  We give an arguably simpler and more direct proof of a recent result by
Miller, Jain and Shi, who proved device-independent security of a protocol for
quantum key distribution in which the devices can be used in parallel. Our
proof combines existing results on immunization (Kempe et al., SICOMP 2011) and
parallel repetition (Bavarian et al., STOC 2017) of entangled games.
