  The security of two-state quantum key distribution against individual attack
is estimated when the channel has losses and noises. We assume that Alice and
Bob use two nonorthogonal single-photon polarization states. To make our
analysis simple, we propose a modified B92 protocol in which Alice and Bob make
use of inconclusive results and Bob performs a kind of symmetrization of
received states. Using this protocol, Alice and Bob can estimate Eve's
information gain as a function of a few parameters which reflect the
imperfections of devices or Eve's disturbance. In some parameter regions, Eve's
maximum information gain shows counter-intuitive behavior, namely, it decreases
as the amount of disturbances increases. For a small noise rate Eve can extract
perfect information in the case where the angle between Alice's two states is
small or large, while she cannot extract perfect information for intermediate
angles. We also estimate the secret key gain which is the net growth of the
secret key per one pulse. We show the region where the modified B92 protocol
over a realistic channel is secure against individual attack.
