# Information Leakage Games

## TL;DR

This paper introduces a game-theoretic model for information leakage involving attacker and defender strategies, demonstrating the existence of Nash equilibria and showing that optimal attack strategies are often probabilistic.

## Contribution

It develops a novel zero-sum leakage game framework with convex utilities and algorithms for computing optimal strategies, highlighting the probabilistic nature of optimal attacks.

## Key findings

- Nash equilibria exist in the proposed leakage games.
- Optimal defender strategies are often mixed to reduce leaks.
- First formal proof that optimal attacker strategies are probabilistic in some cases.

## Abstract

We consider a game-theoretic setting to model the interplay between attacker and defender in the context of information flow, and to reason about their optimal strategies. In contrast with standard game theory, in our games the utility of a mixed strategy is a convex function of the distribution on the defender's pure actions, rather than the expected value of their utilities. Nevertheless, the important properties of game theory, notably the existence of a Nash equilibrium, still hold for our (zero-sum) leakage games, and we provide algorithms to compute the corresponding optimal strategies. As typical in (simultaneous) game theory, the optimal strategy is usually mixed, i.e., probabilistic, for both the attacker and the defender. From the point of view of information flow, this was to be expected in the case of the defender, since it is well known that randomization at the level of the system design may help to reduce information leaks. Regarding the attacker, however, this seems the first work (w.r.t. the literature in information flow) proving formally that in certain cases the optimal attack strategy is necessarily probabilistic.