Security analysis of measurement-device-independent quantum conference key agreement with weak randomness

Quantum conference key agreement (QCKA) allows multiple users to distribute secret conference keys over long distances. Measurement-device-independent QCKA (MDI-QCKA) is an effective QCKA scheme, which closes all detection loopholes and greatly enhances QCKA’s security in practical application. However, an eavesdropper (Eve) may compromise the security of practical systems and acquire conference key information by taking advantage of the weak randomness from the imperfect quantum devices. In this article, we analyze the performance of the MDI-QCKA scheme based on the weak randomness model. Our simulation results show that even a small proportion of weak randomness may lead to a noticeable fluctuation in the conference key rate. For the case with finite-key size, we find that the weak randomness damages the performance of MDI-QCKA to different degrees according to the data size of total pulses transmitted. Furthermore, we infer that QCKA based on single-photon interference technology may perform better in resisting weak randomness vulnerabilities. Our work contributes to the practical security analysis of multiparty quantum communication and takes a further step in the development of quantum networks.