隐藏符号和函数：信息理论安全的新概念和新结构
Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security
摘要：
我们提出了信息理论的定义和结果分析的公钥加密方案超出了完美的保密制度，即当完美的保密性是没有达到。我们采用两条分析线，一个基于无损信源编码，另一个类似于率失真理论。首先，我们提出了一个新的信息理论度量的安全性，称为符号保密，并推导出相关的基本界限。然后，我们介绍了列表源代码（LSC），这是一个通用的框架映射的密钥长度（熵）的列表大小，窃听者必须解决，以恢复秘密消息。我们提供了明确的结构的LSC，并证明，当源是均匀分布的，最高级别的符号保密的一个固定的密钥长度可以实现通过基于最小距离可分离（MDS）码的建设。使用相关的率失真理论的分析，然后，我们展示了如何符号保密可以用来确定窃听者正确地重建原始明文的功能的概率。我们说明了如何将这些界限可以应用到表征安全属性的公钥加密方案，特别是，扩展安全要求的基础上，符号保密的功能设置。
英文摘要：
We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.
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