Abstract
This work explores connections between core-concavity and gain functions, two alternative approaches that emerged in the quantitative information flow community to provide a general framework to study information leakage. In particular (1) we revisit “Axioms for Information Leakage” by replacing averaging with \(\eta \)-averaging and convexity with core-concavity. An interesting consequence of these changes is that the revised axioms capture all Rényi entropies, including the ones not captured by the original formulation of the axioms. (2) We provide an alternative proof for the Coriaceous Theorem based on core-concavity. The general approach of this work is more information theoretical in nature than the work based on gain functions and provides an alternative foundational view of quantitative information flow, rooted on the essential properties of entropy as a measure of uncertainty.
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Notes
- 1.
This is also known in the literature as “conditioning reduces entropy” (CRE).
- 2.
- 3.
Notice that, as F is continuous over a compact set (and thus, bounded), \(\lim _{\epsilon \rightarrow 0^+} G_F(\epsilon \mathbf {u})=0=G_F(0,\dots ,0)\), for all \(\mathbf {u}\in \mathbb {R}^n_{\ge 0}\). Hence, \(G_F\) is continuous.
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Américo, A., Khouzani, M.H.R., Malacaria, P. (2019). Core-concavity, Gain Functions and Axioms for Information Leakage. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_15
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