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arXiv 2605.06802cs.ITmath.IT
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基于互信息安全准则的可变长信源加密框架:通用编码与强逆定理

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

University of Electro-Communications(电波大学)

Yasutada Oohama, Bagus Santoso

AI总结:

针对离散无记忆信源,提出一种基于Shannon密码系统的可变长无损信源加密框架,以互信息度量信息泄露,推导了安全通信的充要条件并证明其与泄露上界无关,进而证明了强逆编码定理及通用加解密方案的存在性。

摘要:

本文考虑离散无记忆信源的可变长无损信源编码。我们提出了一种新的加密框架,用于在无噪声信道上安全传输码字。所提出的信源加密框架基于Shannon密码系统的安全通信框架。在该框架中,我们使用互信息作为对敌手信息泄露的度量。我们建立了在信息泄露由常数$δ\in (0,\infty)$上界约束下安全通信的充要条件,从而为该问题提供了完整解。我们还证明了所得到的充要条件不依赖于常数$δ\in (0,\infty)$,表明我们为所提出的信源加密框架建立了强逆编码定理。我们进一步证明了加解密方案的存在性,这些方案是通用的,即它们对明文分布和加密所用密钥分布均有效。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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