We show that in device-independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise security. We show that a combined attack exploiting test sample and measurement choices compromises the security even with a linear-size test sample and otherwise device-independent security considerations. We explicitly derive the sample size needed to retrieve security as a function of the randomness quality. We demonstrate that exploiting features of genuinely higher-dimensional systems, one can reduce this weakness and provide device-independent security more robust against weak randomness sources.

• Received 31 January 2013

DOI:https://doi.org/10.1103/PhysRevA.88.032309