On the Compositionality of Quantitative Information Flow

TL;DR

This paper investigates how the compositional structure of systems affects information leakage, providing bounds on overall leakage based on component leakages within the $g$-leakage framework, thus aiding scalable security analysis.

Contribution

It derives bounds on the $g$-leakage of complex systems by decomposing them into simpler channels, extending existing results to more general cases and improving computational efficiency.

Findings

Bounds on $g$-leakage for systems with decomposable channels

Extension of results to min-entropy leakage and parallel channels

Demonstration of bounds' effectiveness through examples

Abstract

Information flow is the branch of security that studies the leakage of information due to correlation between secrets and observables. Since in general such correlation cannot be avoided completely, it is important to quantify the leakage. The most followed approaches to defining appropriate measures are those based on information theory. In particular, one of the most successful approaches is the recently proposed $g$-leakage framework, which encompasses most of the information-theoretic ones. A problem with $g$-leakage, however, is that it is defined in terms of a minimization problem, which, in the case of large systems, can be computationally rather heavy. In this paper we study the case in which the channel associated to the system can be decomposed into simpler channels, which typically happens when the observables consist of multiple components. Our main contribution is the derivation of bounds on the (multiplicative version of) $g$-leakage of the whole system in terms of the $g$-leakages of its components. We also consider the particular cases of min-entropy leakage and of parallel channels, generalizing and systematizing results from the literature. We demonstrate the effectiveness of our method and evaluate the precision of our bounds using examples.