We prove the unconditional security of the Bennett 1992 protocol, by using a reduction to an entanglement distillation protocol initiated by a local filtering process. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises.