Perfect Secrecy in the Wild: A Characterization

TL;DR

This paper characterizes the conditions under which perfect secrecy can be achieved in information sharing scenarios, providing a simple criterion based on joint distributions, extending Shannon's one-time pad result.

Contribution

It introduces a necessary and sufficient condition for perfect secrecy in general settings, generalizing classical results like Shannon's one-time pad.

Findings

Derived a simple criterion for perfect secrecy based on joint distribution

Unified and extended Shannon's perfect secrecy results

Provided a framework applicable to various information sharing scenarios

Abstract

Alice wishes to reveal the state $X$ to Bob, if he knows some other information $Y$ also known to her. If Bob does not, she wishes to reveal nothing about $X$ at all. When can Alice accomplish this? We provide a simple necessary and sufficient condition on the joint distribution of $X$ and $Y$. Shannon's result on the perfect secrecy of the one-time pad follows as a special case.