Complete Anonymous Server

Is it possible to prevent a chat server from knowing who is talking to who?

such that there exists a function negl such that
Pr[A(x,y)=1] < 1/2+negl(x,y)

where Pr is probability and A outputs 1 if the server can correctly guess if x and y are communicating. negl is defined as asymptotically negligible (i.e. negl<1/p(x) where p is some polynomial).

>>11
Freenet is java shit, fuck off. If you're too stupid to design your code to be cross-compilable with little manual effort then you can't be trusted for security. And that's to say nothing of the steaming pile of shit that is the JVM. It wouldn't suprise me that Oracle leaves those gaping holes just so they can exploit them.