  In a point-to-point communication system which consists of a sender, a
receiver and a set of noiseless channels, the sender wishes to transmit a
private message to the receiver through the channels which may be eavesdropped
by a wiretapper. The set of wiretap sets is arbitrary. The wiretapper can
access any one but not more than one wiretap set. From each wiretap set, the
wiretapper can obtain some partial information about the private message which
is measured by the equivocation of the message given the symbols obtained by
the wiretapper. The security strategy is to encode the message with some random
key at the sender. Only the message is required to be recovered at the
receiver. Under this setting, we define an achievable rate tuple consisting of
the size of the message, the size of the key, and the equivocation for each
wiretap set. We first prove a tight rate region when both the message and the
key are required to be recovered at the receiver. Then we extend the result to
the general case when only the message is required to be recovered at the
receiver. Moreover, we show that even if stochastic encoding is employed at the
sender, the message rate cannot be increased.
