  Quantum key distribution protocols are known to be vulnerable against a side
channel attack that exploits the time difference in detector responses used to
obtain key bits. The recommended solution against this timing side channel
attack is to use a large time bin width instead of high resolution timing
information. Common notion is that using a large bin width reduces the
resolution of detector responses, hence supposedly minimizes the information
leakage to an eavesdropper. We challenge this conventional wisdom, and
demonstrate that increasing the bin width does not monotonically reduce the
mutual information between the key bits and the eavesdropper's observation of
detector responses. Instead of randomly increasing the bin width, it should be
carefully chosen because the mutual information fluctuates with respect to the
bin width. We also examined the effect of full width half maximums (FWHMs) of
the detectors responses on the mutual information and showed that decreasing
the FWHM increases the mutual information. Lastly, the start time of binning is
also shown to be important in binning process and the mutual information
fluctuates periodically with respect to it.
