Perfect Secrecy can be defined by
$I(M;Z^n) = D(P_{MZ^n}||P_MP_{Z^n}) = 0$
there the true joint distribution $P_{MZ^n}$ is compared to the product distributions $P_M P_{Z^n}$.
The system can be viewed as follows:
M -> Enc E -> X^n -> P_{yz|x} -> Y^n -> Dec -> ^M
-> Z^n -> Eve -> ?
I'm struggeling with the interpretation of the Kullback-Leibler divergence. Can someone give me some intuitive explanation?
The KL-Divergence is defined as
$$ D(p_x || q_x) = \sum _x p(x) \log \frac{p(x)}{q(x)} $$
and the mutual information is defined as
$$ I(X;Y) = H(X) - H(X|Y) = \sum_x \sum_y p(x,y) \log \frac{p(x,y)}{p(x)p(y)} $$
from the above it's clear that $I(X;Y) = D(p_{xy} || p_xp_y )$