to decrypt the secret.
In an ideal world, the company (or, even better, the employee) would have a similar certificate that I could use to encrypt my response with.
In this theoretical system, ideally it’s illegal for anyone other than the person who’s supposed to have the private key to have it - excepting some subset of legal reasons (e.g. parents for their children). So, the only business that would be asking for people’s private keys are the kind that are already operating outside of the law.