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

2026-05-07

AI Summary

This study addresses the problem of achieving reliable and secure communication under variable-length source coding while rigorously controlling decoding error probability and information leakage. Building upon Shannon’s cipher system and employing mutual information to quantify an adversary’s knowledge, the work establishes—for the first time—the necessary and sufficient condition for reliable and secure communication under given constraints on error probability and information leakage. Notably, this condition is shown to be independent of the specific error and leakage thresholds, thereby establishing a strong converse theorem. Furthermore, the paper proposes a universal encryption-decryption scheme applicable to arbitrary plaintext and key distributions, demonstrating its existence and universality.

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 $\varepsilon\in (0,1)$ and $δ\in (0,\infty)$. We also show that the obtained necessary and sufficient condition does not depend on the constants $\varepsilon\in (0,1)$ and $δ\in (0,\infty)$, 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.

Problem

• source encryption
• mutual information
• information leakage
• reliable communication
• secure communication

Innovation

• source encryption
• mutual information
• strong converse theorem
• universal coding
• Shannon cipher system