  Quantum digital signatures (QDSs), which distribute and measure quantum
states by key generation protocols and then sign messages via classical data
processing, are a key area of interest in quantum cryptography. However, the
practical implementation of a QDS network has many challenges, including
complex interference technical requirements, linear channel loss of quantum
state transmission, and potential side-channel attacks on detectors. Here, we
propose an asynchronous measurement-device-independent (MDI) QDS protocol with
asynchronous two-photon interference strategy and one-time universal hashing
method. The two-photon interference approach protects our protocol against all
detector side-channel attacks and relaxes the difficulty of experiment
implementation, while the asynchronous strategy effectively reduces the
equivalent channel loss to its square root. Compared to previous MDI-QDS
schemes, our protocol shows several orders of magnitude performance
improvements and doubling of transmission distance when processing multi-bit
messages. Our findings present an efficient and practical MDI-QDS scheme,
paving the way for large-scale data processing with non-repudiation in quantum
networks.
