  Device-Independent Quantum Key Distribution (DIQKD) is a formalism that
supersedes traditional quantum key distribution, as its security does not rely
on any detailed modelling of the internal working of the devices. This strong
form of security is possible only using devices producing correlations that
violate a Bell inequality. Full security proofs of DIQKD have been recently
reported, but they tolerate zero or small amounts of noise and are restricted
to protocols based on specific Bell inequalities. Here, we provide a security
proof of DIQKD that is both more efficient and noise resistant, and also more
general as it applies to protocols based on arbitrary Bell inequalities and can
be adapted to cover supra-quantum eavesdroppers limited by the no-signalling
principle only. It requires, however, the extra assumption that the adversary
does not have a long-term quantum memory, a condition that is not a limitation
at present since the best existing quantum memories have very short coherence
times.
