  Recently, a secrecy measure based on list-reconstruction has been proposed
[2], in which a wiretapper is allowed to produce a list of $2^{mR_{L}}$
reconstruction sequences and the secrecy is measured by the minimum distortion
over the entire list. In this paper, we show that this list secrecy problem is
equivalent to the one with secrecy measured by a new quantity
\emph{lossy-equivocation}, which is proven to be the minimum optimistic
1-achievable source coding rate (the minimum coding rate needed to reconstruct
the source within target distortion with positive probability for
\emph{infinitely many blocklengths}) of the source with the wiretapped signal
as two-sided information, and also can be seen as a lossy extension of
conventional equivocation. Upon this (or list) secrecy measure, we study
source-channel secrecy problem in the discrete memoryless Shannon cipher system
with \emph{noisy} wiretap channel. Two inner bounds and an outer bound on the
achievable region of secret key rate, list rate, wiretapper distortion, and
distortion of legitimate user are given. The inner bounds are derived by using
uncoded scheme and (operationally) separate scheme, respectively. Thanks to the
equivalence between lossy-equivocation secrecy and list secrecy, information
spectrum method is leveraged to prove the outer bound. As special cases, the
admissible region for the case of degraded wiretap channel or lossless
communication for legitimate user has been characterized completely. For both
these two cases, separate scheme is proven to be optimal. Interestingly,
however, separation indeed suffers performance loss for other certain cases.
Besides, we also extend our results to characterize the achievable region for
Gaussian communication case. As a side product optimistic lossy source coding
has also been addressed.
