I don't know that crypto is really necessary in this case. It's already standardized, and is there something specific that worries you about the security of it?

I don't know that crypto is really necessary in this case. It's already standardized, and is there something specific that worries you about the security of it? That said, the answer to your question is "yes" - the branch of crypto you are looking for is "verifiable credentials" (searching for that term will get you plenty of info).