  We discuss quantum key distribution protocols and their security analysis,
considering a receiver-device-independent (RDI) model. The sender's (Alice's)
device is partially characterized, in the sense that we assume bounds on the
overlaps of the prepared quantum states. The receiver's (Bob's) device requires
no characterisation and can be represented as a black-box. Our protocols are
therefore robust to any attack on Bob, such as blinding attacks. In particular,
we show that a secret key can be established even when the quantum channel has
arbitrarily low transmission by considering RDI protocols exploiting
sufficiently many states. Finally, we discuss how the hypothesis of bounded
overlaps can be naturally applied to practical devices.
