  Critical infrastructure systems - for which high reliability and availability
are paramount - must operate securely. Attack trees (ATs) are hierarchical
diagrams that offer a flexible modelling language used to assess how systems
can be attacked. ATs are widely employed both in industry and academia but - in
spite of their popularity - little work has been done to give practitioners
instruments to formulate queries on ATs in an understandable yet powerful way.
In this paper we fill this gap by presenting ATM, a logic to express
quantitative security properties on ATs. ATM allows for the specification of
properties involved with security metrics that include "cost", "probability"
and "skill" and permits the formulation of insightful what-if scenarios. To
showcase its potential, we apply ATM to the case study of a CubeSAT, presenting
three different ways in which an attacker can compromise its availability. We
showcase property specification on the corresponding attack tree and we present
theory and algorithms - based on binary decision diagrams - to check properties
and compute metrics of ATM-formulae.
