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In this paper we present a protocol for unlinkable communication, i.e. where an attacker cannot map the sender and receiver node of a communication. Existing anonymity protocols either do not guarantee unlinkability (e.g. Tor and Mix networks), or produce huge overhead -- the dining cryptographers network causes quadratic number of messages. Our protocol needs only a linear number of messages while it still guarantees unlinkability. We introduce a measure of unlinkability and show that our protocol offers the highest possible degree of unlinkability. We show how to use the protocol in practice by adapting it to Internet and ad hoc communication.