  Quantum key distribution is rising as an important cryptographic primitive
for protecting the communication infrastructure in the digital era. However,
its implementation security is often weakened by components whose behavior
deviates from what is expected. Here, we analyse the response of a
self-differencing avalanche photodiode, a key enabler for high speed quantum
key distribution, to intense light shone from a continuous-wave laser. Under
incorrect settings, the cancellation entailed by the self-differencing
circuitry can make the detector insensitive to single photons. However, we
experimentally demonstrate that even in such cases intensity modulation can be
used as an effective measure to restore the detector's expected response to the
input light.
