hostile node anonymity attack scenario

[Paul Forgey]

Your point being the strength of the anonymity depends on the number of 
nodes. If there were, say, 2000 nodes, then one would have to create 
almost 8 billion connections. It is encouraging to know the level of 
effectiveness increases geometrically with the number of new nodes 
introduced.

Geoffrey Goodell wrote:
> A more interesting question to ask might be, "what happens if a client
> creates N independent connections through the network, over a long
> period of time so that circuits are not reused?"  If a malicious
> operator possesses only three nodes, and N is sufficiently large (i.e.
> greater than n*(n-1)*(n-2), where n is the number of Tor nodes), then
> chances are, the attacker would be able to break the anonymity of at
> least one connection...
> 
> Geoff