I think it would be possible but only if the government database itself provides the necessary functionality. One possible way it could work is that the govern

I think it would be possible but only if the government database itself provides the necessary functionality. One possible way it could work is that the government provides a website where a user can enter their name and SSN and receive in return a digitally signed document stating, in effect, that a person of this name has some SSN on file. That document could then be submitted to a company which would only have to validate its signature against a signature published by the government service. But this still has problems. Presumably you would want to be sure that the person submitting the verification actually is the person with the name and SSN (as opposed to someone who stole or otherwise obtained that name/SSN pair), so the government site has to somehow verify that before generating the verification document. There's also the issue that many people can have the same name so just having a certificate that says that there is some John Doe who has an SSN doesn't necessarily tell you that the John Doe submitting the application has an SSN, it could be a different John Doe. Though perhaps this problem could be solved by the previous paragraph.