Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The principal technical contributions are decomposition bounds that allow the representation of a random variable $X$ as a deterministic function of $({S},{Z})$ , where $S$ is a given fixed random variable and $Z$ is constructed to be independent of $S$ . Using the problems of privacy and lossless compression as examples, the utility cost of applying secrecy by design is investigated. Privacy is studied in the setting of the privacy funnel function previously introduced in the literature and new bounds for the regime of zero information leakage are derived. For the problem of lossless compression, it is shown that strong information-theoretic guarantees can be achieved using a reduced secret key size and a quantifiable penalty on the compression rate. The fundamental limits for both problems are characterized with matching lower and upper bounds when the secret $S$ is a deterministic function of the information source $X$ .

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保密设计与隐私和压缩应用

设计保密被视为信息理论保密的一种方法。这种方法背后的主要思想是从头开始设计一个信息处理系统，使其相对于明确的保密约束是完全安全的。主要的技术贡献是分解边界，它允许表示随机变量 $X$ 作为确定性函数 $({S},{Z})$ ， 在哪里 $S$ 是一个给定的固定随机变量并且 $Z$ 被构造为独立于 $S$ . 以隐私和无损压缩问题为例，研究了通过设计应用保密的效用成本。在先前在文献中引入的隐私漏斗函数的设置中研究了隐私，并推导出了零信息泄漏制度的新界限。对于无损压缩问题，研究表明可以使用减小的密钥大小和可量化的压缩率惩罚来实现强大的信息理论保证。这两个问题的基本限制的特征在于当秘密 $S$ 是信息源的确定性函数 $X$ .