An Algebraic Framework for Quantitative Information Flow

Abstract

The field of quantitative information flow (QIF) is concerned with measuring and controlling information leakage in computational systems, aiming to assess and improve their security. Much effort has been put into developing a mathematical framework for QIF, the standard approach being to model systems as monolithic infomation theoretic channels. However, many real-life systems can be best described by a collection of interacting channels instead. This motivates us to investigate the behaviour of channel compositions under the QIF framework. The channel compositions we study capture typical ways in which parts interact in real-world systems. Among other results, we derive relations between the information leakage of compositions and that of their components, establish whether we may substitute a component with a safer one without compromising the security of the whole, and model two anonymity protocols from the literature: the Dining Cryptographers and the Crowds.