  Quantum secret sharing (QSS) is a fundamental quantum secure communication
primitive, which enables a dealer to distribute secret keys to a set of
players. Device-independent (DI) QSS can relax the security assumptions about
the devices' internal working, and effectively enhance QSS's security under
practical experimental conditions. Here, we propose a DI-QSS protocol based on
Greenberger-Horne-Zeilinger state, which guarantees the security of keys by the
observation of the data conclusively violating the Svetlichny inequality. We
estimate the performance of our DI-QSS protocol in practical noisy
communication scenarios by simulating its key generation rate, noise tolerance
threshold, and detection efficiency threshold. Moreover, some active
improvement strategies, such as the noise pre-processing strategy and
post-selection strategy are introduced into the DI-QSS protocol, which can
increase its noise tolerance threshold from 7.148% to 8.072%, and reduce the
detection efficiency threshold from 96.32% to 94.30%. It indicates that the
adoption of the active improvement strategies can enhance DI-QSS's robustness
against the noise and photon loss, which can reduce the experimental difficulty
and promote DI-QSS's experimental realization. Our work may be a promising
guidance for future DI-QSS's experiments.
