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The security of two-state quantum key distribution against individual attackis estimated when the channel has losses and noises. We assume that Alice andBob use two nonorthogonal single-photon polarization states. To make ouranalysis simple, we propose a modified B92 protocol in which Alice and Bob makeuse of inconclusive results and Bob performs a kind of symmetrization ofreceived states. Using this protocol, Alice and Bob can estimate Eve'sinformation gain as a function of a few parameters which reflect theimperfections of devices or Eve's disturbance. In some parameter regions, Eve'smaximum information gain shows counter-intuitive behavior, namely, it decreasesas the amount of disturbances increases. For a small noise rate Eve can extractperfect information in the case where the angle between Alice's two states issmall or large, while she cannot extract perfect information for intermediateangles. We also estimate the secret key gain which is the net growth of thesecret key per one pulse. We show the region where the modified B92 protocolover a realistic channel is secure against individual attack.Comment: 16 pages, 15 figure

Security of the Bennett 1992 quantum-key distribution protocol against individual attack over a realistic channel