An Operational Approach to Information Leakage via Generalized Gain Functions
An Operational Approach to Information Leakage via Generalized Gain Functions
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通过广义增益函数处理信息泄漏的操作方法
DOI：
10.1109/tit.2023.3341148
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发表时间：
2024
影响因子：
2.5
通讯作者：
Kosut, Oliver
中科院分区：
文献类型：
--
作者：
Kurri, Gowtham R.;Sankar, Lalitha;Kosut, Oliver
我们通过提出最大泄漏来引入信息泄漏的增益函数观点，最大泄漏是一类丰富的具有操作意义的泄漏度量，它包含了最近引入的泄漏度量——最大泄漏和最大泄漏。在最大泄漏中，对手在猜测未知随机变量时的增益是使用应用于正确猜测概率的增益函数来测量的。特别是，根据观察，在对手猜测随机函数的期望增益中，最大泄漏捕获了乘法增长，在所有这些随机函数中最大化。我们还考虑了对手可以多次尝试猜测感兴趣的随机函数的场景。我们证明了对于任何非负增益函数，在多次猜测下，最大泄漏是最大泄漏的上界。我们得到了一类凹增益函数在多次猜测下的最大泄漏的封闭表达式。我们还研究了与损耗相关的一类增益函数的最大泄漏度量，该函数插值对数损耗（）和（软）0-1损耗（）。特别是，我们首先完整地描述了多次猜测下的最小期望损失，并分析了相应的泄漏度量是如何随猜测次数而受到影响的。我们展示了一种新的散度度量，它属于Bregman散度类，它捕获了任意对抗策略相对于最小化预期损失的最优策略的相对性能。最后，我们研究了两种依赖于对手类型的最大泄漏变量，并得到了它们的封闭表达式，只要满足一些温和的正则性条件，就不依赖于所考虑的特定增益函数。我们通过发展无穷阶rsamnyi散度的变分特征来做到这一点，它自然地将点向最大泄漏的定义推广到包含任意增益函数。
We introduce a gain function viewpoint of information leakage by proposing maximal-leakage, a rich class of operationally meaningful leakage measures that subsumes recently introduced leakage measures — maximal leakage and maximal-leakage. In maximal-leakage, the gain of an adversary in guessing an unknown random variable is measured using a gain function applied to the probability of correctly guessing. In particular, maximal-leakage captures the multiplicative increase, upon observing, in the expected gain of an adversary in guessing a randomized function of, maximized over all such randomized functions. We also consider the scenario where an adversary can make multiple attempts to guess the randomized function of interest. We show that maximal leakage is an upper bound on maximal-leakage under multiple guesses, for any non-negative gain function. We obtain a closed-form expression for maximal-leakage under multiple guesses for a class of concave gain functions. We also study maximal-leakage measure for a specific class of gain functions related to the-loss, that interpolates log-loss () and (soft) 0–1 loss (). In particular, we first completely characterize the minimal expected-loss under multiple guesses and analyze how the corresponding leakage measure is affected with the number of guesses. We show that a new measure of divergence that belongs to the class of Bregman divergences captures the relative performance of an arbitrary adversarial strategy with respect to an optimal strategy in minimizing the expected-loss. Finally, we study two variants of maximal-leakage depending on the type of adversary and obtain closed-form expressions for them, which do not depend on the particular gain function considered as long as it satisfies some mild regularity conditions. We do this by developing a variational characterization for the Rényi divergence of order infinity which naturally generalizes the definition of pointwise maximal leakage to incorporate arbitrary gain functions.
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期刊：
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