  Quantum key distribution(QKD) allows two remote parties to share
information-theoretic secret keys. Many QKD protocols assume the phase of
encoding state can be continuous randomized from 0 to 2 pi, which, however, may
be questionable in experiment. This is particularly the case in the recently
proposed twin-field(TF) QKD, which has received a lot of attention, since it
can increase key rate significantly and even beat some theoretical rate-loss
limits. As an intuitive solution, one may introduce discrete
phase-randomization instead of continuous one. However, a security proof for a
QKD protocol with discrete phase-randomization in finite-key region is still
missing. Here we develop a technique based on conjugate measurement and quantum
state distinguishment to ana-lyze the security in this case. Our result shows
that TF-QKD with reasonable number of discrete random phases, e.g. 8 phases
from {0, pi/4, pi/2, ..., 7pi/4}, can achieve satisfactory performance. More
importantly, as a the first proof for TF-QKD with discrete phase-randomization
in finite-key region, our method is also applicable in other QKD protocols.
