  For quantum key distribution (QKD) using spontaneous
parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol
has been proved to be efficiently close to the theoretical limit of an infinite
decoy-state protocol. In this paper, we apply a tight finite-key analysis for
the passive decoy-state QKD using SPDCSs. Combining the security bound based on
the uncertainty principle with the passive decoy-state protocol, a concise and
stringent formula for calculating the key generation rate for QKD using SPDCSs
is presented. The simulation shows that the secure distance under our formula
can reach up to 182 km when the number of sifted data is $10^{10}$. Our results
also indicate that, under the same deviation of statistical fluctuation due to
finite-size effects, the passive decoy-state QKD with SPDCSs can perform as
well as the active decoy-state QKD with a weak coherent source.
