  We present the optimal collective attack on a Quantum Key Distribution (QKD)
protocol in the "device-independent" security scenario, where no assumptions
are made about the way the QKD devices work or on what quantum system they
operate. Our main result is a tight bound on the Holevo information between one
of the authorized parties and the eavesdropper, as a function of the amount of
violation of a Bell-type inequality.
