distributed key generation

From: vertigo (ax178_at_wp.pl)
Date: 12/27/04 

Date: Mon, 27 Dec 2004 09:00:21 +0100

Hello
I have computer network with nodes: Node1, Node2, Node3.
Each node have unique id. New node (let's call it Node4) want to connect
to my network. He sends connect packets to Node1, Node2 and Node3
requesting to generate: seed1, seed2 and seed3.
I am looking for function f such as:

key=f(seed1,seed2,seed3); // Node4's key

Then the Node4's key will be send to Node1, Node2, Node3.
And each of the Nodes (Node1, Node2, Node3) knowing function f (and
maybe some other 'special' function) may check that received key was
generated using it's seed, as one of f parameters.

The point is that: i want to generate key for new node (Node4), but i
want to be sure that nobody alone was able to control what value that
key will have.

Number of nodes may be different.
Is there any such algoritm ?

Very important is that: because of structure of that network Node1,
Node2 and Node3 can not send any packets to each other.

Thanx
Michal

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