  Several mathematical ideas have been investigated for Quantitative
Information Flow. Information theory, probability, guessability are the main
ideas in most proposals. They aim to quantify how much information is leaked,
how likely is to guess the secret and how long does it take to guess the secret
respectively. In this paper, we show how the Lattice of Information provides a
valuable foundation for all these approaches; not only it provides an elegant
algebraic framework for the ideas, but also to investigate their relationship.
In particular we will use this lattice to prove some results establishing order
relation correspondences between the different quantitative approaches. The
implications of these results w.r.t. recent work in the community is also
investigated. While this work concentrates on the foundational importance of
the Lattice of Information its practical relevance has been recently proven,
notably with the quantitative analysis of Linux kernel vulnerabilities. Overall
we believe these works set the case for establishing the Lattice of Information
as one of the main reference structure for Quantitative Information Flow.
