  We present a general theorem for the efficient verification of the lower
bound of single-photon transmittance. We show how to do decoy-state quantum key
distribution efficiently with large random errors in the intensity control. In
our protocol, the linear terms of fluctuation disappear and only the quadratic
terms take effect. We then show the unconditional security of decoy-state
method with whatever error pattern in intensities of decoy pulses and signal
pulses provided that the intensity of each decoy pulse is less than $\mu$ and
the intensity of each signal pulse is larger than $\mu'$.
