The asymptotic behaviour of information leakage metrics

Journal article

Information leakage metrics quantify the amount of information about a private random variable X that is leaked through a correlated variable Y . They can be used to evaluate the privacy of a system in which an adversary, from whom X should be kept private, observes Y . Global information leakage metrics quantify the overall information leaked upon observing Y , whilst their pointwise counterparts define leakage as a function of the particular realisation Y = y, and thus can be viewed as random variables. We consider an adversary who observes many conditionally independent identically distributed realisations of Y . We formalise the essential asymptotic behaviour of an information leakage metric, considering in turn what this means for pointwise and global metrics. With these requirements in mind, we take an axiomatic approach to defining a set of pointwise leakage metrics, and a set of global leakage metrics constructed from them. The global set encompasses many known measures including mutual information, Sibson mutual information, Arimoto mutual information, maximal leakage, min entropy leakage, fdivergence metrics, and g-leakage. We prove that both sets follow the desired asymptotic behaviour. Finally, we derive composition theorems quantifying the rate of privacy degradation as an adversary is given access to many conditionally independent observations of Y . We find that, for pointwise and global metrics, privacy degrades exponentially with increasing observations, at a rate governed by the minimum Chernoff information. This extends the work of Wu et al. (2024), who derived this result for certain known metrics, including some from our global set.

Authors: Taylor, S; Vippathalla, PK; Coon, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Journal: IEEE Transactions on Information Theory
• Volume: 72
• Issue: 2
• Pages: 811-831
• Publication date: 2025-12-22
• Acceptance date: 2025-12-12
• DOI: 10.1109/tit.2025.3646586
• EISSN: 1557-9654
• ISSN: 0018-9448
• Language: English
• Keywords: information theoretic leakage metrics; privacy; composition theorems; pointwise leakage; global leakage; method of types