  We derive the time-dependent photo-detection probability equation of a
superconducting single photon detector (SSPD) to study the responsive property
for a pulse train at high repetition rate. Using this equation, we analyze the
characteristics of SSPDs when illuminated by bright pulses in blinding attack
on a quantum key distribution (QKD). We obtain good agreement between expected
values based on our equation and actual experimental values. Such a
time-dependent probability analysis contributes to security analysis.
