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 $δ\in (0,\infty)$, thereby providing a complete solution to the problem. We also show that the obtained necessary and sufficient condition does not depend on the constant $δ\in (0,\infty)$, 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.

翻译：本文研究了离散无记忆信源的可变长无损信源编码问题。我们提出了一种新的加密框架，用于在无噪信道上安全传输码字。该信源加密框架基于Shannon保密系统的安全通信框架。在所提出的框架中，我们使用互信息作为衡量敌手信息泄露的指标。在信息泄露量受常数δ∈(0,∞)上界约束的条件下，我们建立了安全通信的充要条件，从而为该问题提供了完整解决方案。我们还证明，所获得的充要条件不依赖于常数δ∈(0,∞)，这表明针对所提出的信源加密框架存在强逆编码定理。我们进一步证明了加密/解密方案的存在性，这些方案具有通用性，即它们能对任意分布的明文以及用于加密的密钥均有效工作。