A Framework of Variable-Length Source Encryption using Mutual Information Security Criterion: Universal Coding, Strong Converse Theorem

TL;DR

This paper introduces a universal variable-length source encryption framework based on mutual information security, establishing necessary and sufficient conditions for secure communication and proving a strong converse theorem.

Contribution

It provides a complete characterization of secure source encryption using mutual information, independent of leakage bounds, and demonstrates universal encryption schemes.

Findings

Established necessary and sufficient conditions for secure communication.

Proved the strong converse theorem for the proposed encryption framework.

Demonstrated the existence of universal encryption/decryption schemes.

Abstract

In this paper we consider the variable-length lossless source coding for discrete memoryless sources. We proposes a new encryption framework for securely transmitting codewords over a noiseless channel. 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. We establish the necessary and sufficient condition for secure communication under the condition that the information leakage is upper bounded by a constant $\delta\in (0,\infty)$, thereby providing a complete solution to the problem. We also show that the obtained necessary and sufficient condition does not depend on the constant $\delta \in (0,\infty)$, demonstrating that we have the strong converse coding 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.