  We propose two quantum key distribution (QKD) protocols based on Bell's
inequality, which can be considered as modified time-reversed E91 protocol.
Similar to the measurement-device-independent quantum key distribution
(MDI-QKD) protocol, the first scheme requires the assumption that Alice and Bob
perfectly characterize the encoded quantum states. However, our second protocol
does not require this assumption, which can defeat more known and unknown
source-side attacks compared with the MDI-QKD. The two protocols are naturally
immune to all hacking attacks with respect to detections. Therefore, the
security of the two protocols can be proven based on the violation of Bell's
inequality with measurement data under fair-sampling assumption. In our
simulation, the results of both protocols show that long-distance quantum key
distribution over 200 km remains secure with conventional lasers in the
asymptotic-data case. We present a new technique to estimate the Bell's
inequality violation, which can also be applied to other fields of quantum
information processing.
