A relation between conditional entropy and conditional expectation to evaluate secrecy systems

We demonstrate an intuitive relation between conditional entropy and conditional expectation that is useful when one want to compare them as measurement tools to evaluate secrecy systems. In particular, we give a Security Property applicable to general n-dimensional vector variables, using measurement based on vector quadratic distance, and we show that one can derive variables that can be measured with Csiszar and Korner secrecy capacity measurement, based on conditional entropy, with conserving the same order relation. V2: correction of a too approximative proof of Lemma.