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Entropy 2018, 20(9), 675; https://doi.org/10.3390/e20090675

Optimal Channel Design: A Game Theoretical Analysis

School of Electronic Engineering and Computer Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK
These authors contributed equally to this work.
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Received: 22 August 2018 / Revised: 31 August 2018 / Accepted: 3 September 2018 / Published: 5 September 2018
(This article belongs to the Special Issue Information Theory in Game Theory)
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Abstract

This paper studies the problem of optimal channel design. For a given input probability distribution and for hard and soft design constraints, the aim here is to design a (probabilistic) channel whose output leaks minimally from its input. To analyse this problem, general notions of entropy and information leakage are introduced. It can be shown that, for all notions of leakage here defined, the optimal channel design problem can be solved using convex programming with zero duality gap. Subsequently, the optimal channel design problem is studied in a game-theoretical framework: games allow for analysis of optimal strategies of both the defender and the adversary. It is shown that all channel design problems can be studied in this game-theoretical framework, and that the defender’s Bayes–Nash equilibrium strategies are equivalent to the solutions of the convex programming problem. Moreover, the adversary’s equilibrium strategies correspond to a robust inference problem. View Full-Text
Keywords: entropy; game theory; convex optimisation; quantitative information flow entropy; game theory; convex optimisation; quantitative information flow
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Khouzani, M.; Malacaria, P. Optimal Channel Design: A Game Theoretical Analysis. Entropy 2018, 20, 675.

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