  We derive a device-independent quantum key distribution protocol based on
synchronous correlations and their Bell inequalities. This protocol offers
several advantages over other device-independent schemes including symmetry
between the two users and no need for preshared randomness. We close a
"synchronicity" loophole by showing that an almost synchronous correlation
inherits the self-testing property of the associated synchronous correlation.
We also pose a new security assumption that closes the "locality" (or
"causality") loophole: an unbounded adversary with even a small uncertainty
about the users' choice of measurement bases cannot produce any almost
synchronous correlation that approximately maximally violates a synchronous
Bell inequality.
