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We provide an analysis of a new family of device independent quantum keydistribution (QKD) protocols with several novel features: (a) The bits used forthe secret key do not come from the results of the measurements on an entangledstate but from the choices of settings; (b) Instead of a single securityparameter (a violation of some Bell inequality) a set of them is used toestimate the level of trust in the secrecy of the key. The main advantage ofthese protocols is a smaller vulnerability to imperfect random numbergenerators made possible by feature (a). We prove the security and therobustness of such protocols. We show that using our method it is possible toconstruct a QKD protocol which retains its security even if the source ofrandomness used by communicating parties is strongly biased. As a proof ofprinciple, an explicit example of a protocol based on the Hardy's paradox ispresented. Moreover, in the noiseless case, the protocol is secure in a naturalway against any type of memory attack, and thus allows to reuse the device insubsequent rounds. We also analyse the robustness of the protocol usingsemi-definite programming methods. Finally, we present a post-processingmethod, and observe a paradoxical property that rejecting some random part ofthe private data can increase the key rate of the protocol.

Device-independent quantum key distribution based on measurement inputs