In the Granovetter diagram to the right Bob is about to gain a new acquaintance. All Bob will know about this acquaintance is what Alice tells him, and that only to the degree that Bob believes that Alice knows and is telling him what she knows.

If Bob decides to speak to Carol, what Carol hears will sound as if it came from Alice or at least that is the nominal interpretation of the diagram.

Thus Alice is generally in a position to interpose a man-in-the-middle between Bob and Carol.

The capability in the Foo message might be to an intermediary, specially fabricated by Alice, that prepends the following text to any message sent to it, and then relays the larger message to Carol.

Carol is now in a position to begin judging Bob independently from Alice. If Bob and Carol strike it off, they can never be sure that Alice is out of the loop.

Redundant Introductions

There may be another agent Dave known to both Bob and Carol. If Dave sends to Bob a message like Foo containing a capability to Carol, then Bob is in a position to compare the capabilities from the two messages for equality. If equal he knows that the compared capability is indeed to a new player, or that Alice and Dave are conspiring to invent a new player.

The Crypto Connection

When crypto keys replace capabilities a public key is suitable for the role of the key to Carol. Either RSA or Diffie-Hellman work here. This allows Bob to compare keys to discover that there is only one Carol. He can then combine the recommendations that he received from Alice and Dave. For this scenario all other capabilities can be done with a shared key for each pair of communicating agents. If Bob and Carol choose to share a symmetric key between them, neither Alice nor Dave will be in a position to intervene, unless they are conspiring together.

One moral to all this is that a public key serves well as a name. I think it is an open question of how much entropy from the public key must be remembered to recognize the key again.

This note depends on the vague concept of conspire. It would be good to clarify it.

A small variation on Granvetter