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We give a Shor-Preskill type security-proof to the quantum key distributionwithout 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 finallyreduces 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 thatin the checked bits in the proposed protocol, that is the central point of theproof. We discuss the problem of imperfect sources and that of large deviationin the error rate distributions. We discuss when the bases sequence must bediscarded.Comment: very minor correction, 5 pages, RevTe

Shor-Preskill-type security proof for quantum key distribution without public announcement of bases