Measuring Information Leakage using Generalized Gain Functions

Abstract : This paper introduces g-leakage, a rich general- ization of the min-entropy model of quantitative information flow. In g-leakage, the benefit that an adversary derives from a certain guess about a secret is specified using a gain function g. Gain functions allow a wide variety of operational scenarios to be modeled, including those where the adversary benefits from guessing a value close to the secret, guessing a part of the secret, guessing a property of the secret, or guessing the secret within some number of tries. We prove important properties of g-leakage, including bounds between min-capacity, g-capacity, and Shannon capacity. We also show a deep connection between a strong leakage ordering on two channels, C1 and C2, and the possibility of factoring C1 into C2 C3 , for some C3 . Based on this connection, we propose a generalization of the Lattice of Information from deterministic to probabilistic channels.
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Submitted on : Thursday, September 20, 2012 - 3:38:22 PM
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Mário S. Alvim, Konstantinos Chatzikokolakis, Catuscia Palamidessi, Geoffrey Smith. Measuring Information Leakage using Generalized Gain Functions. Computer Security Foundations, 2012, Cambridge MA, United States. pp.265-279, ⟨10.1109/CSF.2012.26⟩. ⟨hal-00734044⟩

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