A Framework of Distributed Source Encryption using Mutual Information Security Criterion and the Strong Converse Theorem

TL;DR

This paper revisits distributed secure source coding, establishing rate region bounds under the standard mutual information security criterion using information spectrum methods and a variant of Birkhoff-von Neumann theorem.

Contribution

It provides new bounds for the rate region in distributed source encryption based on the standard mutual information security criterion, improving upon previous non-standard criteria.

Findings

Established bounds of the rate region under standard mutual information security.

Utilized information spectrum method and Birkhoff-von Neumann theorem in derivations.

Reinforced theoretical foundations for distributed source encryption security.

Abstract

We reinvestigate the general distributed secure source coding based on the common key cryptosystem proposed by Oohama and Santoso (ITW 2021). They proposed a framework of distributed source encryption and derived the necessary and sufficient conditions to have reliable and secure transmission. However, the bounds of the rate region, which specifies both necessary and sufficient conditions to have reliable and secure transmission under the proposed cryptosystem, were derived based on a self-tailored non-standard} security criterion. In this paper we adopt the standard security criterion, i.e., standard mutual information. We successfully establish the bounds of the rate region based on this security criterion. Information spectrum method and a variant of Birkhoff-von Neumann theorem play an important role in deriving the result.