  We give a Shor-Preskill type security-proof to the quantum key distribution
without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489
(1998)]. First, we modify the Lo-Chau protocol once more so that it finally
reduces to the quantum key distribution without public announcement of bases.
Then we show how we can estimate the error rate in the code bits based on that
in the checked bits in the proposed protocol, that is the central point of the
proof. We discuss the problem of imperfect sources and that of large deviation
in the error rate distributions. We discuss when the bases sequence must be
discarded.
