A Framework of Variable-Length Source Encryption using Mutual Information Security Criterion: Universal Coding, Strong Converse Theorem
For information theorists and cryptographers, this work provides a theoretical foundation for source encryption with universal guarantees, though it is an incremental extension of existing Shannon cipher system concepts.
This paper proposes a framework for variable-length source encryption using mutual information as a security criterion, establishing necessary and sufficient conditions for reliable and secure communication. It proves a strong converse theorem and demonstrates the existence of universal encryption/decryption schemes that work for any plaintext and key distributions.
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.