The first bit seems possibly solvable with private set intersection. You can publish a salted hash of everybody you trust, and I can compute hashes of everyone I trust with your salt to see if we have anyone in common. Then I check the signature corresponding to the salted hash I like, and hopefully it doesn't reveal anything you don't want to reveal.
I don't know if anyone has actually done this in practice. Does it work?
I don't know if anyone has actually done this in practice. Does it work?