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.
Highlights
A channel is defined as a conditional distribution, modelling the probability of outputs that an adversary can observe given secret inputs
Based on Reference [2], it can be shown that, for any choice of the entropy measure, this problem is solved via convex programming with zero duality gap, for which the Karush–Kuhn–Tucker (KKT) conditions can be used to solve for the optimal channel
We investigated the problem of designing constrained channels that leak minimally about their input in a general information-theoretical setting
Summary
A channel is defined as a conditional distribution, modelling the probability of outputs that an adversary can observe given secret inputs. An optimal channel can be seen as an optimal countermeasure to information leakage To explore this design problem, one needs to specify what constraints should be considered and how the leakage of information is quantified. In the cryptographic example above, one may want, for example, to design a channel of minimal leakage (in terms of the number of key bits that can be reconstructed by an adversary) under the constraint that the average encryption per block should take less time than some given duration. Hard constraints are the ones establishing which outputs are allowed given each inputs. Based on Reference [2], it can be shown that, for any choice of the entropy measure, this problem is solved via convex programming with zero duality gap, for which the Karush–Kuhn–Tucker (KKT) conditions can be used to solve for the optimal channel
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