A Framework of Secure Source Coding using Mutual Information Security Criterion: Universal Coding, Strong Converse Theorem

TL;DR

This paper introduces a universal framework for secure source coding based on mutual information, establishing conditions for reliable and secure communication with a strong converse theorem.

Contribution

It provides necessary and sufficient conditions for secure source coding using mutual information, and demonstrates the existence of universal encryption schemes effective across various distributions.

Findings

Established the strong converse theorem for the proposed framework.

Derived necessary and sufficient conditions for reliable and secure communication.

Proved the existence of universal encryption/decryption schemes.

Abstract

In this paper, we propose a framework of source encryption, where cryptographic processing is applied to a prescribed fixed length source code. The proposed source encryption framework is based on the secure communication framework of the Shannon cipher system. In the proposed framework, we use the mutual information as a measure of information leakage to an adversary. For the proposed framework, we explicitly establish the necessary and sufficient condition for reliable and secure communication under the condition that error probability and information leakage, respectively, are upper bounded by prescribed constants $\epsilon\in (0,1)$ and $\delta \in (0,\infty)$. We also show that the obtained necessary and sufficient condition does not depend on the constants $\epsilon\in (0,1)$ and $\delta\in (0,\infty)$, demonstrating that we have the strong converse theorem for the proposed framework of source encryption. We further prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text and those of the key used for the encryption.