  Imperfect secrecy in communication systems is investigated. Instead of using
equivocation as a measure of secrecy, the distortion that an eavesdropper
incurs in producing an estimate of the source sequence is examined. The
communication system consists of a source and a broadcast (wiretap) channel,
and lossless reproduction of the source sequence at the legitimate receiver is
required. A key aspect of this model is that the eavesdropper's actions are
allowed to depend on the past behavior of the system. Achievability results are
obtained by studying the performance of source and channel coding operations
separately, and then linking them together digitally. Although the problem
addressed here has been solved when the secrecy resource is shared secret key,
it is found that substituting secret key for a wiretap channel brings new
insights and challenges: the notion of weak secrecy provides just as much
distortion at the eavesdropper as strong secrecy, and revealing public messages
freely is detrimental.
