  We present a generic study on the information-theoretic security of
multi-setting device-independent quantum key distribution protocols, i.e., ones
that involve more than two measurements (or inputs) for each party to perform,
and yield dichotomic results (or outputs). The approach we develop, when
applied in protocols with either symmetric or asymmetric Bell experiments,
yields nontrivial upper bounds on the secure key rates, along with the
detection efficiencies required upon the measuring devices. The results imply
that increasing the number of measurements may lower the detection efficiency
required by the security criterion. The improvement, however, depends on (i)
the choice of multi-setting Bell inequalities chosen to be tested in a
protocol, and (ii) either a symmetric or asymmetric Bell experiment is
considered. Our results serve as an advance toward the quest for evaluating
security and reducing efficiency requirement of applying device-independent
quantum key distribution in scenarios without heralding.
