  We propose and experimentally implement a novel reconfigurable quantum key
distribution (QKD) scheme, where the users can switch in real time between
conventional QKD and the recently-introduced measurement-device-independent
(MDI) QKD. Through this setup, we demonstrate the distribution of quantum keys
between three remote parties connected by only two quantum channels, a
previously unattempted task. Moreover, as a prominent application, we extract
the first quantum digital signature (QDS) rates from a network that uses a
measurement-device-independent link. In so doing, we introduce an efficient
protocol to distil multiple signatures from the same block of data, thus
reducing the statistical fluctuations in the sample and increasing the final
QDS rate.
