  Secrecy in communication systems is measured herein by the distortion that an
adversary incurs. The transmitter and receiver share secret key, which they use
to encrypt communication and ensure distortion at an adversary. A model is
considered in which an adversary not only intercepts the communication from the
transmitter to the receiver, but also potentially has side information.
Specifically, the adversary may have causal or noncausal access to a signal
that is correlated with the source sequence or the receiver's reconstruction
sequence. The main contribution is the characterization of the optimal tradeoff
among communication rate, secret key rate, distortion at the adversary, and
distortion at the legitimate receiver. It is demonstrated that causal side
information at the adversary plays a pivotal role in this tradeoff. It is also
shown that measures of secrecy based on normalized equivocation are a special
case of the framework.
