An Operational Approach to Information Leakage
An Operational Approach to Information Leakage
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DOI：
10.1109/tit.2019.2962804
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发表时间：
2020-03-01
影响因子：
2.5
通讯作者：
Kamath, Sudeep
中科院分区：
文献类型：
--
作者：
Issa, Ibrahim;Wagner, Aaron B.;Kamath, Sudeep
给定两个随机变量 X 和 Y ，采用一种操作方法来量化从 X 到 Y 的信息“泄漏”。得到的度量 L (X -> Y) 称为最大泄漏，并被定义为在观察 Y 时，正确猜测 X 的随机函数的概率的乘法增长，在所有此类随机函数上最大化。对于离散 X 和 Y 给出了 L(X -> Y) 的封闭式表达式，随后将其推广到处理一大类随机变量。结果表明，所得属性与泄漏测量的公理化视图一致，并且该定义对设置的变化具有鲁棒性。此外，还研究了香农密码系统的一种变体，其中使用最大泄漏来测量加密方案的性能。导出了（归一化）最大泄漏的最佳限制的单字母特征，并演示了渐近最佳加密方案。此外，估计数据最大泄漏的样本复杂性被表征为次多项式因子。最后，用于定义最大泄漏的猜测框架用于给出常用泄漏度量的操作解释，例如香农容量、最大相关性和局部差分隐私。
Given two random variables X and Y , an operational approach is undertaken to quantify the "leakage" of information from X to Y . The resulting measure L (X -> Y) is called maximal leakage, and is defined as the multiplicative increase, upon observing Y , of the probability of correctly guessing a randomized function of X , maximized over all such randomized functions. A closed-form expression for L(X -> Y) is given for discrete X and Y , and it is subsequently generalized to handle a large class of random variables. The resulting properties are shown to be consistent with an axiomatic view of a leakage measure, and the definition is shown to be robust to variations in the setup. Moreover, a variant of the Shannon cipher system is studied, in which performance of an encryption scheme is measured using maximal leakage. A single-letter characterization of the optimal limit of (normalized) maximal leakage is derived and asymptotically-optimal encryption schemes are demonstrated. Furthermore, the sample complexity of estimating maximal leakage from data is characterized up to subpolynomial factors. Finally, the guessing framework used to define maximal leakage is used to give operational interpretations of commonly used leakage measures, such as Shannon capacity, maximal correlation, and local differential privacy.