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arXiv · 2304.07722

Pointwise Maximal Leakage on General Alphabets

Sara Saeidian·Giulia Cervia·Tobias J. Oechtering·Mikael Skoglund
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Abstract

Pointwise maximal leakage (PML) is an operationally meaningful privacy measure that quantifies the amount of information leaking about a secret $X$ to a single outcome of a related random variable $Y$. In this paper, we extend the notion of PML to random variables on arbitrary probability spaces. We develop two new definitions: First, we extend PML to countably infinite random variables by considering adversaries who aim to guess the value of discrete (finite or countably infinite) functions of $X$. Then, we consider adversaries who construct estimates of $X$ that maximize the expected value of their corresponding gain functions. We use this latter setup to introduce a highly versatile form of PML that captures many scenarios of practical interest whose definition requires no assumptions about the underlying probability spaces.

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Sara Saeidian, Giulia Cervia, Tobias J. Oechtering, Mikael Skoglund. 2023-04-16. Pointwise Maximal Leakage on General Alphabets. https://arxiv.org/abs/2304.07722

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