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

TL;DR

This paper explores the relationship between conditional entropy and conditional expectation to evaluate secrecy systems, introducing a security property for vector variables and comparing measurement tools.

Contribution

It establishes an intuitive relation between conditional entropy and expectation, and develops a security property applicable to n-dimensional vector variables for evaluating secrecy.

Findings

Derived variables measurable with Csiszar and Korner secrecy capacity

Established order relation conservation between measurement tools

Proposed a security property for vector variables

Abstract

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.