  An essential step in quantum key distribution is the estimation of parameters
related to the leaked amount of information, which is usually done by sampling
of the communication data. When the data size is finite, the final key rate
depends on how the estimation process handles statistical fluctuations. Many of
the present security analyses are based on the method with simple random
sampling, where hypergeometric distribution or its known bounds are used for
the estimation. Here we propose a concise method based on Bernoulli sampling,
which is related to binomial distribution. Our method is suitable for the BB84
protocol with weak coherent pulses, reducing the number of estimated parameters
to achieve a higher key generation rate compared to the method with simple
random sampling. We also applied the method to prove the security of the
differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime.
The result indicates that, the advantage of the DQPS protocol over the
phase-encoding BB84 protocol in terms of the key rate, which was previously
confirmed in the asymptotic regime, persists in the finite-key regime.
