Cryptanalysis and improvement of the measurement-device-independent quantum key distribution with hyper-encoding

Recently, Cui et al. [Sci. China Phys. 62, 110311 (2019)] proposed a measurement-device-independent quantum key distribution (MDI-QKD) scheme based on high-dimensional encoding to increase the channel capacity of each individual photon. A secret key is shared among two legitimate parties via the help of a dishonest third-party (TP). They claimed that the proposed protocol can improve the drawback of the low-key generation rate that existed in the past MDI-QKD schemes. However, this study pointed out a loophole during the security check of TP. That is, the two legitimate participants merely use the corresponding qubit pairs that are both generated in the diagonal basis for the discussion, which leads to a potential attack that not only allows TP to avoid the security check but also creates partial inconsistency of key bits for both communicating sides. Fortunately, this problem can be fixed by a minor correction of the protocol.

Automated summary

Recently, Cui et al. proposed a measurement-device-independent quantum key distribution (MDI-QKD) scheme based on high-dimensional encoding to increase the channel capacity of each individual photon. While claiming to improve the low-key generation rate drawback of past MDI-QKD schemes, this study identified a loophole during the security check of the third-party. By using only qubit pairs generated in the diagonal basis, a potential attack and partial inconsistency of key bits were discovered. Fortunately, a minor correction of the protocol fixed this issue.