There's something in-between, though it doesn't actually break the paradox, just makes some different tradeoffs:

In cryptography, a ring signature is a type of digital signature that can be performed by any member of a group of users that each have keys. Therefore, a message signed with a ring signature is endorsed by someone in a particular group of people. One of the security properties of a ring signature is that it should be difficult to determine which of the group members' keys was used to produce the signature

http://en.wikipedia.org/wiki/Ring_signature