  We propose an efficient four-intensity decoy-state BB84 protocol and derive
concise security bounds for this protocol with the universally composable
finite-key analysis method. Comparing with the efficient three-intensity
protocol, we find that our efficient four-intensity protocol can increase the
secret key rate by at least $30\%$. Particularly, this increasing rate of
secret key rate will be raised as the transmission distance increases. At a
large transmission distance, our efficient four-intensity protocol can improve
the performance of quantum key distribution profoundly.
