  The quantum states corresponding to a secret key are characterized using the
so-called private states, where the key part consisting of a secret key is
shielded by the additional systems. Based on the construction, it was shown
that a secret key can be distilled from bound entangled states. In this work, I
consider the shielded two-qubit states in a key-distillation scenario and
derive the conditions under which a secret key can be distilled using the
recurrence protocol or the two-way classical distillation, advantage
distillation together with one-way postprocessing. From the security
conditions, it is shown that a secret key can be distilled from bound entangled
states in a much wider range. In addition, I consider the case that in which
white noise is added to quantum states and show that the classical distillation
protocol still works despite a certain amount of noise although the recurrence
protocol does not.
