We introduce a privacy measure called pointwise maximal leakage, defined based on the pre-existing notion of maximal leakage, which quantifies the amount of information leaking about a secret $X$ by disclosing a single outcome of a (randomized) function calculated on $X$. Pointwise maximal leakage is a robust and operationally meaningful privacy measure that captures the largest amount of information leaking about $X$ to adversaries seeking to guess arbitrary (possibly randomized) functions of $X$, or equivalently, aiming to maximize arbitrary gain functions. We study several properties of pointwise maximal leakage, e.g., how it composes over multiple outcomes, how it is affected by pre- and post-processing, etc. Furthermore, we propose to view privacy leakage as a random variable which, in turn, allows us to regard privacy guarantees as requirements imposed on different statistical properties of the privacy leakage random variable. We define several privacy guarantees and study how they behave under pre-processing, post-processing and composition. Finally, we examine the relationship between pointwise maximal leakage and other privacy notions such as local differential privacy, local information privacy, $f$-information, and so on.
翻译:我们引入了一种称为点针最大渗漏的隐私措施,其定义基于原先存在的最大渗漏概念,该措施通过披露用美元计算出来的(随机)功能的单一结果,对关于秘密美元的信息泄漏量进行量化。 点尖最大渗漏是一种稳健和操作上有意义的隐私措施,该措施捕捉了向对手泄漏的关于大约X美元的最大数量的信息,试图猜测任意(可能随机)美元或同等的功能,以最大限度地实现任意获取功能。我们研究了点最大渗漏的若干特性,例如,它如何构成多种结果,它如何受到预处理和后处理的影响。 此外,我们提议将隐私渗漏视为一种随机变量,这反过来又使我们能够将隐私渗漏视为对隐私泄漏随机变异的不同统计属性的要求。我们界定了几种隐私保障,并研究它们在预处理、后处理和构成中的行为方式。最后,我们研究了点最大渗漏与其他隐私概念之间的关系,例如地方差异隐私、当地信息隐私、美元信息、美元信息以及等。