  This paper considers a state dependent broadcast channel with one
transmitter, Alice, and two receivers, Bob and Eve. The problem is to
effectively convey ("amplify") the channel state sequence to Bob while
"masking" it from Eve. The extent to which the state sequence cannot be masked
from Eve is referred to as leakage. This can be viewed as a secrecy problem,
where we desire that the channel state itself be minimally leaked to Eve while
being communicated to Bob. The paper is aimed at characterizing the trade-off
region between amplification and leakage rates for such a system. An achievable
coding scheme is presented, wherein the transmitter transmits a partial state
information over the channel to facilitate the amplification process. For the
case when Bob observes a stronger signal than Eve, the achievable coding scheme
is enhanced with secure refinement. Outer bounds on the trade-off region are
also derived, and used in characterizing some special case results. In
particular, the optimal amplification-leakage rate difference, called as
differential amplification capacity, is characterized for the reversely
degraded discrete memoryless channel, the degraded binary, and the degraded
Gaussian channels. In addition, for the degraded Gaussian model, the extremal
corner points of the trade-off region are characterized, and the gap between
the outer bound and achievable rate-regions is shown to be less than half a bit
for a wide set of channel parameters.
