Lossless Secure Source Coding: Yamamoto's Setting

TL;DR

This paper explores secure lossless encoding of correlated sources, ensuring the public source is recoverable while minimizing private source leakage, with theoretical bounds and optimal schemes in certain scenarios.

Contribution

It provides general converse bounds and achievability results for secure source coding with side information, extending Yamamoto's setting.

Findings

Derived bounds on information leakage about the private source.

Established optimal encoding schemes in specific cases.

Provided theoretical limits for secure source coding systems.

Abstract

Given a private source of information, $X^n$ and a public correlated source, $Y^n$, we study the problem of encoding the two-dimensional source $(X^n, Y^n)$ into an index $J$ such that a remote party, knowing $J$ and some external side information $Z^n$, can losslessly recover $Y^n$ while any eavesdropper knowing $J$ and possibly a correlated side information $E^n$ can retrieve very little information about $X^n$. We give general converse results for the amount of information about $X^n$ that might be leaked in such systems and and also achievability results that are optimal in some special cases.