  A prominent application of quantum cryptography is the distribution of
cryptographic keys that are provably secure. Recently, such security proofs
were extended by Vazirani and Vidick (Physical Review Letters, 113, 140501,
2014) to the device-independent (DI) scenario, where the users do not need to
trust the integrity of the underlying quantum devices. The protocols analyzed
by them and by subsequent authors all require a sequential execution of N
multiplayer games, where N is the security parameter. In this work, we prove
unconditional security of a protocol where all games are executed in parallel.
Besides decreasing the number of time-steps necessary for key generation, this
result reduces the security requirements for DI-QKD by allowing arbitrary
information leakage of each user's inputs within his or her lab. To the best of
our knowledge, this is the first parallel security proof for a fully
device-independent QKD protocol. Our protocol tolerates a constant level of
device imprecision and achieves a linear key rate.
