  The existing decoy-state quantum key distribution (QKD) beating
photon-number-splitting (PNS) attack provides a more accurate method to
estimate secure key rate, while it still considers that only single-photon
pulses can generate secure keys in any case. However, multiphoton pulses can
also generate secure keys if we can confirm that there is no attack. In this
paper, under the null hypothesis of no PNS attack, we first determine whether
there is an attack or not by retrieving the missing information of the existing
decoy-state protocols, extract a Cauchy distribution statistic, and further
provide a detection method and the Type I error probability. If the result is
judged to be an attack, we can use the existing decoy-state method and the GLLP
formula to estimate secure key rate. Otherwise, all pulses received including
both single-photon pulses and multiphoton pulses, can be used to generate the
keys and we give the secure key rate in this case. Finally, the associated
experiments we performed (i.e., the significance level is $5\%$) show the
correctness of our method.
